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 23317 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
432.734	$C_3^2:\GL(2,3)$	$2^{4} \cdot 3^{3}$	$2^{3} \cdot 3$	$-1$	$5$	$7$	$2$	11	$646$	$46$	$6$	$C_1$	$C_3^2:\GL(2,3)$	$\PU(3,2)$	$C_{2}$	$2^{4} \cdot 3^{3}$	$1$	$9$	$9$	$8$	$8$	$8$	$8$	$8$	$8$	Solvable - 5
648.531	$\He_3.\SL(2,3)$	$2^{3} \cdot 3^{4}$	$2^{2} \cdot 3^{2}$	$-1$	$5$	$7$	$2$	24	$252$	$26$	$6$	$C_3$	$\PU(3,2)$	$\SU(3,2)$	$C_{3}$	$2^{4} \cdot 3^{4}$	$2 \cdot 3$	$81$	$81$	$3$	$6$	$18$	$3$	$6$	$18$	Solvable - 5
648.532	$\He_3.\SL(2,3)$	$2^{3} \cdot 3^{4}$	$2^{2} \cdot 3^{2}$	$-1$	$5$	$7$	$2$	24	$324$	$27$	$6$	$C_3$	$\PU(3,2)$	$\SU(3,2)$	$C_{3}$	$2^{4} \cdot 3^{4}$	$2 \cdot 3$	$81$	$81$	$3$	$6$	$18$	$3$	$6$	$18$	Solvable - 5
648.533	$\Unitary(3,2)$	$2^{3} \cdot 3^{4}$	$2^{2} \cdot 3^{2}$	$-1$	$5$	$7$	$2$	24	$495$	$41$	$6$	$C_3$	$\PU(3,2)$	$\SU(3,2)$	$C_{3}$	$2^{4} \cdot 3^{4}$	$2 \cdot 3$	$27$	$27$	$3$	$6$	$6$	$3$	$6$	$6$	Solvable - 5
864.4053	$(C_3\times C_6).\GL(2,3)$	$2^{5} \cdot 3^{3}$	$2^{3} \cdot 3$	$-1$	$5$	$8$	$2$	22	$1022$	$78$	$12$	$C_2$	$C_3^2:\GL(2,3)$	$\PU(3,2)$	$C_{4}$	$2^{5} \cdot 3^{3}$	$2$	$36$	$13$	$8$	$16$	$16$	$8$	$10$	$10$	Solvable - 5
864.4661	$C_2\times C_3^2:\GL(2,3)$	$2^{5} \cdot 3^{3}$	$2^{3} \cdot 3$	$-1$	$5$	$8$	$2$	22	$2306$	$144$	$14$	$C_2$	$C_3^2:\GL(2,3)$	$\PU(3,2)$	$C_{2}^{2}$	$2^{5} \cdot 3^{3}$	$2$	$18$	$11$	$8$	$8$	$8$	$8$	$8$	$8$	Solvable - 5
1296.2892	$C_3^3.\GL(2,3)$	$2^{4} \cdot 3^{4}$	$2^{3} \cdot 3^{2}$	$-1$	$5$	$8$	$2$	21	$1720$	$73$	$10$	$C_1$	$C_3^3.\GL(2,3)$	$C_3^3.\SL(2,3)$	$C_{2}$	$2^{4} \cdot 3^{5}$	$3$	$72$	$18$	$16$	$16$	$48$	$10$	$10$	$14$	Solvable - 5
1296.2893	$\SU(3,2):C_6$	$2^{4} \cdot 3^{4}$	$2^{2} \cdot 3^{2}$	$-1$	$5$	$8$	$2$	48	$857$	$68$	$13$	$C_6$	$\PU(3,2)$	$\SU(3,2)$	$C_{6}$	$2^{4} \cdot 3^{4}$	$2 \cdot 3$	$162$	$83$	$3$	$6$	$18$	$3$	$6$	$18$	Solvable - 5
1296.2894	$\SU(3,2).C_6$	$2^{4} \cdot 3^{4}$	$2^{2} \cdot 3^{2}$	$-1$	$5$	$8$	$2$	48	$713$	$66$	$13$	$C_6$	$\PU(3,2)$	$\SU(3,2)$	$C_{6}$	$2^{4} \cdot 3^{4}$	$2 \cdot 3$	$162$	$83$	$3$	$6$	$18$	$3$	$6$	$18$	Solvable - 5
1296.2895	$C_2\times \Unitary(3,2)$	$2^{4} \cdot 3^{4}$	$2^{2} \cdot 3^{2}$	$-1$	$5$	$8$	$2$	48	$1343$	$102$	$13$	$C_6$	$\PU(3,2)$	$\SU(3,2)$	$C_{6}$	$2^{4} \cdot 3^{4}$	$2 \cdot 3$	$54$	$29$	$3$	$6$	$6$	$3$	$6$	$6$	Solvable - 5
1296.3487	$C_3^3:\GL(2,3)$	$2^{4} \cdot 3^{4}$	$2^{3} \cdot 3$	$-1$	$5$	$8$	$2$	33	$1808$	$115$	$12$	$C_3$	$C_3^2:\GL(2,3)$	$\PU(3,2)$	$C_{6}$	$2^{5} \cdot 3^{3}$	$2$	$24$	$12$	$8$	$16$	$16$	$8$	$10$	$10$	Solvable - 5
1296.3488	$C_3^3:\GL(2,3)$	$2^{4} \cdot 3^{4}$	$2^{3} \cdot 3$	$-1$	$5$	$8$	$3$	21	$3940$	$151$	$13$	$C_1$	$C_3^3:\GL(2,3)$	$C_3^3:\SL(2,3)$	$C_{2}$	$2^{5} \cdot 3^{5}$	$2 \cdot 3$	$24$	$12$	$16$	$16$	$16$	$10$	$10$	$10$	Solvable - 5
1728.31095	$(C_3\times C_{12}).\GL(2,3)$	$2^{6} \cdot 3^{3}$	$2^{3} \cdot 3$	$-1$	$5$	$9$	$2$	44	$1518$	$114$	$18$	$C_4$	$C_3^2:\GL(2,3)$	$\PU(3,2)$	$C_{8}$	$2^{6} \cdot 3^{3}$	$2^{2}$	$72$	$17$	$8$	$16$	$32$	$8$	$10$	$12$	Solvable - 5
1728.31096	$C_6^2.\GL(2,3)$	$2^{6} \cdot 3^{3}$	$2^{3} \cdot 3$	$-1$	$5$	$9$	$2$	20	$3866$	$133$	$9$	$C_1$	$C_6^2.\GL(2,3)$	$C_6^2.\SL(2,3)$	$C_{2}$	$2^{7} \cdot 3^{3}$	$2$	$48$	$21$	$24$	$24$	$24$	$11$	$14$	$14$	Solvable - 5
1728.46190	$(C_3\times C_{12}).\GL(2,3)$	$2^{6} \cdot 3^{3}$	$2^{3} \cdot 3$	$-1$	$5$	$9$	$2$	32	$2802$	$180$	$20$	$C_2$	$C_2\times C_3^2:\GL(2,3)$	$C_2\times \PU(3,2)$	$C_{2}^{2}$	$2^{7} \cdot 3^{3}$	$2^{2}$	$72$	$17$	$16$	$32$	$32$	$10$	$12$	$12$	Solvable - 5
1728.46191	$C_4\times C_3^2:\GL(2,3)$	$2^{6} \cdot 3^{3}$	$2^{3} \cdot 3$	$-1$	$5$	$9$	$2$	44	$4086$	$246$	$22$	$C_4$	$C_3^2:\GL(2,3)$	$\PU(3,2)$	$C_{2} \times C_{4}$	$2^{6} \cdot 3^{3}$	$2^{2}$	$36$	$13$	$8$	$16$	$16$	$8$	$10$	$10$	Solvable - 5
1728.46192	$\PSU(3,2):D_{12}$	$2^{6} \cdot 3^{3}$	$2^{3} \cdot 3$	$-1$	$5$	$9$	$2$	32	$5610$	$252$	$20$	$C_2$	$C_2\times C_3^2:\GL(2,3)$	$C_2\times \PU(3,2)$	$C_{2}^{2}$	$2^{7} \cdot 3^{3}$	$2^{2}$	$36$	$13$	$16$	$16$	$16$	$10$	$10$	$10$	Solvable - 5
1728.46193	$C_6^2.\GL(2,3)$	$2^{6} \cdot 3^{3}$	$2^{3} \cdot 3$	$-1$	$5$	$9$	$2$	44	$3822$	$264$	$34$	$C_2^2$	$C_3^2:\GL(2,3)$	$\PU(3,2)$	$C_{2} \times C_{4}$	$2^{7} \cdot 3^{3}$	$2^{3}$	$72$	$15$	$-$	$-$	$-$	$9$	$10$	$10$	Solvable - 5
1728.46194	$C_6^2:\GL(2,3)$	$2^{6} \cdot 3^{3}$	$2^{3} \cdot 3$	$-1$	$5$	$9$	$2$	32	$5106$	$260$	$20$	$C_2$	$C_2\times C_3^2:\GL(2,3)$	$C_2\times \PU(3,2)$	$C_{2}^{2}$	$2^{6} \cdot 3^{3}$	$2$	$36$	$13$	$16$	$16$	$16$	$10$	$10$	$10$	Solvable - 5
1728.47845	$C_6^2:\GL(2,3)$	$2^{6} \cdot 3^{3}$	$2^{3} \cdot 3$	$-1$	$5$	$9$	$3$	44	$10622$	$592$	$42$	$C_2^2$	$C_3^2:\GL(2,3)$	$\PU(3,2)$	$C_{2}^{3}$	$2^{7} \cdot 3^{4}$	$2^{3} \cdot 3$	$36$	$13$	$-$	$-$	$-$	?	?	?	Solvable - 5
1728.47846	$C_6^2:\GL(2,3)$	$2^{6} \cdot 3^{3}$	$2^{3} \cdot 3$	$-1$	$5$	$9$	$2$	20	$4746$	$187$	$11$	$C_1$	$C_6^2:\GL(2,3)$	$C_6^2:\SL(2,3)$	$C_{2}$	$2^{7} \cdot 3^{3}$	$2$	$36$	$13$	$24$	$24$	$24$	$11$	$11$	$11$	Solvable - 5
1944.2292	$\SU(3,2):C_9$	$2^{3} \cdot 3^{5}$	$2^{2} \cdot 3^{2}$	$-1$	$5$	$8$	$2$	72	$885$	$73$	$13$	$C_3^2$	$\PU(3,2)$	$\SU(3,2)$	$C_{9}$	$2^{4} \cdot 3^{5}$	$2 \cdot 3^{2}$	$243$	$36$	$-$	$-$	$-$	$4$	$8$	$12$	Solvable - 5
1944.2293	$\SU(3,2).C_9$	$2^{3} \cdot 3^{5}$	$2^{2} \cdot 3^{3}$	$-1$	$5$	$8$	$2$	72	$336$	$38$	$10$	$C_9$	$\PU(3,2)$	$\SU(3,2)$	$C_{9}$	$2^{4} \cdot 3^{5}$	$2 \cdot 3^{2}$	$243$	$243$	$3$	$6$	$54$	$3$	$6$	$54$	Solvable - 5
1944.2294	$\SU(3,2).C_9$	$2^{3} \cdot 3^{5}$	$2^{2} \cdot 3^{3}$	$-1$	$5$	$8$	$2$	72	$336$	$38$	$10$	$C_9$	$\PU(3,2)$	$\SU(3,2)$	$C_{9}$	$2^{4} \cdot 3^{5}$	$2 \cdot 3^{2}$	$243$	$243$	$3$	$6$	$54$	$3$	$6$	$54$	Solvable - 5
1944.3442	$\SU(3,2):C_3^2$	$2^{3} \cdot 3^{5}$	$2^{2} \cdot 3^{2}$	$-1$	$5$	$8$	$2$	72	$1440$	$99$	$16$	$C_3^2$	$\PU(3,2)$	$\SU(3,2)$	$C_{3}^{2}$	$2^{5} \cdot 3^{6}$	$2^{2} \cdot 3^{3}$	$243$	$84$	$-$	$-$	$-$	$4$	$8$	$20$	Solvable - 5
1944.3443	$\SU(3,2):C_3^2$	$2^{3} \cdot 3^{5}$	$2^{2} \cdot 3^{2}$	$-1$	$5$	$8$	$2$	40	$1440$	$89$	$13$	$C_3$	$C_3^3:\SL(2,3)$	$\SU(3,2)$	$C_{3}^{2}$	$2^{4} \cdot 3^{6}$	$2 \cdot 3^{2}$	$81$	$81$	$9$	$18$	$18$	$9$	$18$	$18$	Solvable - 5
1944.3444	$\SU(3,2).C_3^2$	$2^{3} \cdot 3^{5}$	$2^{2} \cdot 3^{2}$	$-1$	$5$	$8$	$2$	72	$1008$	$93$	$16$	$C_3^2$	$\PU(3,2)$	$\SU(3,2)$	$C_{3}^{2}$	$2^{5} \cdot 3^{6}$	$2^{2} \cdot 3^{3}$	$243$	$84$	$-$	$-$	$-$	$4$	$8$	$20$	Solvable - 5
1944.3445	$\SU(3,2).C_3^2$	$2^{3} \cdot 3^{5}$	$2^{2} \cdot 3^{2}$	$-1$	$5$	$8$	$2$	40	$1008$	$83$	$13$	$C_3$	$C_3^3:\SL(2,3)$	$\SU(3,2)$	$C_{3}^{2}$	$2^{4} \cdot 3^{6}$	$2 \cdot 3^{2}$	$81$	$81$	$9$	$18$	$18$	$9$	$18$	$18$	Solvable - 5
1944.3446	$C_3\times \Unitary(3,2)$	$2^{3} \cdot 3^{5}$	$2^{2} \cdot 3^{2}$	$-1$	$5$	$8$	$2$	72	$2682$	$192$	$16$	$C_3^2$	$\PU(3,2)$	$\SU(3,2)$	$C_{3}^{2}$	$2^{5} \cdot 3^{6}$	$2^{2} \cdot 3^{3}$	$81$	$30$	$-$	$-$	$-$	?	?	?	Solvable - 5
1944.3447	$\Unitary(3,2):C_3$	$2^{3} \cdot 3^{5}$	$2^{2} \cdot 3^{2}$	$-1$	$5$	$8$	$2$	40	$1737$	$98$	$13$	$C_3$	$C_3^3:\SL(2,3)$	$\SU(3,2)$	$C_{3}^{2}$	$2^{4} \cdot 3^{6}$	$2 \cdot 3^{2}$	$81$	$81$	$9$	$18$	$18$	$9$	$18$	$18$	Solvable - 5
1944.3448	$\Unitary(3,2):C_3$	$2^{3} \cdot 3^{5}$	$2^{2} \cdot 3^{2}$	$-1$	$5$	$8$	$2$	72	$1089$	$90$	$13$	$C_9$	$\PU(3,2)$	$\SU(3,2)$	$C_{3}^{2}$	$2^{4} \cdot 3^{5}$	$2 \cdot 3^{2}$	$81$	$81$	$3$	$6$	$18$	$3$	$6$	$18$	Solvable - 5
1944.3449	$\Unitary(3,2):C_3$	$2^{3} \cdot 3^{5}$	$2^{2} \cdot 3^{2}$	$-1$	$5$	$8$	$2$	40	$1089$	$80$	$13$	$C_3$	$C_3^3:\SL(2,3)$	$\SU(3,2)$	$C_{3}^{2}$	$2^{3} \cdot 3^{5}$	$3$	$81$	$81$	$9$	$18$	$18$	$9$	$18$	$18$	Solvable - 5
2160.cv	$C_5\times C_3^2:\GL(2,3)$	$2^{4} \cdot 3^{3} \cdot 5$	$2^{3} \cdot 3 \cdot 5$	$-1$	$5$	$8$	$2$	55	$1292$	$92$	$12$	$C_5$	$C_3^2:\GL(2,3)$	$\PU(3,2)$	$C_{10}$	$2^{6} \cdot 3^{3}$	$2^{2}$	$45$	$14$	$8$	$16$	$32$	$8$	$10$	$12$	Solvable - 5
2160.cw	$\PSU(3,2):D_{15}$	$2^{4} \cdot 3^{3} \cdot 5$	$2^{3} \cdot 3 \cdot 5$	$-1$	$5$	$8$	$2$	31	$3148$	$92$	$11$	$C_1$	$\PSU(3,2):D_{15}$	$C_5\times \PU(3,2)$	$C_{2}$	$2^{6} \cdot 3^{3} \cdot 5$	$2^{2}$	$45$	$14$	$16$	$16$	$32$	$10$	$10$	$12$	Solvable - 5
2304.a	$\GOrthPlus(4,3)$	$2^{8} \cdot 3^{2}$	$2^{3} \cdot 3$	$-1$	$5$	$10$	$2$	29	$9097$	$310$	$9$	$C_2$	$S_4\wr C_2$	$\SOPlus(4,3)$	$C_{2}^{2}$	$2^{9} \cdot 3^{2}$	$2^{2}$	$32$	$32$	$4$	$8$	$8$	$4$	$8$	$8$	Solvable - 5
2304.bey	$\OmegaPlus(4,3):D_4$	$2^{8} \cdot 3^{2}$	$2^{3} \cdot 3$	$-1$	$5$	$10$	$2$	29	$9129$	$301$	$9$	$C_2$	$S_4\wr C_2$	$\SOPlus(4,3)$	$C_{2}^{2}$	$2^{9} \cdot 3^{2}$	$2^{2}$	$48$	$48$	$4$	$4$	$8$	$4$	$4$	$8$	Solvable - 5
2400.dc	$C_5^2:\Unitary(2,3)$	$2^{5} \cdot 3 \cdot 5^{2}$	$2^{3} \cdot 3 \cdot 5$	$-1$	$5$	$8$	$2$	20	$2064$	$63$	$9$	$C_1$	$C_5^2:\Unitary(2,3)$	$C_5^2:\SL(2,3)$	$C_{4}$	$2^{5} \cdot 3 \cdot 5^{2}$	$1$	$25$	$25$	$24$	$24$	$24$	$24$	$24$	$24$	Solvable - 5
2592.fv	$S_3\times C_3^2:\GL(2,3)$	$2^{5} \cdot 3^{4}$	$2^{3} \cdot 3$	$-1$	$5$	$9$	$2$	33	$10404$	$335$	$20$	$C_1$	$S_3\times C_3^2:\GL(2,3)$	$C_3^3:\SL(2,3)$	$C_{2}^{2}$	$2^{5} \cdot 3^{4}$	$1$	$24$	$12$	$16$	$16$	$16$	$10$	$10$	$10$	Solvable - 5
2592.nv	$C_6\times C_3^2:\GL(2,3)$	$2^{5} \cdot 3^{4}$	$2^{3} \cdot 3$	$-1$	$5$	$9$	$2$	66	$5924$	$343$	$28$	$C_6$	$C_3^2:\GL(2,3)$	$\PU(3,2)$	$C_{2} \times C_{6}$	$2^{6} \cdot 3^{3}$	$2^{2}$	$48$	$14$	$8$	$16$	$16$	$8$	$10$	$10$	Solvable - 5
2592.nx	$C_2\times C_3^3:\GL(2,3)$	$2^{5} \cdot 3^{4}$	$2^{3} \cdot 3$	$-1$	$5$	$9$	$3$	42	$13776$	$456$	$29$	$C_2$	$C_3^3:\GL(2,3)$	$C_3^3:\SL(2,3)$	$C_{2}^{2}$	$2^{6} \cdot 3^{5}$	$2^{2} \cdot 3$	$48$	$14$	$16$	$16$	$16$	$10$	$10$	$10$	Solvable - 5
3000.ba	$\He_5:\SL(2,3)$	$2^{3} \cdot 3 \cdot 5^{3}$	$2^{2} \cdot 3 \cdot 5$	$-1$	$5$	$7$	$2$	36	$873$	$27$	$6$	$C_5$	$C_5^2:\SL(2,3)$	$\He_5:Q_8$	$C_{3}$	$2^{5} \cdot 3 \cdot 5^{2}$	$2^{2}$	$125$	$125$	$5$	$10$	$20$	$5$	$10$	$20$	Solvable - 5
3456.cx	$(C_2\times C_6^2):\GL(2,3)$	$2^{7} \cdot 3^{3}$	$2^{3} \cdot 3$	$-1$	$5$	$10$	$2$	31	$16920$	$491$	$15$	$C_2$	$C_6^2:\GL(2,3)$	$(C_2\times C_6^2):\SL(2,3)$	$C_{2}$	$2^{8} \cdot 3^{3}$	$2^{2}$	$24$	$17$	$8$	$8$	$8$	$8$	$8$	$8$	Solvable - 5
3456.in	$C_2^4.\SL(3,3)$	$2^{7} \cdot 3^{3}$	$2^{3} \cdot 3$	$-1$	$5$	$10$	$3$	55	$26194$	$1056$	$50$	$C_2$	$C_6^2:\GL(2,3)$	$C_2\times \PU(3,2)$	$C_{2}^{3}$	$2^{8} \cdot 3^{3}$	$2^{2}$	$36$	$13$	$16$	$16$	$16$	$10$	$10$	$10$	Solvable - 5
3456.kp	$C_2\times C_6^2:\GL(2,3)$	$2^{7} \cdot 3^{3}$	$2^{3} \cdot 3$	$-1$	$5$	$10$	$2$	40	$21430$	$771$	$25$	$C_2$	$C_6^2:\GL(2,3)$	$C_6^2:\SL(2,3)$	$C_{2}^{2}$	$2^{8} \cdot 3^{3}$	$2^{2}$	$54$	$15$	$24$	$24$	$24$	$11$	$11$	$11$	Solvable - 5
3456.kr	$C_2\times C_6^2:\GL(2,3)$	$2^{7} \cdot 3^{3}$	$2^{3} \cdot 3$	$-1$	$5$	$10$	$3$	64	$25290$	$1144$	$62$	$C_2^2$	$C_2\times C_3^2:\GL(2,3)$	$C_2\times \PU(3,2)$	$C_{2}^{3}$	$2^{9} \cdot 3^{3}$	$2^{4}$	$72$	$15$	$-$	$-$	$-$	$10$	$10$	$10$	Solvable - 5
3456.ks	$\GL(2,3).C_2^6$	$2^{7} \cdot 3^{3}$	$2^{3} \cdot 3$	$-1$	$5$	$10$	$4$	88	$64138$	$3256$	$166$	$C_2^3$	$C_3^2:\GL(2,3)$	$\PU(3,2)$	$C_{2}^{4}$	$2^{10} \cdot 3^{4} \cdot 7$	$2^{6} \cdot 3 \cdot 7$	$72$	$15$	$-$	$-$	$-$	?	?	?	Solvable - 5
3456.kt	$(C_6\times C_{12}):\GL(2,3)$	$2^{7} \cdot 3^{3}$	$2^{3} \cdot 3$	$-1$	$5$	$10$	$3$	64	$27658$	$1088$	$62$	$C_2^2$	$C_2\times C_3^2:\GL(2,3)$	$C_2\times \PU(3,2)$	$C_{2}^{3}$	$2^{10} \cdot 3^{3}$	$2^{5}$	$72$	$15$	$-$	$-$	$-$	?	?	?	Solvable - 5
3456.pz	$(C_6\times C_{12}):\GL(2,3)$	$2^{7} \cdot 3^{3}$	$2^{3} \cdot 3$	$-1$	$5$	$10$	$3$	88	$19418$	$1056$	$70$	$C_2\times C_4$	$C_3^2:\GL(2,3)$	$\PU(3,2)$	$C_{2}^{2} \times C_{4}$	$2^{9} \cdot 3^{3}$	$2^{5}$	$72$	$15$	$-$	$-$	$-$	?	?	?	Solvable - 5
3888.br	$C_3^4:\GL(2,3)$	$2^{4} \cdot 3^{5}$	$2^{3} \cdot 3^{2}$	$-1$	$5$	$9$	$2$	21	$12418$	$214$	$7$	$C_1$	$C_3^4:\GL(2,3)$	$C_3^4:\SL(2,3)$	$C_{2}$	$2^{4} \cdot 3^{5}$	$1$	$12$	$12$	$8$	$8$	$8$	$8$	$8$	$8$	Solvable - 5
3888.cc	$C_3^3:S_3.S_4$	$2^{4} \cdot 3^{5}$	$2^{3} \cdot 3$	$-1$	$5$	$9$	$2$	15	$8346$	$128$	$6$	$C_1$	$C_3^3:S_3.S_4$	$C_3^4:\SL(2,3)$	$C_{2}$	$2^{7} \cdot 3^{5}$	$2^{3}$	$18$	$18$	$16$	$16$	$16$	$16$	$16$	$16$	Solvable - 5

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