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	Min. transitive degree	Min. permutation degree

Number of subgroups	Num. of normal subs	Num. of conj. classes

Order statistics	Family	Order factorization	Commutator length

Min. degree of $\C$-irrep	Min. degree of $\Q$-irrep	Min. degree of $\C$-rep	Min. 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

Num. of char. subgroups	Num. of aut. classes	Number of divisions

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Results (1-50 of 1962 matches)

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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
1.1	$C_1$	$1$	$1$	$0$	$0$	$0$	$0$	1	$1$	$1$	$1$	$C_1$	$C_1$	$C_1$	$C_1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$0$	$0$	$0$	Trivial
60.5	$A_5$	$2^{2} \cdot 3 \cdot 5$	$2 \cdot 3 \cdot 5$	$-1$	$0$	$1$	$2$	5	$59$	$9$	$2$	$C_1$	$A_5$	$A_5$	$C_1$	$2^{3} \cdot 3 \cdot 5$	$2$	$5$	$5$	$3$	$3$	$4$	$3$	$3$	$4$	Simple
120.5	$\SL(2,5)$	$2^{3} \cdot 3 \cdot 5$	$2^{2} \cdot 3 \cdot 5$	$-1$	$0$	$2$	$2$	9	$76$	$12$	$3$	$C_2$	$A_5$	$\SL(2,5)$	$C_1$	$2^{3} \cdot 3 \cdot 5$	$2$	$24$	$24$	$2$	$4$	$8$	$2$	$4$	$8$	Non-Solvable - 2
168.42	$\PSL(2,7)$	$2^{3} \cdot 3 \cdot 7$	$2^{2} \cdot 3 \cdot 7$	$-1$	$0$	$1$	$2$	6	$179$	$15$	$2$	$C_1$	$\PSL(2,7)$	$\PSL(2,7)$	$C_1$	$2^{4} \cdot 3 \cdot 7$	$2$	$7$	$7$	$3$	$6$	$6$	$3$	$6$	$6$	Simple
336.114	$\SL(2,7)$	$2^{4} \cdot 3 \cdot 7$	$2^{3} \cdot 3 \cdot 7$	$-1$	$0$	$2$	$2$	11	$224$	$19$	$3$	$C_2$	$\PSL(2,7)$	$\SL(2,7)$	$C_1$	$2^{4} \cdot 3 \cdot 7$	$2$	$16$	$16$	$4$	$8$	$8$	$4$	$8$	$8$	Non-Solvable - 2
360.118	$A_6$	$2^{3} \cdot 3^{2} \cdot 5$	$2^{2} \cdot 3 \cdot 5$	$-1$	$0$	$1$	$2$	7	$501$	$22$	$2$	$C_1$	$A_6$	$A_6$	$C_1$	$2^{5} \cdot 3^{2} \cdot 5$	$2^{2}$	$6$	$6$	$5$	$5$	$5$	$5$	$5$	$5$	Simple
504.156	$\SL(2,8)$	$2^{3} \cdot 3^{2} \cdot 7$	$2 \cdot 3^{2} \cdot 7$	$-1$	$0$	$1$	$2$	9	$386$	$12$	$2$	$C_1$	$\SL(2,8)$	$\SL(2,8)$	$C_1$	$2^{3} \cdot 3^{3} \cdot 7$	$3$	$9$	$9$	$7$	$7$	$7$	$7$	$7$	$7$	Simple
660.13	$\PSL(2,11)$	$2^{2} \cdot 3 \cdot 5 \cdot 11$	$2 \cdot 3 \cdot 5 \cdot 11$	$-1$	$0$	$1$	$2$	8	$620$	$16$	$2$	$C_1$	$\PSL(2,11)$	$\PSL(2,11)$	$C_1$	$2^{3} \cdot 3 \cdot 5 \cdot 11$	$2$	$11$	$11$	$5$	$10$	$10$	$5$	$10$	$10$	Simple
720.409	$\SL(2,9)$	$2^{4} \cdot 3^{2} \cdot 5$	$2^{3} \cdot 3 \cdot 5$	$-1$	$0$	$2$	$2$	13	$588$	$27$	$3$	$C_2$	$A_6$	$\SL(2,9)$	$C_1$	$2^{5} \cdot 3^{2} \cdot 5$	$2^{2}$	$80$	$80$	$4$	$8$	$8$	$4$	$8$	$8$	Non-Solvable - 2
960.11357	$C_2^4:A_5$	$2^{6} \cdot 3 \cdot 5$	$2^{2} \cdot 3 \cdot 5$	$-1$	$0$	$5$	$2$	9	$2331$	$77$	$3$	$C_1$	$C_2^4:A_5$	$C_2^4:A_5$	$C_1$	$2^{9} \cdot 3^{2} \cdot 5$	$2^{3} \cdot 3$	$16$	$16$	$15$	$15$	$15$	$15$	$15$	$15$	Non-Solvable - 5
960.11358	$C_2^4:A_5$	$2^{6} \cdot 3 \cdot 5$	$2^{2} \cdot 3 \cdot 5$	$-1$	$0$	$5$	$2$	12	$1708$	$63$	$3$	$C_1$	$C_2^4:A_5$	$C_2^4:A_5$	$C_1$	$2^{7} \cdot 3 \cdot 5$	$2$	$10$	$10$	$5$	$5$	$5$	$5$	$5$	$5$	Non-Solvable - 5
1080.260	$C_3.A_6$	$2^{3} \cdot 3^{3} \cdot 5$	$2^{2} \cdot 3 \cdot 5$	$-1$	$0$	$2$	$2$	17	$1111$	$42$	$3$	$C_3$	$A_6$	$C_3.A_6$	$C_1$	$2^{5} \cdot 3^{2} \cdot 5$	$2^{2}$	$18$	$18$	$3$	$6$	$12$	$3$	$6$	$12$	Non-Solvable - 2
1092.25	$\PSL(2,13)$	$2^{2} \cdot 3 \cdot 7 \cdot 13$	$2 \cdot 3 \cdot 7 \cdot 13$	$-1$	$0$	$1$	$2$	9	$942$	$16$	$2$	$C_1$	$\PSL(2,13)$	$\PSL(2,13)$	$C_1$	$2^{3} \cdot 3 \cdot 7 \cdot 13$	$2$	$14$	$14$	$7$	$7$	$13$	$7$	$7$	$13$	Simple
1320.13	$\SL(2,11)$	$2^{3} \cdot 3 \cdot 5 \cdot 11$	$2^{2} \cdot 3 \cdot 5 \cdot 11$	$-1$	$0$	$2$	$2$	15	$766$	$21$	$3$	$C_2$	$\PSL(2,11)$	$\SL(2,11)$	$C_1$	$2^{3} \cdot 3 \cdot 5 \cdot 11$	$2$	$24$	$24$	$6$	$12$	$12$	$6$	$12$	$12$	Non-Solvable - 2
1344.814	$C_2^3.\GL(3,2)$	$2^{6} \cdot 3 \cdot 7$	$2^{3} \cdot 3 \cdot 7$	$-1$	$0$	$4$	$2$	11	$2331$	$72$	$3$	$C_1$	$C_2^3.\GL(3,2)$	$C_2^3.\GL(3,2)$	$C_1$	$2^{7} \cdot 3 \cdot 7$	$2$	$14$	$14$	$7$	$7$	$7$	$7$	$7$	$7$	Non-Solvable - 4
1344.11686	$C_2^3:\GL(3,2)$	$2^{6} \cdot 3 \cdot 7$	$2^{2} \cdot 3 \cdot 7$	$-1$	$0$	$4$	$2$	11	$3299$	$95$	$3$	$C_1$	$C_2^3:\GL(3,2)$	$C_2^3:\GL(3,2)$	$C_1$	$2^{7} \cdot 3 \cdot 7$	$2$	$8$	$8$	$7$	$7$	$7$	$7$	$7$	$7$	Non-Solvable - 4
1920.240998	$C_2^5:A_5$	$2^{7} \cdot 3 \cdot 5$	$2^{2} \cdot 3 \cdot 5$	$-1$	$0$	$6$	$2$	16	$7858$	$219$	$4$	$C_2$	$C_2^4:A_5$	$C_2^5:A_5$	$C_1$	$2^{9} \cdot 3 \cdot 5$	$2^{3}$	$12$	$12$	$6$	$6$	$6$	$6$	$6$	$6$	Non-Solvable - 6
1920.240999	$C_2^5.A_5$	$2^{7} \cdot 3 \cdot 5$	$2^{2} \cdot 3 \cdot 5$	$-1$	$0$	$6$	$2$	16	$3730$	$121$	$4$	$C_2$	$C_2^4:A_5$	$C_2^5.A_5$	$C_1$	$2^{9} \cdot 3 \cdot 5$	$2^{3}$	$24$	$24$	$6$	$12$	$12$	$6$	$12$	$12$	Non-Solvable - 6
1920.241001	$C_2^5.A_5$	$2^{7} \cdot 3 \cdot 5$	$2^{2} \cdot 3 \cdot 5$	$-1$	$0$	$6$	$2$	14	$2846$	$73$	$4$	$C_1$	$C_2^5.A_5$	$C_2^5.A_5$	$C_1$	$2^{9} \cdot 3 \cdot 5$	$2^{2}$	$40$	$40$	$15$	$30$	$30$	$15$	$30$	$30$	Non-Solvable - 6
1920.241002	$C_2^4:\SL(2,5)$	$2^{7} \cdot 3 \cdot 5$	$2^{2} \cdot 3 \cdot 5$	$-1$	$0$	$6$	$2$	22	$3387$	$117$	$5$	$C_2$	$C_2^4:A_5$	$C_2^4:\SL(2,5)$	$C_1$	$2^{7} \cdot 3 \cdot 5$	$2$	$40$	$34$	$10$	$20$	$20$	$7$	$9$	$13$	Non-Solvable - 6
1920.241003	$C_2.C_2^4:A_5$	$2^{7} \cdot 3 \cdot 5$	$2^{3} \cdot 3 \cdot 5$	$-1$	$0$	$6$	$2$	17	$2155$	$73$	$4$	$C_2$	$C_2^4:A_5$	$C_2.C_2^4:A_5$	$C_1$	$2^{7} \cdot 3 \cdot 5$	$2$	$80$	$80$	$4$	$8$	$8$	$4$	$8$	$8$	Non-Solvable - 6
1920.241004	$C_2.C_2^4:A_5$	$2^{7} \cdot 3 \cdot 5$	$2^{3} \cdot 3 \cdot 5$	$-1$	$0$	$6$	$2$	16	$3243$	$86$	$4$	$C_2$	$C_2^4:A_5$	$C_2.C_2^4:A_5$	$C_1$	$2^{7} \cdot 3 \cdot 5$	$2$	$32$	$32$	$8$	$8$	$16$	$8$	$8$	$16$	Non-Solvable - 6
2160.a	$C_6.A_6$	$2^{4} \cdot 3^{3} \cdot 5$	$2^{3} \cdot 3 \cdot 5$	$-1$	$0$	$3$	$2$	31	$1355$	$51$	$5$	$C_6$	$A_6$	$C_6.A_6$	$C_1$	$2^{5} \cdot 3^{2} \cdot 5$	$2^{2}$	$432$	$98$	$6$	$12$	$24$	$6$	$12$	$20$	Non-Solvable - 3
2184.a	$\SL(2,13)$	$2^{3} \cdot 3 \cdot 7 \cdot 13$	$2^{2} \cdot 3 \cdot 7 \cdot 13$	$-1$	$0$	$2$	$2$	17				$C_2$	$\PSL(2,13)$	$\SL(2,13)$	$C_1$	$2^{3} \cdot 3 \cdot 7 \cdot 13$	$2$		$56$	$6$	$12$	$24$	?	?	?	Non-Solvable - 2
2448.a	$\PSL(2,17)$	$2^{4} \cdot 3^{2} \cdot 17$	$2^{3} \cdot 3^{2} \cdot 17$	$-1$	$0$	$1$	$2$	11	$2420$	$22$	$2$	$C_1$	$\PSL(2,17)$	$\PSL(2,17)$	$C_1$	$2^{5} \cdot 3^{2} \cdot 17$	$2$	$18$	$18$	$9$	$9$	$16$	$9$	$9$	$16$	Simple
2520.a	$A_7$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 7$	$2^{2} \cdot 3 \cdot 5 \cdot 7$	$-1$	$0$	$1$	$2$	9	$3786$	$40$	$2$	$C_1$	$A_7$	$A_7$	$C_1$	$2^{4} \cdot 3^{2} \cdot 5 \cdot 7$	$2$	$7$	$7$	$6$	$6$	$6$	$6$	$6$	$6$	Simple
2688.b	$C_2^3:\SL(2,7)$	$2^{7} \cdot 3 \cdot 7$	$2^{3} \cdot 3 \cdot 7$	$-1$	$0$	$5$	$2$	19	$4194$	$116$	$5$	$C_2$	$C_2^3:\GL(3,2)$	$C_2^3:\SL(2,7)$	$C_1$	$2^{7} \cdot 3 \cdot 7$	$2$	$112$	$24$	$14$	$28$	$56$	$11$	$15$	$15$	Non-Solvable - 5
2688.c	$C_2^3.\SL(2,7)$	$2^{7} \cdot 3 \cdot 7$	$2^{3} \cdot 3 \cdot 7$	$-1$	$0$	$5$	$2$	19	$3394$	$98$	$5$	$C_2$	$C_2^3.\GL(3,2)$	$C_2^3.\SL(2,7)$	$C_1$	$2^{7} \cdot 3 \cdot 7$	$2$	$112$	$30$	$14$	$28$	$56$	$11$	$15$	$15$	Non-Solvable - 5
2688.ci	$C_2^4:\PSL(2,7)$	$2^{7} \cdot 3 \cdot 7$	$2^{3} \cdot 3 \cdot 7$	$-1$	$0$	$5$	$2$	16	$5770$	$129$	$4$	$C_2$	$C_2^3:\GL(3,2)$	$C_2^4:\PSL(2,7)$	$C_1$	$2^{6} \cdot 3 \cdot 7$	$1$	$16$	$16$	$8$	$8$	$8$	$8$	$8$	$8$	Non-Solvable - 5
3000.a	$C_5^2.\SL(2,5)$	$2^{3} \cdot 3 \cdot 5^{3}$	$2^{2} \cdot 3 \cdot 5$	$-1$	$0$	$4$	$2$	14	$2228$	$32$	$4$	$C_1$	$C_5^2.\SL(2,5)$	$C_5^2.\SL(2,5)$	$C_1$	$2^{5} \cdot 3 \cdot 5^{3}$	$2^{2}$	$25$	$25$	$24$	$24$	$24$	?	?	?	Non-Solvable - 4
3420.a	$\PSL(2,19)$	$2^{2} \cdot 3^{2} \cdot 5 \cdot 19$	$2 \cdot 3^{2} \cdot 5 \cdot 19$	$-1$	$0$	$1$	$2$	12	$2912$	$19$	$2$	$C_1$	$\PSL(2,19)$	$\PSL(2,19)$	$C_1$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$	$2$	$20$	$20$	$9$	$18$	$18$	$9$	$18$	$18$	Simple
3600.a	$A_5^2$	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2 \cdot 3 \cdot 5$	$-1$	$0$	$2$	$2$	25	$8381$	$113$	$4$	$C_1$	$A_5^2$	$A_5^2$	$C_1$	$2^{7} \cdot 3^{2} \cdot 5^{2}$	$2^{3}$	$25$	$10$	$9$	$9$	$16$	$6$	$6$	$8$	Non-Solvable - 2
3840.a	$C_4.C_2^4:A_5$	$2^{8} \cdot 3 \cdot 5$	$2^{3} \cdot 3 \cdot 5$	$-1$	$0$	$7$	$2$	24	$9989$	$246$	$5$	$C_4$	$C_2^4:A_5$	$C_4.C_2^4:A_5$	$C_1$	$2^{8} \cdot 3 \cdot 5$	$2^{2}$	$64$	$64$	$8$	$16$	$32$	$8$	$16$	$32$	Non-Solvable - 7
3840.b	$C_4.C_2^4:A_5$	$2^{8} \cdot 3 \cdot 5$	$2^{3} \cdot 3 \cdot 5$	$-1$	$0$	$7$	$2$	26	$10089$	$251$	$5$	$C_4$	$C_2^4:A_5$	$C_4.C_2^4:A_5$	$C_1$	$2^{8} \cdot 3 \cdot 5$	$2^{2}$	$64$	$64$	$4$	$8$	$8$	$4$	$8$	$8$	Non-Solvable - 7
3840.c	$C_2^6.A_5$	$2^{8} \cdot 3 \cdot 5$	$2^{2} \cdot 3 \cdot 5$	$-1$	$0$	$7$	$2$	30	$14865$	$411$	$7$	$C_2^2$	$C_2^4:A_5$	$C_2^6.A_5$	$C_1$	$2^{9} \cdot 3 \cdot 5$	$2^{3}$	$48$	$36$	$-$	$-$	$-$	?	?	?	Non-Solvable - 7
3840.d	$C_2^5.\SL(2,5)$	$2^{8} \cdot 3 \cdot 5$	$2^{2} \cdot 3 \cdot 5$	$-1$	$0$	$7$	$2$	28	$15045$	$408$	$8$	$C_2^2$	$C_2^4:A_5$	$C_2^5.\SL(2,5)$	$C_1$	$2^{9} \cdot 3 \cdot 5$	$2^{3}$	$48$	$36$	$-$	$-$	$-$	?	?	?	Non-Solvable - 7
3840.e	$C_2^5.\SL(2,5)$	$2^{8} \cdot 3 \cdot 5$	$2^{3} \cdot 3 \cdot 5$	$-1$	$0$	$7$	$2$	28	$3625$	$99$	$5$	$C_2$	$C_2^5.A_5$	$C_2^5.\SL(2,5)$	$C_1$	$2^{9} \cdot 3 \cdot 5$	$2^{2}$	$48$	$48$	$6$	$12$	$24$	$6$	$12$	$24$	Non-Solvable - 7
3840.f	$C_2.C_2^4:\SL(2,5)$	$2^{8} \cdot 3 \cdot 5$	$2^{3} \cdot 3 \cdot 5$	$-1$	$0$	$7$	$2$	31	$6166$	$162$	$8$	$C_2^2$	$C_2^4:A_5$	$C_2.C_2^4:\SL(2,5)$	$C_1$	$2^{7} \cdot 3 \cdot 5$	$2$	$160$	$56$	$-$	$-$	$-$	$6$	$12$	$16$	Non-Solvable - 7
3840.dc	$C_2^6.A_5$	$2^{8} \cdot 3 \cdot 5$	$2^{2} \cdot 3 \cdot 5$	$-1$	$0$	$7$	$2$	30	$42433$	$1043$	$7$	$C_2^2$	$C_2^4:A_5$	$C_2^6.A_5$	$C_1$	$2^{9} \cdot 3^{2} \cdot 5$	$2^{3} \cdot 3$	$24$	$24$	$-$	$-$	$-$	?	?	?	Non-Solvable - 7
4080.a	$\SL(2,16)$	$2^{4} \cdot 3 \cdot 5 \cdot 17$	$2 \cdot 3 \cdot 5 \cdot 17$	$-1$	$0$	$1$	$2$	17	$3455$	$21$	$2$	$C_1$	$\SL(2,16)$	$\SL(2,16)$	$C_1$	$2^{6} \cdot 3 \cdot 5 \cdot 17$	$2^{2}$	$17$	$17$	$15$	$15$	$16$	$15$	$15$	$16$	Simple
4860.j	$C_3^4:A_5$	$2^{2} \cdot 3^{5} \cdot 5$	$2 \cdot 3^{2} \cdot 5$	$-1$	$0$	$5$	$2$	24	$8100$	$118$	$3$	$C_1$	$C_3^4:A_5$	$C_3^4:A_5$	$C_1$	$2^{4} \cdot 3^{6} \cdot 5$	$2^{2} \cdot 3$	$15$	$15$	$5$	$10$	$10$	$5$	$10$	$10$	Non-Solvable - 5
4860.s	$C_3^4.A_5$	$2^{2} \cdot 3^{5} \cdot 5$	$2 \cdot 3^{2} \cdot 5$	$-1$	$0$	$5$	$2$	24	$4557$	$70$	$3$	$C_1$	$C_3^4.A_5$	$C_3^4.A_5$	$C_1$	$2^{3} \cdot 3^{6} \cdot 5$	$2 \cdot 3$	$30$	$30$	$5$	$10$	$20$	$5$	$10$	$20$	Non-Solvable - 5
4896.a	$\SL(2,17)$	$2^{5} \cdot 3^{2} \cdot 17$	$2^{4} \cdot 3^{2} \cdot 17$	$-1$	$0$	$2$	$2$	21				$C_2$	$\PSL(2,17)$	$\SL(2,17)$	$C_1$	$2^{5} \cdot 3^{2} \cdot 17$	$2$		$288$	$8$	$16$	$32$	?	?	?	Non-Solvable - 2
5040.a	$C_2.A_7$	$2^{4} \cdot 3^{2} \cdot 5 \cdot 7$	$2^{3} \cdot 3 \cdot 5 \cdot 7$	$-1$	$0$	$2$	$2$	16	$4398$	$47$	$3$	$C_2$	$A_7$	$C_2.A_7$	$C_1$	$2^{4} \cdot 3^{2} \cdot 5 \cdot 7$	$2$	$240$	$240$	$4$	$8$	$8$	$4$	$8$	$8$	Non-Solvable - 2
5376.a	$C_2^4:\SL(2,7)$	$2^{8} \cdot 3 \cdot 7$	$2^{3} \cdot 3 \cdot 7$	$-1$	$0$	$6$	$2$	29	$10633$	$205$	$8$	$C_2^2$	$C_2^3:\GL(3,2)$	$C_2^4:\SL(2,7)$	$C_1$	$2^{7} \cdot 3 \cdot 7$	$2$	$32$	$32$	$-$	$-$	$-$	$12$	$16$	$16$	Non-Solvable - 6
5616.a	$\SL(3,3)$	$2^{4} \cdot 3^{3} \cdot 13$	$2^{3} \cdot 3 \cdot 13$	$-1$	$0$	$1$	$2$	12	$6374$	$51$	$2$	$C_1$	$\SL(3,3)$	$\SL(3,3)$	$C_1$	$2^{5} \cdot 3^{3} \cdot 13$	$2$	$13$	$13$	$12$	$12$	$12$	$12$	$12$	$12$	Simple
5760.cg	$C_2^4:A_6$	$2^{7} \cdot 3^{2} \cdot 5$	$2^{3} \cdot 3 \cdot 5$	$-1$	$0$	$5$	$2$	12	$16176$	$139$	$3$	$C_1$	$C_2^4:A_6$	$C_2^4:A_6$	$C_1$	$2^{9} \cdot 3^{2} \cdot 5$	$2^{2}$	$16$	$16$	$15$	$15$	$15$	$15$	$15$	$15$	Non-Solvable - 5
6048.a	$\SU(3,3)$	$2^{5} \cdot 3^{3} \cdot 7$	$2^{3} \cdot 3 \cdot 7$	$-1$	$0$	$1$	$2$	14	$5150$	$36$	$2$	$C_1$	$\SU(3,3)$	$\SU(3,3)$	$C_1$	$2^{6} \cdot 3^{3} \cdot 7$	$2$	$28$	$28$	$6$	$7$	$7$	$6$	$7$	$7$	Simple
6072.a	$\PSL(2,23)$	$2^{3} \cdot 3 \cdot 11 \cdot 23$	$2^{2} \cdot 3 \cdot 11 \cdot 23$	$-1$	$0$	$1$	$2$	14	$5915$	$23$	$2$	$C_1$	$\PSL(2,23)$	$\PSL(2,23)$	$C_1$	$2^{4} \cdot 3 \cdot 11 \cdot 23$	$2$	$24$	$24$	$11$	$22$	$22$	$11$	$22$	$22$	Simple
6840.a	$\SL(2,19)$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$	$2^{2} \cdot 3^{2} \cdot 5 \cdot 19$	$-1$	$0$	$2$	$2$	23				$C_2$	$\PSL(2,19)$	$\SL(2,19)$	$C_1$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$	$2$		$40$	$10$	?	?	?	?	?	Non-Solvable - 2

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

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