Abstract group search results

Note: Search results may be incomplete due to uncomputed quantities: Automorphism group order (4830 objects)

Results (12 matches)

 

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
18.1	$D_9$	$2 \cdot 3^{2}$	$2 \cdot 3^{2}$	$-1$	$2$	$3$	$2$	$6$	$16$	$6$	$4$	$C_1$	$D_9$	$C_9$	$C_{2}$	$2 \cdot 3^{3}$	$3$	$9$	$9$	$2$	$2$	$6$	$2$	$2$	$6$	Solvable - 2
20.1	$C_5:C_4$	$2^{2} \cdot 5$	$2^{2} \cdot 5$	$-1$	$2$	$3$	$2$	$8$	$10$	$6$	$5$	$C_2$	$D_5$	$C_5$	$C_{4}$	$2^{3} \cdot 5$	$2^{2}$	$20$	$9$	$2$	$4$	$8$	$2$	$4$	$6$	Solvable - 2
20.4	$D_{10}$	$2^{2} \cdot 5$	$2 \cdot 5$	$-1$	$2$	$3$	$2$	$8$	$22$	$10$	$7$	$C_2$	$D_5$	$C_5$	$C_{2}^{2}$	$2^{3} \cdot 5$	$2^{2}$	$10$	$7$	$2$	$2$	$4$	$2$	$2$	$4$	Solvable - 2
28.1	$C_7:C_4$	$2^{2} \cdot 7$	$2^{2} \cdot 7$	$-1$	$2$	$3$	$2$	$10$	$12$	$6$	$5$	$C_2$	$D_7$	$C_7$	$C_{4}$	$2^{2} \cdot 3 \cdot 7$	$2 \cdot 3$	$28$	$11$	$2$	$4$	$12$	$2$	$4$	$8$	Solvable - 2
28.3	$D_{14}$	$2^{2} \cdot 7$	$2 \cdot 7$	$-1$	$2$	$3$	$2$	$10$	$28$	$10$	$7$	$C_2$	$D_7$	$C_7$	$C_{2}^{2}$	$2^{2} \cdot 3 \cdot 7$	$2 \cdot 3$	$14$	$9$	$2$	$2$	$6$	$2$	$2$	$6$	Solvable - 2
36.1	$C_9:C_4$	$2^{2} \cdot 3^{2}$	$2^{2} \cdot 3^{2}$	$-1$	$2$	$4$	$2$	$12$	$19$	$9$	$7$	$C_2$	$D_9$	$C_9$	$C_{4}$	$2^{2} \cdot 3^{3}$	$2 \cdot 3$	$36$	$13$	$2$	$4$	$12$	$2$	$4$	$8$	Solvable - 2
36.3	$C_2^2:C_9$	$2^{2} \cdot 3^{2}$	$2 \cdot 3^{2}$	$-1$	$2$	$4$	$2$	$12$	$15$	$8$	$5$	$C_3$	$A_4$	$C_2^2$	$C_{9}$	$2^{3} \cdot 3^{2}$	$2 \cdot 3$	$18$	$13$	$3$	$6$	$6$	$3$	$5$	$6$	Solvable - 2
36.4	$D_{18}$	$2^{2} \cdot 3^{2}$	$2 \cdot 3^{2}$	$-1$	$2$	$4$	$2$	$12$	$45$	$15$	$9$	$C_2$	$D_9$	$C_9$	$C_{2}^{2}$	$2^{2} \cdot 3^{3}$	$2 \cdot 3$	$18$	$11$	$2$	$2$	$6$	$2$	$2$	$6$	Solvable - 2
36.10	$S_3^2$	$2^{2} \cdot 3^{2}$	$2 \cdot 3$	$-1$	$2$	$4$	$2$	$9$	$60$	$22$	$10$	$C_1$	$S_3^2$	$C_3^2$	$C_{2}^{2}$	$2^{3} \cdot 3^{2}$	$2$	$6$	$6$	$4$	$4$	$4$	$4$	$4$	$4$	Solvable - 2
50.3	$C_5\times D_5$	$2 \cdot 5^{2}$	$2 \cdot 5$	$-1$	$2$	$3$	$2$	$20$	$20$	$10$	$6$	$C_5$	$D_5$	$C_5$	$C_{10}$	$2^{4} \cdot 5$	$2^{3}$	$10$	$10$	$2$	$4$	$8$	$2$	$4$	$8$	Solvable - 2
63.1	$C_7:C_9$	$3^{2} \cdot 7$	$3^{2} \cdot 7$	$-1$	$2$	$3$	$2$	$15$	$12$	$6$	$5$	$C_3$	$C_7:C_3$	$C_7$	$C_{9}$	$2 \cdot 3^{2} \cdot 7$	$2 \cdot 3$	$63$	$16$	$3$	$6$	$36$	$3$	$6$	$12$	Solvable - 2
100.9	$C_5\times F_5$	$2^{2} \cdot 5^{2}$	$2^{2} \cdot 5$	$-1$	$2$	$4$	$2$	$25$	$32$	$13$	$8$	$C_5$	$F_5$	$C_5$	$C_{20}$	$2^{4} \cdot 5$	$2^{2}$	$20$	$10$	$4$	$8$	$16$	$4$	$6$	$8$	Solvable - 2