LMFDB - Abstract group search results

Refine search

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

		Sort order	Select

Results (1-50 of 228 matches)

Next Download displayed columns for results to

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
256.539	$D_{128}$	$2^{8}$	$2^{7}$	$7$	$2$	$8$	$2$	$67$	$263$	$23$	$11$	$C_2$	$D_{64}$	$C_{64}$	$C_{2}^{2}$	$2^{13}$	$2^{6}$	$128$	$128$	$2$	$2$	$64$	$2$	$2$	$64$	Nilpotent - 7
256.540	$\SD_{256}$	$2^{8}$	$2^{7}$	$7$	$2$	$8$	$2$	$67$	$199$	$22$	$11$	$C_2$	$D_{64}$	$C_{64}$	$C_{2}^{2}$	$2^{12}$	$2^{5}$	$128$	$128$	$2$	$4$	$64$	$2$	$4$	$64$	Nilpotent - 7
256.541	$Q_{256}$	$2^{8}$	$2^{7}$	$7$	$2$	$8$	$2$	$67$	$135$	$21$	$11$	$C_2$	$D_{64}$	$C_{64}$	$C_{2}^{2}$	$2^{13}$	$2^{6}$	$256$	$256$	$2$	$4$	$128$	$2$	$4$	$128$	Nilpotent - 7
512.2015	$C_8^2.D_4$	$2^{9}$	$2^{4}$	$7$	$3$	$9$	$2$	$32$	$1046$	$128$	$16$	$C_2$	$D_4^2:C_4$	$C_4:D_8$	$C_{2} \times C_{4}$	$2^{11}$	$2^{3}$	$32$	$32$	$4$	$4$	$16$	$4$	$4$	$16$	Nilpotent - 7
512.2016	$C_8^2.D_4$	$2^{9}$	$2^{4}$	$7$	$3$	$9$	$2$	$32$	$822$	$118$	$16$	$C_2$	$D_4^2:C_4$	$C_4:D_8$	$C_{2} \times C_{4}$	$2^{11}$	$2^{3}$	$32$	$32$	$4$	$8$	$16$	$4$	$8$	$16$	Nilpotent - 7
512.2017	$C_8^2.D_4$	$2^{9}$	$2^{4}$	$7$	$3$	$9$	$2$	$32$	$822$	$118$	$16$	$C_2$	$D_4^2:C_4$	$C_4:Q_{16}$	$C_{2} \times C_{4}$	$2^{11}$	$2^{3}$	$32$	$32$	$4$	$8$	$16$	$4$	$8$	$16$	Nilpotent - 7
512.2018	$C_8^2.D_4$	$2^{9}$	$2^{4}$	$7$	$3$	$9$	$2$	$32$	$662$	$114$	$16$	$C_2$	$D_4^2:C_4$	$C_4:Q_{16}$	$C_{2} \times C_{4}$	$2^{11}$	$2^{3}$	$32$	$32$	$4$	$8$	$16$	$4$	$8$	$16$	Nilpotent - 7
512.2020	$(C_8\times C_{16}):C_4$	$2^{9}$	$2^{4}$	$7$	$2$	$9$	$2$	$41$	$990$	$115$	$16$	$C_2$	$C_8^2:C_4$	$C_8^2$	$C_{2} \times C_{4}$	$2^{14}$	$2^{6}$	$32$	$32$	$4$	$8$	$16$	$4$	$8$	$16$	Nilpotent - 7
512.2021	$(C_8\times C_{16}).C_4$	$2^{9}$	$2^{4}$	$7$	$2$	$9$	$2$	$41$	$862$	$112$	$16$	$C_2$	$C_8^2:C_4$	$C_8^2$	$C_{2} \times C_{4}$	$2^{14}$	$2^{6}$	$32$	$32$	$4$	$8$	$16$	$4$	$8$	$16$	Nilpotent - 7
512.2023	$C_8^2.(C_2\times C_4)$	$2^{9}$	$2^{4}$	$7$	$2$	$9$	$2$	$29$	$1022$	$115$	$16$	$C_2$	$C_8^2:C_4$	$C_8^2$	$C_{2} \times C_{4}$	$2^{13}$	$2^{5}$	$32$	$32$	$8$	$8$	$16$	$8$	$8$	$16$	Nilpotent - 7
512.2024	$C_8^2.(C_2\times C_4)$	$2^{9}$	$2^{4}$	$7$	$2$	$9$	$2$	$29$	$766$	$104$	$16$	$C_2$	$C_8^2:C_4$	$C_8^2$	$C_{2} \times C_{4}$	$2^{13}$	$2^{5}$	$64$	$64$	$8$	$16$	$32$	$8$	$16$	$32$	Nilpotent - 7
512.2025	$(C_8\times C_{16}):C_4$	$2^{9}$	$2^{4}$	$7$	$2$	$9$	$2$	$41$	$670$	$90$	$16$	$C_2$	$C_8^2:C_4$	$C_8^2$	$C_{2} \times C_{4}$	$2^{12}$	$2^{4}$	$64$	$64$	$4$	$8$	$32$	$4$	$8$	$32$	Nilpotent - 7
512.2026	$C_8^2.(C_2\times C_4)$	$2^{9}$	$2^{4}$	$7$	$2$	$9$	$2$	$29$	$894$	$99$	$16$	$C_2$	$C_8^2:C_4$	$C_8^2$	$C_{2} \times C_{4}$	$2^{13}$	$2^{5}$	$32$	$32$	$8$	$8$	$16$	$8$	$8$	$16$	Nilpotent - 7
512.2028	$D_{64}:C_4$	$2^{9}$	$2^{7}$	$7$	$2$	$9$	$2$	$134$	$658$	$57$	$26$	$C_2^2$	$D_{64}$	$C_{64}$	$C_{2} \times C_{4}$	$2^{14}$	$2^{7}$	$256$	$132$	$-$	$-$	$-$	$3$	$4$	$66$	Nilpotent - 7
512.2030	$C_4.D_{64}$	$2^{9}$	$2^{7}$	$7$	$2$	$9$	$2$	$134$	$402$	$52$	$24$	$C_4$	$D_{64}$	$C_{64}$	$C_{2} \times C_{4}$	$2^{13}$	$2^{6}$	$256$	$256$	$2$	$4$	$128$	$2$	$4$	$128$	Nilpotent - 7
512.2031	$D_{64}:C_4$	$2^{9}$	$2^{7}$	$7$	$2$	$9$	$2$	$86$	$466$	$53$	$24$	$C_2$	$D_{32}:C_4$	$C_{64}$	$C_{2} \times C_{4}$	$2^{13}$	$2^{5}$	$128$	$128$	$4$	$8$	$64$	$4$	$8$	$64$	Nilpotent - 7
512.2032	$\OD_{256}:C_2$	$2^{9}$	$2^{7}$	$7$	$2$	$9$	$2$	$86$	$594$	$55$	$24$	$C_2$	$D_{32}:C_4$	$C_{64}$	$C_{2} \times C_{4}$	$2^{14}$	$2^{6}$	$128$	$128$	$4$	$4$	$64$	$4$	$4$	$64$	Nilpotent - 7
512.2038	$C_{128}.C_4$	$2^{9}$	$2^{7}$	$7$	$2$	$9$	$2$	$134$	$150$	$35$	$24$	$C_4$	$D_{64}$	$C_{64}$	$C_{2} \times C_{4}$	$2^{14}$	$2^{7}$	$256$	$256$	$2$	$4$	$128$	$2$	$4$	$128$	Nilpotent - 7
512.60901	$D_{128}:C_2$	$2^{9}$	$2^{7}$	$7$	$2$	$9$	$3$	$134$	$658$	$75$	$32$	$C_4$	$D_{64}$	$C_{64}$	$C_{2}^{3}$	$2^{14}$	$2^{7}$	$256$	$256$	$2$	$4$	$128$	$2$	$4$	$128$	Nilpotent - 7
768.539	$C_3\times D_{128}$	$2^{8} \cdot 3$	$2^{7} \cdot 3$	$7$	$2$	$9$	$2$	$201$	$526$	$46$	$22$	$C_6$	$D_{64}$	$C_{64}$	$C_{2} \times C_{6}$	$2^{14}$	$2^{7}$	$384$	$131$	$2$	$4$	$128$	$2$	$4$	$66$	Nilpotent - 7
768.541	$C_3\times Q_{256}$	$2^{8} \cdot 3$	$2^{7} \cdot 3$	$7$	$2$	$9$	$2$	$201$	$270$	$42$	$22$	$C_6$	$D_{64}$	$C_{64}$	$C_{2} \times C_{6}$	$2^{14}$	$2^{7}$	$768$	$259$	$2$	$4$	$128$	$2$	$4$	$128$	Nilpotent - 7
1024.dco	$C_8.D_{64}$	$2^{10}$	$2^{7}$	$7$	$2$	$10$	$2$	$268$	$617$	$88$	$37$	$C_8$	$D_{64}$	$C_{64}$	$C_{2} \times C_{8}$	$2^{14}$	$2^{7}$	$256$	$256$	$2$	$4$	$128$	$2$	$4$	$128$	Nilpotent - 7
1024.dcq	$D_{128}:C_4$	$2^{10}$	$2^{7}$	$7$	$2$	$10$	$3$	$268$	$1065$	$133$	$53$	$C_8$	$D_{64}$	$C_{64}$	$C_{2}^{2} \times C_{4}$	$2^{15}$	$2^{8}$	$256$	$256$	$2$	$4$	$128$	$2$	$4$	$128$	Nilpotent - 7
1024.dcr	$C_{128}.C_8$	$2^{10}$	$2^{7}$	$7$	$2$	$10$	$2$	$268$	$177$	$55$	$37$	$C_8$	$D_{64}$	$C_{64}$	$C_{2} \times C_{8}$	$2^{15}$	$2^{8}$	$256$	$256$	$2$	$4$	$128$	$2$	$4$	$128$	Nilpotent - 7
1024.ddc	$Q_{16}^2:C_2^2$	$2^{10}$	$2^{4}$	$7$	$3$	$10$	$3$	$49$	$3133$	$386$	$31$	$C_2$	$D_8\wr C_2$	$C_8:Q_{16}$	$C_{2}^{3}$	$2^{13}$	$2^{4}$	$32$	$32$	$4$	$8$	$16$	$4$	$8$	$16$	Nilpotent - 7
1024.det	$(C_2^2\times C_4^2).\OD_{16}$	$2^{10}$	$2^{3}$	$7$	$3$	$10$	$2$	$37$	$5129$	$512$	$25$	$C_2$	$None$	$D_4\times C_2^3$	$C_{2} \times C_{8}$	$2^{14}$	$2^{5}$	$16$	$16$	$8$	$8$	$8$	$8$	$8$	$8$	Nilpotent - 7
1024.dfb	$C_2^6.\OD_{16}$	$2^{10}$	$2^{4}$	$7$	$3$	$10$	$2$	$37$	$6665$	$682$	$25$	$C_2$	$None$	$C_2^4:C_4$	$C_{2} \times C_{8}$	$2^{14}$	$2^{5}$	$16$	$16$	$8$	$8$	$8$	?	?	?	Nilpotent - 7
1024.dfd	$C_2^6.\OD_{16}$	$2^{10}$	$2^{3}$	$7$	$3$	$10$	$2$	$37$	$6793$	$686$	$25$	$C_2$	$None$	$C_2^4:C_4$	$C_{2} \times C_{8}$	$2^{14}$	$2^{5}$	$16$	$16$	$8$	$8$	$8$	?	?	?	Nilpotent - 7
1024.dfi	$C_2^7.C_8$	$2^{10}$	$2^{4}$	$7$	$2$	$10$	$2$	$40$	$33433$	$4248$	$25$	$C_2$	$C_2^6:C_8$	$C_2^6$	$C_{2} \times C_{8}$	$2^{15}$	$2^{6}$	$16$	$16$	$8$	$8$	$8$	?	?	?	Nilpotent - 7
1024.dgi	$C_2^7:C_8$	$2^{10}$	$2^{3}$	$7$	$2$	$10$	$2$	$40$	$33561$	$4252$	$25$	$C_2$	$C_2^6:C_8$	$C_2^6$	$C_{2} \times C_{8}$	$2^{15}$	$2^{6}$	$16$	$16$	$8$	$8$	$8$	?	?	?	Nilpotent - 7
1024.dgs	$(C_2\times C_4^3):C_8$	$2^{10}$	$2^{3}$	$7$	$2$	$10$	$2$	$40$	$11289$	$1169$	$25$	$C_2$	$C_2^5.\OD_{16}$	$C_2^2\times C_4^2$	$C_{2} \times C_{8}$	$2^{15}$	$2^{6}$	$16$	$16$	$8$	$8$	$8$	?	?	?	Nilpotent - 7
1024.dhe	$C_2^6.\SD_{16}$	$2^{10}$	$2^{3}$	$7$	$3$	$10$	$2$	$34$	$7061$	$647$	$23$	$C_2$	$C_2^5.\SD_{16}$	$C_2^5:C_4$	$C_{2} \times C_{4}$	$2^{13}$	$2^{4}$	$16$	$16$	$8$	$8$	$8$	$8$	$8$	$8$	Nilpotent - 7
1024.dhf	$C_2^6.D_8$	$2^{10}$	$2^{4}$	$7$	$3$	$10$	$2$	$37$	$9437$	$909$	$23$	$C_2$	$C_2^5.D_8$	$C_2^5.C_4$	$C_{2} \times C_{4}$	$2^{13}$	$2^{4}$	$16$	$16$	$8$	$8$	$8$	$8$	$8$	$8$	Nilpotent - 7
1024.dhg	$C_2^6.\SD_{16}$	$2^{10}$	$2^{4}$	$7$	$3$	$10$	$2$	$34$	$6613$	$622$	$23$	$C_2$	$C_2^5.\SD_{16}$	$C_2^5.C_4$	$C_{2} \times C_{4}$	$2^{13}$	$2^{4}$	$16$	$16$	$8$	$8$	$8$	$8$	$8$	$8$	Nilpotent - 7
1024.dhh	$C_2^4.C_2\wr C_4$	$2^{10}$	$2^{4}$	$7$	$3$	$10$	$2$	$34$	$11885$	$1112$	$23$	$C_2$	$C_2^5.D_8$	$C_2^4.D_4$	$C_{2} \times C_{4}$	$2^{13}$	$2^{4}$	$16$	$16$	$8$	$8$	$8$	?	?	?	Nilpotent - 7
1024.dhl	$(D_4\times C_2^3).Q_{16}$	$2^{10}$	$2^{3}$	$7$	$3$	$10$	$2$	$34$	$4949$	$478$	$23$	$C_2$	$None$	$C_2^5:C_4$	$C_{2} \times C_{4}$	$2^{13}$	$2^{4}$	$16$	$16$	$8$	$8$	$8$	$8$	$8$	$8$	Nilpotent - 7
1024.dhm	$(C_2^2\times C_4^2).D_8$	$2^{10}$	$2^{3}$	$7$	$3$	$10$	$2$	$37$	$6685$	$692$	$23$	$C_2$	$C_2^5.\SD_{16}$	$C_2^5:C_4$	$C_{2} \times C_{4}$	$2^{13}$	$2^{4}$	$16$	$16$	$8$	$8$	$8$	$8$	$8$	$8$	Nilpotent - 7
1024.dhr	$C_2^4.C_2\wr C_4$	$2^{10}$	$2^{3}$	$7$	$3$	$10$	$2$	$34$	$3477$	$395$	$23$	$C_2$	$(C_2^2\times Q_8).Q_{16}$	$C_2^4.D_4$	$C_{2} \times C_{4}$	$2^{12}$	$2^{3}$	$16$	$16$	$8$	$8$	$8$	$8$	$8$	$8$	Nilpotent - 7
1024.dht	$C_2^4.C_2\wr C_4$	$2^{10}$	$2^{4}$	$7$	$3$	$10$	$2$	$31$	$4293$	$444$	$23$	$C_2$	$C_2^5.\SD_{16}$	$C_2^4.D_4$	$C_{2} \times C_{4}$	$2^{13}$	$2^{4}$	$16$	$16$	$8$	$8$	$8$	$8$	$8$	$8$	Nilpotent - 7
1024.dhv	$C_2^6.D_8$	$2^{10}$	$2^{3}$	$7$	$3$	$10$	$2$	$37$	$9821$	$930$	$23$	$C_2$	$C_2^5.D_8$	$C_2^5:C_4$	$C_{2} \times C_{4}$	$2^{13}$	$2^{4}$	$16$	$16$	$8$	$8$	$8$	$8$	$8$	$8$	Nilpotent - 7
1024.dhw	$C_2^4.C_2\wr C_4$	$2^{10}$	$2^{3}$	$7$	$3$	$10$	$2$	$31$	$6653$	$610$	$23$	$C_2$	$(C_2^2\times D_4).D_8$	$C_2^4.D_4$	$C_{2} \times C_{4}$	$2^{12}$	$2^{3}$	$16$	$16$	$8$	$8$	$8$	$8$	$8$	$8$	Nilpotent - 7
1024.dig	$C_4^2.C_2\wr C_4$	$2^{10}$	$2^{4}$	$7$	$3$	$10$	$2$	$40$	$3429$	$339$	$27$	$C_2$	$C_4^2.C_4\wr C_2$	$C_2^3.C_4^2$	$C_{2} \times C_{4}$	$2^{14}$	$2^{5}$	$32$	$32$	$16$	$16$	$16$	$16$	$16$	$16$	Nilpotent - 7
1024.dih	$C_4^2.C_2\wr C_4$	$2^{10}$	$2^{4}$	$7$	$2$	$10$	$2$	$46$	$3813$	$363$	$27$	$C_2$	$C_4^2.C_4\wr C_2$	$C_2\times C_8^2$	$C_{2} \times C_{4}$	$2^{15}$	$2^{6}$	$32$	$32$	$8$	$8$	$16$	$8$	$8$	$16$	Nilpotent - 7
1024.dii	$C_4:D_8.D_8$	$2^{10}$	$2^{4}$	$7$	$3$	$10$	$2$	$43$	$2901$	$313$	$27$	$C_2$	$C_2^3.C_2\wr C_4$	$C_4^2.Q_8$	$C_{2} \times C_{4}$	$2^{13}$	$2^{4}$	$32$	$32$	$16$	$16$	$16$	$16$	$16$	$16$	Nilpotent - 7
1024.dik	$(C_2\times C_8^2).D_4$	$2^{10}$	$2^{4}$	$7$	$3$	$10$	$2$	$61$	$2165$	$297$	$27$	$C_4$	$(C_4\times C_8).D_4$	$C_4^2.D_4$	$C_{2} \times C_{4}$	$2^{13}$	$2^{5}$	$32$	$32$	$4$	$8$	$16$	$4$	$8$	$16$	Nilpotent - 7
1024.dil	$C_2^4.C_4^2:C_4$	$2^{10}$	$2^{3}$	$7$	$3$	$10$	$2$	$37$	$4125$	$509$	$23$	$C_2$	$C_2^5.D_8$	$(C_2\times Q_8).D_4$	$C_{2} \times C_{4}$	$2^{12}$	$2^{3}$	$32$	$32$	$8$	$16$	$16$	$8$	$16$	$16$	Nilpotent - 7
1024.dim	$C_2^4.C_2\wr C_4$	$2^{10}$	$2^{4}$	$7$	$3$	$10$	$2$	$34$	$5901$	$633$	$23$	$C_2$	$C_2^5.D_8$	$C_2^4.C_2^3$	$C_{2} \times C_{4}$	$2^{13}$	$2^{4}$	$32$	$32$	$8$	$16$	$16$	$8$	$16$	$16$	Nilpotent - 7
1024.din	$(D_4\times C_2^3).D_8$	$2^{10}$	$2^{3}$	$7$	$3$	$10$	$2$	$31$	$6877$	$652$	$23$	$C_2$	$C_2^5.D_8$	$C_2^5:C_4$	$C_{2} \times C_{4}$	$2^{13}$	$2^{4}$	$32$	$32$	$16$	$16$	$16$	$16$	$16$	$16$	Nilpotent - 7
1024.dll	$(C_2\times C_8^2).D_4$	$2^{10}$	$2^{4}$	$7$	$3$	$10$	$2$	$61$	$2933$	$324$	$29$	$C_2^2$	$D_4^2:C_4$	$C_4^2.Q_8$	$C_{2} \times C_{4}$	$2^{13}$	$2^{5}$	$64$	$40$	$-$	$-$	$-$	$6$	$6$	$20$	Nilpotent - 7
1024.dlm	$C_4^2.C_2\wr C_4$	$2^{10}$	$2^{4}$	$7$	$2$	$10$	$2$	$58$	$4581$	$397$	$29$	$C_2^2$	$C_8^2:C_4$	$C_2\times C_8^2$	$C_{2} \times C_{4}$	$2^{15}$	$2^{7}$	$64$	$40$	$-$	$-$	$-$	?	?	?	Nilpotent - 7

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi
Siegel

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Modular curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Galois groups
Sato-Tate groups
Abstract groups
Lattices

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Motives

Groups

Database

Learn more

Refine search

Results (1-50 of 228 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Learn more

Refine search Advanced search options

Results (1-50 of 228 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Refine search