Abstract group search results

Results (19 matches)

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Label	Name	Family 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
36.10	$S_3^2$	$\OmegaPlus(4,2)$	$2^{2} \cdot 3^{2}$	$2 \cdot 3$	$-1$	$2$	$4$	$2$	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
288.860	$\OmegaPlus(4,3)$	$\OmegaPlus(4,3)$	$2^{5} \cdot 3^{2}$	$2^{2} \cdot 3$	$-1$	$3$	$7$	$2$	25	$339$	$52$	$12$	$C_2$	$A_4^2$	$D_4:C_2^2$	$C_{3}^{2}$	$2^{7} \cdot 3^{2}$	$2^{3}$	$24$	$24$	$4$	$4$	$4$	$4$	$4$	$4$	Solvable - 3
3600.a	$A_5^2$	$\OmegaPlus(4,4)$	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2 \cdot 3 \cdot 5$	$-1$	$0$	$2$	$2$	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
7200.c	$\OmegaPlus(4,5)$	$\OmegaPlus(4,5)$	$2^{5} \cdot 3^{2} \cdot 5^{2}$	$2^{2} \cdot 3 \cdot 5$	$-1$	$0$	$3$	$2$	41	$14896$	$150$	$5$	$C_2$	$A_5^2$	$\OmegaPlus(4,5)$	$C_1$	$2^{7} \cdot 3^{2} \cdot 5^{2}$	$2^{3}$	$120$	$120$	$4$	$4$	$8$	$4$	$4$	$8$	Non-Solvable - 3
20160.a	$A_8$	$\OmegaPlus(6,2)$	$2^{6} \cdot 3^{2} \cdot 5 \cdot 7$	$2^{2} \cdot 3 \cdot 5 \cdot 7$	$-1$	$0$	$1$	$2$	14	$48337$	$137$	$2$	$C_1$	$A_8$	$A_8$	$C_1$	$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$	$2$	$8$	$8$	$7$	$7$	$7$	$7$	$7$	$7$	Simple
56448.a	$\OmegaPlus(4,7)$	$\OmegaPlus(4,7)$	$2^{7} \cdot 3^{2} \cdot 7^{2}$	$2^{3} \cdot 3 \cdot 7$	$-1$	$0$	$3$	$2$	61	$164849$	$438$	$5$	$C_2$	$\GL(3,2)^2$	$\OmegaPlus(4,7)$	$C_1$	$2^{9} \cdot 3^{2} \cdot 7^{2}$	$2^{3}$	$128$	$128$	$16$	$32$	$32$	?	?	?	Non-Solvable - 3
254016.a	$\SL(2,8)^2$	$\OmegaPlus(4,8)$	$2^{6} \cdot 3^{4} \cdot 7^{2}$	$2 \cdot 3^{2} \cdot 7$	$-1$	$0$	$2$	$2$	81	$682507$	$276$	$4$	$C_1$	$\SL(2,8)^2$	$\SL(2,8)^2$	$C_1$	$2^{7} \cdot 3^{6} \cdot 7^{2}$	$2 \cdot 3^{2}$	$81$	$18$	$49$	$49$	$49$	?	?	?	Non-Solvable - 2
259200.a	$\OmegaPlus(4,9)$	$\OmegaPlus(4,9)$	$2^{7} \cdot 3^{4} \cdot 5^{2}$	$2^{3} \cdot 3 \cdot 5$	$-1$	$0$	$3$	$2$	85	$1750321$	$1011$	$5$	$C_2$	$A_6^2$	$\OmegaPlus(4,9)$	$C_1$	$2^{11} \cdot 3^{4} \cdot 5^{2}$	$2^{5}$	$720$	$720$	$16$	$16$	$16$	?	?	?	Non-Solvable - 3
871200.a	$\OmegaPlus(4,11)$	$\OmegaPlus(4,11)$	$2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2}$	$2^{2} \cdot 3 \cdot 5 \cdot 11$	$-1$	$0$	$3$	$2$	113	$2489056$	$503$	$5$	$C_2$	$\PSL(2,11)^2$	$\OmegaPlus(4,11)$	$C_1$	$2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2}$	$2^{3}$	$288$	$288$	$36$	$72$	$72$	?	?	?	Non-Solvable - 3
2384928.a	$\OmegaPlus(4,13)$	$\OmegaPlus(4,13)$	$2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 13^{2}$	$2^{2} \cdot 3 \cdot 7 \cdot 13$	$-1$	$0$	$3$	$2$	145	$6496028$	$600$	$5$	$C_2$	$\PSL(2,13)^2$	$\OmegaPlus(4,13)$	$C_1$	$2^{7} \cdot 3^{2} \cdot 7^{2} \cdot 13^{2}$	$2^{3}$	$784$	$784$	$36$	$36$	$72$	?	?	?	Non-Solvable - 3
6065280.a	$\PSL(4,3)$	$\OmegaPlus(6,3)$	$2^{7} \cdot 3^{6} \cdot 5 \cdot 13$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 13$	$-1$	$0$	$1$	$2$	29	$25742756$	$817$	$2$	$C_1$	$\PSL(4,3)$	$\PSL(4,3)$	$C_1$	$2^{9} \cdot 3^{6} \cdot 5 \cdot 13$	$2^{2}$	$40$	$40$	$26$	$26$	$26$	?	?	?	Simple
16646400.a	$\SL(2,16)^2$	$\OmegaPlus(4,16)$	$2^{8} \cdot 3^{2} \cdot 5^{2} \cdot 17^{2}$	$2 \cdot 3 \cdot 5 \cdot 17$	$-1$	$0$	$2$	$2$	289				$C_1$	$\SL(2,16)^2$	$\SL(2,16)^2$	$C_1$	$2^{13} \cdot 3^{2} \cdot 5^{2} \cdot 17^{2}$	$2^{5}$		$34$	$225$	$225$	$256$	?	?	?	Non-Solvable - 2
174182400.a	$\OmegaPlus(8,2)$	$\OmegaPlus(8,2)$	$2^{12} \cdot 3^{5} \cdot 5^{2} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 7$	$-1$	$0$	$1$	$2$	53				$C_1$	$\OmegaPlus(8,2)$	$\OmegaPlus(8,2)$	$C_1$	$2^{13} \cdot 3^{6} \cdot 5^{2} \cdot 7$	$2 \cdot 3$		$120$	$28$	$28$	$28$	?	?	?	Simple
987033600.a	$\SL(4,4)$	$\OmegaPlus(6,4)$	$2^{12} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 17$	$2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17$	$-1$	$0$	$1$	$2$	84			$2$	$C_1$	$\SL(4,4)$	$\SL(4,4)$	$C_1$	$2^{14} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 17$	$2^{2}$	$85$	$85$	$84$	$84$	$84$	?	?	?	Simple
14508000000.a	$\OmegaPlus(6,5)$	$\OmegaPlus(6,5)$	$2^{8} \cdot 3^{2} \cdot 5^{6} \cdot 13 \cdot 31$	$2^{3} \cdot 3 \cdot 5 \cdot 13 \cdot 31$	$-1$	$0$	$2$	$2$	97				$C_2$	$\PSL(4,5)$	$\OmegaPlus(6,5)$	$C_1$	$2^{10} \cdot 3^{2} \cdot 5^{6} \cdot 13 \cdot 31$	$2^{3}$		$312$	$156$	?	?	?	?	?	Non-Solvable - 2
2317591180800.a	$\PSL(4,7)$	$\OmegaPlus(6,7)$	$2^{9} \cdot 3^{4} \cdot 5^{2} \cdot 7^{6} \cdot 19$	$2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19$	$-1$	$0$	$1$	$2$	217			$2$	$C_1$	$\PSL(4,7)$	$\PSL(4,7)$	$C_1$	$2^{11} \cdot 3^{4} \cdot 5^{2} \cdot 7^{6} \cdot 19$	$2^{2}$	$400$	$400$	$399$	?	?	?	?	?	Simple
9904359628800.a	$\OmegaPlus(8,3)$	$\OmegaPlus(8,3)$	$2^{13} \cdot 3^{12} \cdot 5^{2} \cdot 7 \cdot 13$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$	$-1$	$0$	$2$	$2$	194			$3$	$C_2$	$\POmegaPlus(8,3)$	$\OmegaPlus(8,3)$	$C_1$	$2^{15} \cdot 3^{12} \cdot 5^{2} \cdot 7 \cdot 13$	$2^{3}$	$2160$	$2160$	$520$	?	?	?	?	?	Non-Solvable - 2
23499295948800.a	$\OmegaPlus(10,2)$	$\OmegaPlus(10,2)$	$2^{20} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 17 \cdot 31$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 \cdot 31$	$-1$	$0$	$1$	$2$	97			$2$	$C_1$	$\OmegaPlus(10,2)$	$\OmegaPlus(10,2)$	$C_1$	$2^{21} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 17 \cdot 31$	$2$	$496$	$496$	$155$	?	?	?	?	?	Simple
34558531338240.a	$\SL(4,8)$	$\OmegaPlus(6,8)$	$2^{18} \cdot 3^{4} \cdot 5 \cdot 7^{3} \cdot 13 \cdot 73$	$2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \cdot 73$	$-1$	$0$	$1$	$2$	584			$2$	$C_1$	$\SL(4,8)$	$\SL(4,8)$	$C_1$	$2^{19} \cdot 3^{5} \cdot 5 \cdot 7^{3} \cdot 13 \cdot 73$	$2 \cdot 3$	$585$	$585$	$584$	?	?	?	?	?	Simple

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