LMFDB - Abstract group search results

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Order	Exponent	Nilpotency class	Nilpotent

Center	Commutator	Central quotient	Abelianization

Abelian	Cyclic	Solvable	Simple

Perfect	Direct product	Semidirect product	Wreath product

Automorphism group	Automorphisms	Transitive degree	Permutation degree

Minimal degree of $\C$-irrep	Minimal degree of $\Q$-irrep	Minimal degree of $\C$-rep	Minimal degree of $\Q$-rep

Outer aut. group	Outer automorphisms	Metabelian	Metacyclic

Almost simple	Quasisimple	A-group	Z-group

Frattini subgroup	Derived length	Rank	Schur multiplier

Supersolvable	Monomial	Rational

Number of subgroups	Number of normal subgroups	Number of conjugacy classes

Number of characteristic subgroups	Number of autjugacy classes	Number of divisions

Order statistics	Order factorization	Commutator length

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Label	Name	Order	Exponent	Nilp. class	Der. length	Comp. length	Rank	$\card{\mathrm{conj}(G)}$	Subgroups	Subgroup classes	Normal subgroups	Center	Central quotient	Commutator	Abelianization	$\card{\mathrm{Aut}(G)}$	$\card{\mathrm{Out}(G)}$	Tr. deg	Perm. deg	$\C$-irrep deg	$\R$-irrep deg	$\Q$-irrep deg	$\C$-rep deg	$\R$-rep deg	$\Q$-rep deg	Type - length
1001.1	$C_{1001}$	$7 \cdot 11 \cdot 13$	$7 \cdot 11 \cdot 13$	$1$	$1$	$3$	$1$	$1001$	$8$	$8$	$8$	$C_{1001}$	$C_1$	$C_1$	$C_{1001}$	$2^{4} \cdot 3^{2} \cdot 5$	$2^{4} \cdot 3^{2} \cdot 5$	$1001$	$31$	$1$	?	?	$1$	?	?	Cyclic
1002.1	$S_3\times C_{167}$	$2 \cdot 3 \cdot 167$	$2 \cdot 3 \cdot 167$	$-1$	$2$	$3$	$2$	$501$	$12$	$8$	$6$	$C_{167}$	$S_3$	$C_3$	$C_{334}$	$2^{2} \cdot 3 \cdot 83$	$2 \cdot 83$	$501$	$170$	$2$	$4$	$332$	$2$	$4$	$168$	Solvable - 2
1002.2	$C_3\times D_{167}$	$2 \cdot 3 \cdot 167$	$2 \cdot 3 \cdot 167$	$-1$	$2$	$3$	$2$	$255$	$340$	$8$	$6$	$C_3$	$D_{167}$	$C_{167}$	$C_{6}$	$2^{2} \cdot 83 \cdot 167$	$2 \cdot 83$	$501$	$170$	$2$	$4$	$332$	$2$	$4$	$168$	Solvable - 2
1002.3	$D_{501}$	$2 \cdot 3 \cdot 167$	$2 \cdot 3 \cdot 167$	$-1$	$2$	$3$	$2$	$252$	$676$	$8$	$5$	$C_1$	$D_{501}$	$C_{501}$	$C_{2}$	$2^{2} \cdot 3 \cdot 83 \cdot 167$	$2 \cdot 83$	$501$	$170$	$2$	$2$	$332$	$2$	$2$	$168$	Solvable - 2
1002.4	$C_{1002}$	$2 \cdot 3 \cdot 167$	$2 \cdot 3 \cdot 167$	$1$	$1$	$3$	$1$	$1002$	$8$	$8$	$8$	$C_{1002}$	$C_1$	$C_1$	$C_{1002}$	$2^{2} \cdot 83$	$2^{2} \cdot 83$	$1002$	$172$	$1$	?	$332$	$1$	?	?	Cyclic
1003.1	$C_{1003}$	$17 \cdot 59$	$17 \cdot 59$	$1$	$1$	$2$	$1$	$1003$	$4$	$4$	$4$	$C_{1003}$	$C_1$	$C_1$	$C_{1003}$	$2^{5} \cdot 29$	$2^{5} \cdot 29$	$1003$	$76$	$1$	?	?	$1$	?	?	Cyclic
1004.1	$C_{251}:C_4$	$2^{2} \cdot 251$	$2^{2} \cdot 251$	$-1$	$2$	$3$	$2$	$254$	$256$	$6$	$5$	$C_2$	$D_{251}$	$C_{251}$	$C_{4}$	$2^{2} \cdot 5^{3} \cdot 251$	$2 \cdot 5^{3}$	$1004$	$255$	$2$	$4$	$500$	$2$	$4$	$252$	Solvable - 2
1004.2	$C_{1004}$	$2^{2} \cdot 251$	$2^{2} \cdot 251$	$1$	$1$	$3$	$1$	$1004$	$6$	$6$	$6$	$C_{1004}$	$C_1$	$C_1$	$C_{1004}$	$2^{2} \cdot 5^{3}$	$2^{2} \cdot 5^{3}$	$1004$	$255$	$1$	?	?	$1$	?	?	Cyclic
1004.3	$D_{502}$	$2^{2} \cdot 251$	$2 \cdot 251$	$-1$	$2$	$3$	$2$	$254$	$760$	$10$	$7$	$C_2$	$D_{251}$	$C_{251}$	$C_{2}^{2}$	$2^{2} \cdot 5^{3} \cdot 251$	$2 \cdot 5^{3}$	$502$	$253$	$2$	$2$	$250$	$2$	$2$	$250$	Solvable - 2
1004.4	$C_2\times C_{502}$	$2^{2} \cdot 251$	$2 \cdot 251$	$1$	$1$	$3$	$2$	$1004$	$10$	$10$	$10$	$C_2\times C_{502}$	$C_1$	$C_1$	$C_{2} \times C_{502}$	$2^{2} \cdot 3 \cdot 5^{3}$	$2^{2} \cdot 3 \cdot 5^{3}$	$1004$	$255$	$-$	?	$-$	$2$	?	?	Abelian - 2
1005.1	$C_{335}:C_3$	$3 \cdot 5 \cdot 67$	$3 \cdot 5 \cdot 67$	$-1$	$2$	$3$	$2$	$125$	$140$	$8$	$6$	$C_5$	$C_{67}:C_3$	$C_{67}$	$C_{15}$	$2^{3} \cdot 3 \cdot 11 \cdot 67$	$2^{3} \cdot 11$	$335$	$72$	$3$	$6$	$264$	$3$	$6$	$70$	Solvable - 2
1005.2	$C_{1005}$	$3 \cdot 5 \cdot 67$	$3 \cdot 5 \cdot 67$	$1$	$1$	$3$	$1$	$1005$	$8$	$8$	$8$	$C_{1005}$	$C_1$	$C_1$	$C_{1005}$	$2^{4} \cdot 3 \cdot 11$	$2^{4} \cdot 3 \cdot 11$	$1005$	$75$	$1$	?	?	$1$	?	?	Cyclic
1006.1	$D_{503}$	$2 \cdot 503$	$2 \cdot 503$	$-1$	$2$	$2$	$2$	$253$	$506$	$4$	$3$	$C_1$	$D_{503}$	$C_{503}$	$C_{2}$	$2 \cdot 251 \cdot 503$	$251$	$503$	$503$	$2$	$2$	$502$	$2$	$2$	$502$	Solvable - 2
1006.2	$C_{1006}$	$2 \cdot 503$	$2 \cdot 503$	$1$	$1$	$2$	$1$	$1006$	$4$	$4$	$4$	$C_{1006}$	$C_1$	$C_1$	$C_{1006}$	$2 \cdot 251$	$2 \cdot 251$	$1006$	$505$	$1$	?	$502$	$1$	?	?	Cyclic
1007.1	$C_{1007}$	$19 \cdot 53$	$19 \cdot 53$	$1$	$1$	$2$	$1$	$1007$	$4$	$4$	$4$	$C_{1007}$	$C_1$	$C_1$	$C_{1007}$	$2^{3} \cdot 3^{2} \cdot 13$	$2^{3} \cdot 3^{2} \cdot 13$	$1007$	$72$	$1$	?	?	$1$	?	?	Cyclic
1008.1	$C_7:C_{144}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{4} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$168$	$72$	$30$	$23$	$C_{24}$	$F_7$	$C_7$	$C_{144}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3$	$1008$	$32$	$6$	$12$	$144$	$6$	$8$	$20$	Solvable - 2
1008.2	$C_7:C_{144}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{4} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$240$	$60$	$30$	$25$	$C_{48}$	$C_7:C_3$	$C_7$	$C_{144}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{4} \cdot 3$	$1008$	$32$	$3$	$6$	$288$	$3$	$6$	$20$	Solvable - 2
1008.3	$C_9:C_{112}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{4} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$336$	$50$	$30$	$26$	$C_{56}$	$D_9$	$C_9$	$C_{112}$	$2^{5} \cdot 3^{4}$	$2^{4} \cdot 3^{2}$	$1008$	$32$	$2$	$4$	$288$	$2$	$4$	$20$	Solvable - 2
1008.4	$C_7:C_{144}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{4} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$360$	$48$	$30$	$27$	$C_{72}$	$D_7$	$C_7$	$C_{144}$	$2^{5} \cdot 3^{2} \cdot 7$	$2^{4} \cdot 3^{2}$	$1008$	$32$	$2$	$4$	$144$	$2$	$4$	$20$	Solvable - 2
1008.5	$C_{63}:C_{16}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{4} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$264$	$128$	$30$	$25$	$C_8$	$D_{63}$	$C_{63}$	$C_{16}$	$2^{5} \cdot 3^{4} \cdot 7$	$2^{4} \cdot 3^{2}$	$1008$	$32$	$2$	$4$	$144$	$2$	$4$	$20$	Solvable - 2
1008.6	$C_{1008}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{4} \cdot 3^{2} \cdot 7$	$1$	$1$	$7$	$1$	$1008$	$30$	$30$	$30$	$C_{1008}$	$C_1$	$C_1$	$C_{1008}$	$2^{5} \cdot 3^{2}$	$2^{5} \cdot 3^{2}$	$1008$	$32$	$1$	?	$288$	$1$	?	?	Cyclic
1008.7	$C_{56}:C_{18}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$168$	$216$	$66$	$41$	$C_{24}$	$F_7$	$C_7$	$C_{2} \times C_{72}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3$	$504$	$24$	$6$	$12$	$144$	$6$	$8$	$16$	Solvable - 2
1008.8	$C_{56}:C_{18}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$114$	$216$	$60$	$35$	$C_{12}$	$C_2\times F_7$	$C_{14}$	$C_{2} \times C_{36}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{2} \cdot 3$	$504$	$24$	$6$	$12$	$144$	$6$	$10$	$16$	Solvable - 2
1008.9	$C_{56}:C_{18}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$87$	$312$	$60$	$29$	$C_6$	$C_{28}:C_6$	$C_{28}$	$C_{2} \times C_{18}$	$2^{5} \cdot 3^{2} \cdot 7$	$2^{2} \cdot 3$	$504$	$24$	$6$	$12$	$144$	$6$	$10$	$16$	Solvable - 2
1008.10	$C_{56}:C_{18}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$87$	$408$	$66$	$29$	$C_6$	$C_{28}:C_6$	$C_{28}$	$C_{2} \times C_{18}$	$2^{6} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3$	$504$	$24$	$6$	$12$	$144$	$6$	$8$	$16$	Solvable - 2
1008.11	$C_{168}.C_6$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$87$	$216$	$54$	$29$	$C_6$	$C_{28}:C_6$	$C_{28}$	$C_{2} \times C_{18}$	$2^{6} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3$	$1008$	$32$	$6$	$12$	$144$	$6$	$10$	$20$	Solvable - 2
1008.12	$C_{14}:C_{72}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$168$	$168$	$66$	$49$	$C_2\times C_{12}$	$F_7$	$C_7$	$C_{2} \times C_{72}$	$2^{5} \cdot 3^{2} \cdot 7$	$2^{4} \cdot 3$	$1008$	$26$	$-$	$-$	$-$	$7$	$8$	$16$	Solvable - 2
1008.13	$C_{28}.C_{36}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$114$	$168$	$60$	$39$	$C_{12}$	$C_2\times F_7$	$C_{14}$	$C_{2} \times C_{36}$	$2^{5} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3$	$504$	$24$	$6$	$12$	$144$	$6$	$10$	$16$	Solvable - 2
1008.14	$C_{28}:C_{36}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{2} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$168$	$264$	$90$	$61$	$C_2\times C_{12}$	$F_7$	$C_7$	$C_{4} \times C_{36}$	$2^{6} \cdot 3^{2} \cdot 7$	$2^{5} \cdot 3$	$1008$	$24$	$-$	$-$	$-$	$7$	$10$	$16$	Solvable - 2
1008.15	$C_{14}.(C_2\times C_{36})$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{2} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$114$	$264$	$78$	$45$	$C_2\times C_6$	$C_2\times F_7$	$C_{14}$	$C_{2} \times C_{36}$	$2^{5} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3$	$1008$	$24$	$-$	$-$	$-$	$7$	$10$	$16$	Solvable - 2
1008.16	$C_{28}:C_{36}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{2} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$114$	$264$	$78$	$49$	$C_2\times C_6$	$C_2\times F_7$	$C_{14}$	$C_{2} \times C_{36}$	$2^{6} \cdot 3^{2} \cdot 7$	$2^{4} \cdot 3$	$1008$	$24$	$-$	$-$	$-$	$7$	$8$	$16$	Solvable - 2
1008.17	$D_{14}:C_{36}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{2} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$114$	$456$	$102$	$45$	$C_2\times C_6$	$C_2\times F_7$	$C_{14}$	$C_{2} \times C_{36}$	$2^{5} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3$	$504$	$24$	$-$	$-$	$-$	$7$	$8$	$16$	Solvable - 2
1008.18	$D_{28}:C_{18}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$78$	$336$	$66$	$29$	$C_6$	$D_{14}:C_6$	$C_{28}$	$C_{2} \times C_{18}$	$2^{5} \cdot 3^{2} \cdot 7$	$2^{2} \cdot 3$	$504$	$24$	$12$	$24$	$72$	$8$	$10$	$16$	Solvable - 2
1008.19	$C_7:(C_9\times \SD_{16})$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$78$	$240$	$60$	$29$	$C_6$	$D_{14}:C_6$	$C_{28}$	$C_{2} \times C_{18}$	$2^{5} \cdot 3^{2} \cdot 7$	$2^{2} \cdot 3$	$504$	$24$	$12$	$24$	$144$	$8$	$10$	$16$	Solvable - 2
1008.20	$D_{28}.C_{18}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$78$	$288$	$60$	$29$	$C_6$	$D_{14}:C_6$	$C_{28}$	$C_{2} \times C_{18}$	$2^{5} \cdot 3^{2} \cdot 7$	$2^{2} \cdot 3$	$504$	$24$	$12$	$24$	$144$	$8$	$10$	$16$	Solvable - 2
1008.21	$C_7:(C_9\times Q_{16})$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$78$	$192$	$54$	$29$	$C_6$	$D_{14}:C_6$	$C_{28}$	$C_{2} \times C_{18}$	$2^{5} \cdot 3^{2} \cdot 7$	$2^{2} \cdot 3$	$1008$	$32$	$12$	$24$	$72$	$8$	$10$	$20$	Solvable - 2
1008.22	$(C_2\times C_{14}):C_{36}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{2} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$114$	$360$	$102$	$49$	$C_2\times C_6$	$C_2\times F_7$	$C_{14}$	$C_{2} \times C_{36}$	$2^{6} \cdot 3^{2} \cdot 7$	$2^{4} \cdot 3$	$504$	$24$	$-$	$-$	$-$	$7$	$10$	$16$	Solvable - 2
1008.23	$C_{28}.D_{18}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$120$	$380$	$66$	$33$	$C_4$	$D_7\times D_9$	$C_{63}$	$C_{2} \times C_{8}$	$2^{5} \cdot 3^{4} \cdot 7$	$2^{3} \cdot 3^{2}$	$504$	$24$	$4$	$8$	$72$	$4$	$6$	$16$	Solvable - 2
1008.24	$D_{63}:C_8$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$120$	$692$	$66$	$29$	$C_4$	$D_7\times D_9$	$C_{63}$	$C_{2} \times C_{8}$	$2^{5} \cdot 3^{4} \cdot 7$	$2^{3} \cdot 3^{2}$	$504$	$24$	$4$	$8$	$72$	$4$	$6$	$16$	Solvable - 2
1008.25	$C_{63}:\OD_{16}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$114$	$380$	$60$	$29$	$C_4$	$D_7\times D_9$	$C_{126}$	$C_{2} \times C_{4}$	$2^{5} \cdot 3^{4} \cdot 7$	$2^{3} \cdot 3^{2}$	$504$	$24$	$4$	$8$	$72$	$4$	$6$	$16$	Solvable - 2
1008.26	$C_{63}:\OD_{16}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$114$	$692$	$60$	$27$	$C_4$	$D_7\times D_9$	$C_{126}$	$C_{2} \times C_{4}$	$2^{5} \cdot 3^{4} \cdot 7$	$2^{3} \cdot 3^{2}$	$504$	$24$	$4$	$8$	$72$	$4$	$6$	$16$	Solvable - 2
1008.27	$C_{63}:\SD_{16}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$102$	$640$	$60$	$25$	$C_2$	$C_7:D_{36}$	$C_{252}$	$C_{2}^{2}$	$2^{6} \cdot 3^{4} \cdot 7$	$2^{3} \cdot 3^{2}$	$504$	$24$	$4$	$8$	$144$	$4$	$6$	$16$	Solvable - 2
1008.28	$C_{63}:\SD_{16}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$102$	$952$	$60$	$25$	$C_2$	$C_7:D_{36}$	$C_{252}$	$C_{2}^{2}$	$2^{6} \cdot 3^{4} \cdot 7$	$2^{3} \cdot 3^{2}$	$504$	$24$	$4$	$4$	$72$	$4$	$4$	$16$	Solvable - 2
1008.29	$C_7:D_{72}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$102$	$1056$	$66$	$25$	$C_2$	$C_7:D_{36}$	$C_{252}$	$C_{2}^{2}$	$2^{6} \cdot 3^{4} \cdot 7$	$2^{3} \cdot 3^{2}$	$504$	$24$	$4$	$4$	$72$	$4$	$4$	$16$	Solvable - 2
1008.30	$C_{63}:Q_{16}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$102$	$536$	$54$	$25$	$C_2$	$C_7:D_{36}$	$C_{252}$	$C_{2}^{2}$	$2^{6} \cdot 3^{4} \cdot 7$	$2^{3} \cdot 3^{2}$	$1008$	$32$	$4$	$8$	$144$	$4$	$6$	$20$	Solvable - 2
1008.31	$C_{28}.D_{18}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$120$	$372$	$66$	$37$	$C_4$	$D_7\times D_9$	$C_{63}$	$C_{2} \times C_{8}$	$2^{5} \cdot 3^{4} \cdot 7$	$2^{3} \cdot 3^{2}$	$504$	$24$	$4$	$8$	$72$	$4$	$6$	$16$	Solvable - 2
1008.32	$C_{63}:\OD_{16}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$114$	$372$	$60$	$31$	$C_4$	$D_7\times D_9$	$C_{126}$	$C_{2} \times C_{4}$	$2^{5} \cdot 3^{4} \cdot 7$	$2^{3} \cdot 3^{2}$	$504$	$24$	$4$	$8$	$72$	$4$	$6$	$16$	Solvable - 2
1008.33	$C_{63}:D_8$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$90$	$576$	$66$	$25$	$C_2$	$C_{63}:D_4$	$C_{252}$	$C_{2}^{2}$	$2^{6} \cdot 3^{4} \cdot 7$	$2^{3} \cdot 3^{2}$	$504$	$24$	$4$	$8$	$72$	$4$	$6$	$16$	Solvable - 2
1008.34	$C_9:D_{56}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$99$	$1044$	$66$	$25$	$C_2$	$C_9:D_{28}$	$C_{252}$	$C_{2}^{2}$	$2^{6} \cdot 3^{4} \cdot 7$	$2^{3} \cdot 3^{2}$	$504$	$24$	$4$	$4$	$144$	$4$	$4$	$16$	Solvable - 2
1008.35	$C_{63}:\SD_{16}$	$2^{4} \cdot 3^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 7$	$-1$	$2$	$7$	$2$	$90$	$472$	$60$	$25$	$C_2$	$C_{63}:D_4$	$C_{252}$	$C_{2}^{2}$	$2^{6} \cdot 3^{4} \cdot 7$	$2^{3} \cdot 3^{2}$	$504$	$24$	$4$	$8$	$72$	$4$	$6$	$16$	Solvable - 2

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