Abstract group search results

Results (43 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
18.3	$C_3\times S_3$	$\Unitary(2,2)$	$2 \cdot 3^{2}$	$2 \cdot 3$	$-1$	$2$	$3$	$2$	9	$14$	$9$	$6$	$C_3$	$S_3$	$C_3$	$C_{6}$	$2^{2} \cdot 3$	$2$	$6$	$6$	$2$	$4$	$4$	$2$	$4$	$4$	Solvable - 2
96.67	$\Unitary(2,3)$	$\Unitary(2,3)$	$2^{5} \cdot 3$	$2^{3} \cdot 3$	$-1$	$4$	$6$	$2$	16	$75$	$24$	$8$	$C_4$	$S_4$	$\SL(2,3)$	$C_{4}$	$2^{5} \cdot 3$	$2^{2}$	$24$	$24$	$2$	$4$	$4$	$2$	$4$	$4$	Solvable - 4
300.22	$C_5\times A_5$	$\Unitary(2,4)$	$2^{2} \cdot 3 \cdot 5^{2}$	$2 \cdot 3 \cdot 5$	$-1$	$1$	$2$	$2$	25	$142$	$20$	$4$	$C_5$	$A_5$	$A_5$	$C_{5}$	$2^{5} \cdot 3 \cdot 5$	$2^{3}$	$25$	$10$	$3$	$6$	$12$	$3$	$5$	$8$	Non-Solvable - 2
648.533	$\Unitary(3,2)$	$\Unitary(3,2)$	$2^{3} \cdot 3^{4}$	$2^{2} \cdot 3^{2}$	$-1$	$5$	$7$	$2$	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
720.411	$\Unitary(2,5)$	$\Unitary(2,5)$	$2^{4} \cdot 3^{2} \cdot 5$	$2^{3} \cdot 3 \cdot 5$	$-1$	$1$	$4$	$2$	36	$576$	$56$	$8$	$C_6$	$S_5$	$\SL(2,5)$	$C_{6}$	$2^{5} \cdot 3 \cdot 5$	$2^{2}$	$120$	$43$	$4$	$8$	$8$	$4$	$8$	$8$	Non-Solvable - 4
2688.a	$\Unitary(2,7)$	$\Unitary(2,7)$	$2^{7} \cdot 3 \cdot 7$	$2^{4} \cdot 3 \cdot 7$	$-1$	$1$	$5$	$2$	64	$1712$	$77$	$8$	$C_8$	$\PGL(2,7)$	$\SL(2,7)$	$C_{8}$	$2^{7} \cdot 3 \cdot 7$	$2^{3}$	$128$	$128$	$6$	$12$	$24$	$6$	$12$	$24$	Non-Solvable - 5
4536.a	$C_9\times \SL(2,8)$	$\Unitary(2,8)$	$2^{3} \cdot 3^{4} \cdot 7$	$2 \cdot 3^{2} \cdot 7$	$-1$	$1$	$3$	$2$	81	$1550$	$43$	$6$	$C_9$	$\SL(2,8)$	$\SL(2,8)$	$C_{9}$	$2^{4} \cdot 3^{4} \cdot 7$	$2 \cdot 3^{2}$	$81$	$18$	$7$	$14$	$42$	$7$	$9$	$13$	Non-Solvable - 3
7200.b	$\Unitary(2,9)$	$\Unitary(2,9)$	$2^{5} \cdot 3^{2} \cdot 5^{2}$	$2^{4} \cdot 3 \cdot 5$	$-1$	$1$	$4$	$2$	100	$3088$	$76$	$8$	$C_{10}$	$\PGL(2,9)$	$\SL(2,9)$	$C_{10}$	$2^{8} \cdot 3^{2} \cdot 5$	$2^{4}$	$720$	$149$	$8$	$16$	$32$	$8$	$16$	$20$	Non-Solvable - 4
15840.a	$\Unitary(2,11)$	$\Unitary(2,11)$	$2^{5} \cdot 3^{2} \cdot 5 \cdot 11$	$2^{3} \cdot 3 \cdot 5 \cdot 11$	$-1$	$1$	$5$	$2$	144	$10346$	$147$	$12$	$C_{12}$	$\PGL(2,11)$	$\SL(2,11)$	$C_{12}$	$2^{6} \cdot 3 \cdot 5 \cdot 11$	$2^{3}$	$288$	$99$	$10$	$20$	$40$	$10$	$20$	$22$	Non-Solvable - 5
24192.a	$\Unitary(3,3)$	$\Unitary(3,3)$	$2^{7} \cdot 3^{3} \cdot 7$	$2^{3} \cdot 3 \cdot 7$	$-1$	$1$	$3$	$2$	56	$32824$	$199$	$6$	$C_4$	$\SU(3,3)$	$\SU(3,3)$	$C_{4}$	$2^{7} \cdot 3^{3} \cdot 7$	$2^{2}$	$112$	$32$	$6$	$12$	$12$	$6$	$9$	$9$	Non-Solvable - 3
30576.a	$\Unitary(2,13)$	$\Unitary(2,13)$	$2^{4} \cdot 3 \cdot 7^{2} \cdot 13$	$2^{3} \cdot 3 \cdot 7 \cdot 13$	$-1$	$1$	$4$	$2$	196	$9332$	$93$	$8$	$C_{14}$	$\PGL(2,13)$	$\SL(2,13)$	$C_{14}$	$2^{5} \cdot 3^{2} \cdot 7 \cdot 13$	$2^{2} \cdot 3$	$784$	$119$	$12$	$24$	$72$	$12$	$24$	$30$	Non-Solvable - 4
69360.a	$C_{17}\times \SL(2,16)$	$\Unitary(2,16)$	$2^{4} \cdot 3 \cdot 5 \cdot 17^{2}$	$2 \cdot 3 \cdot 5 \cdot 17$	$-1$	$1$	$2$	$2$	289	$8830$	$50$	$4$	$C_{17}$	$\SL(2,16)$	$\SL(2,16)$	$C_{17}$	$2^{10} \cdot 3 \cdot 5 \cdot 17$	$2^{6}$	$289$	$34$	$15$	$30$	$240$	$15$	$17$	$32$	Non-Solvable - 2
77760.a	$\Unitary(4,2)$	$\Unitary(4,2)$	$2^{6} \cdot 3^{5} \cdot 5$	$2^{2} \cdot 3^{2} \cdot 5$	$-1$	$1$	$2$	$2$	60	$140038$	$337$	$4$	$C_3$	$\SU(4,2)$	$\SU(4,2)$	$C_{3}$	$2^{8} \cdot 3^{4} \cdot 5$	$2^{2}$	$81$	$30$	$5$	$10$	$10$	$5$	$8$	$8$	Non-Solvable - 2
88128.a	$\Unitary(2,17)$	$\Unitary(2,17)$	$2^{6} \cdot 3^{4} \cdot 17$	$2^{5} \cdot 3^{2} \cdot 17$	$-1$	$1$	$5$	$2$	324	$32857$	$160$	$12$	$C_{18}$	$\PGL(2,17)$	$\SL(2,17)$	$C_{18}$	$2^{7} \cdot 3^{3} \cdot 17$	$2^{2} \cdot 3$	$4896$	$553$	$16$	$32$	$96$	$16$	$32$	$38$	Non-Solvable - 5
136800.a	$\Unitary(2,19)$	$\Unitary(2,19)$	$2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 19$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$	$-1$	$1$	$5$	$2$	400	$48980$	$188$	$12$	$C_{20}$	$\PGL(2,19)$	$\SL(2,19)$	$C_{20}$	$2^{7} \cdot 3^{2} \cdot 5 \cdot 19$	$2^{4}$	$800$	$165$	$18$	$36$	$144$	$18$	$36$	$40$	Non-Solvable - 5
291456.a	$\Unitary(2,23)$	$\Unitary(2,23)$	$2^{7} \cdot 3^{2} \cdot 11 \cdot 23$	$2^{4} \cdot 3 \cdot 11 \cdot 23$	$-1$	$1$	$6$	$2$	576	$134770$	$294$	$16$	$C_{24}$	$\PGL(2,23)$	$\SL(2,23)$	$C_{24}$	$2^{8} \cdot 3 \cdot 11 \cdot 23$	$2^{4}$	$1152$	$387$	$22$	?	$176$	?	?	?	Non-Solvable - 6
312000.a	$\Unitary(3,4)$	$\Unitary(3,4)$	$2^{6} \cdot 3 \cdot 5^{3} \cdot 13$	$2^{2} \cdot 3 \cdot 5 \cdot 13$	$-1$	$1$	$2$	$2$	110	$122338$	$116$	$4$	$C_5$	$\SU(3,4)$	$\SU(3,4)$	$C_{5}$	$2^{10} \cdot 3 \cdot 5^{2} \cdot 13$	$2^{4}$	$325$	$70$	$12$	$24$	$48$	$12$	$24$	$28$	Non-Solvable - 2
405600.a	$\Unitary(2,25)$	$\Unitary(2,25)$	$2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2}$	$2^{4} \cdot 3 \cdot 5 \cdot 13$	$-1$	$1$	$4$	$2$	676	$64392$	$136$	$8$	$C_{26}$	$\PGL(2,25)$	$\SL(2,25)$	$C_{26}$	$2^{8} \cdot 3^{2} \cdot 5^{2} \cdot 13$	$2^{4} \cdot 3$	$5408$	$429$	$24$	?	$288$	?	?	?	Non-Solvable - 4
550368.a	$\Unitary(2,27)$	$\Unitary(2,27)$	$2^{5} \cdot 3^{3} \cdot 7^{2} \cdot 13$	$2^{3} \cdot 3 \cdot 7 \cdot 13$	$-1$	$1$	$5$	$2$	784	$109450$	$187$	$12$	$C_{28}$	$\PGL(2,27)$	$\SL(2,27)$	$C_{28}$	$2^{6} \cdot 3^{5} \cdot 7 \cdot 13$	$2^{3} \cdot 3^{2}$	$1568$	$231$	$26$	?	$312$	?	?	?	Non-Solvable - 5
730800.a	$\Unitary(2,29)$	$\Unitary(2,29)$	$2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 29$	$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 29$	$-1$	$1$	$5$	$2$	900	$240052$	$306$	$16$	$C_{30}$	$\PGL(2,29)$	$\SL(2,29)$	$C_{30}$	$2^{7} \cdot 3 \cdot 5 \cdot 7 \cdot 29$	$2^{4}$	$3600$	$248$	$28$	?	$224$	?	?	?	Non-Solvable - 5
952320.a	$\Unitary(2,31)$	$\Unitary(2,31)$	$2^{11} \cdot 3 \cdot 5 \cdot 31$	$2^{6} \cdot 3 \cdot 5 \cdot 31$	$-1$	$1$	$7$	$2$	1024	$253062$	$274$	$12$	$C_{32}$	$\PGL(2,31)$	$\SL(2,31)$	$C_{32}$	$2^{11} \cdot 3 \cdot 5 \cdot 31$	$2^{5}$	$2048$	$2048$	$30$	?	$480$	?	?	?	Non-Solvable - 7
1080288.a	$C_{33}\times \SL(2,32)$	$\Unitary(2,32)$	$2^{5} \cdot 3^{2} \cdot 11^{2} \cdot 31$	$2 \cdot 3 \cdot 11 \cdot 31$	$-1$	$1$	$3$	$2$	1089	$123040$	$130$	$8$	$C_{33}$	$\SL(2,32)$	$\SL(2,32)$	$C_{33}$	$2^{7} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 31$	$2^{2} \cdot 5^{2}$	$1089$	$47$	$31$	?	?	?	?	?	Non-Solvable - 3
2268000.a	$\Unitary(3,5)$	$\Unitary(3,5)$	$2^{5} \cdot 3^{4} \cdot 5^{3} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 7$	$-1$	$1$	$4$	$2$	192	$3126787$	$653$	$8$	$C_6$	$\PU(3,5)$	$\SU(3,5)$	$C_{6}$	$2^{5} \cdot 3^{4} \cdot 5^{3} \cdot 7$	$2 \cdot 3$	$756$	$380$	$21$	$42$	$42$	?	?	?	Non-Solvable - 4
41057280.a	$\Unitary(5,2)$	$\Unitary(5,2)$	$2^{10} \cdot 3^{6} \cdot 5 \cdot 11$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 11$	$-1$	$1$	$2$	$2$	141				$C_3$	$\SU(5,2)$	$\SU(5,2)$	$C_{3}$	$2^{12} \cdot 3^{5} \cdot 5 \cdot 11$	$2^{2}$		$168$	$10$	$20$	$20$	?	?	?	Non-Solvable - 2
45308928.a	$\Unitary(3,7)$	$\Unitary(3,7)$	$2^{10} \cdot 3 \cdot 7^{3} \cdot 43$	$2^{4} \cdot 3 \cdot 7 \cdot 43$	$-1$	$1$	$4$	$2$	464				$C_8$	$\SU(3,7)$	$\SU(3,7)$	$C_{8}$	$2^{10} \cdot 3 \cdot 7^{3} \cdot 43$	$2^{3}$		$352$	$42$	$84$	$168$	?	?	?	Non-Solvable - 4
52254720.a	$\Unitary(4,3)$	$\Unitary(4,3)$	$2^{11} \cdot 3^{6} \cdot 5 \cdot 7$	$2^{4} \cdot 3^{2} \cdot 5 \cdot 7$	$-1$	$1$	$5$	$2$	188				$C_4$	$\PU(4,3)$	$\SU(4,3)$	$C_{4}$	$2^{12} \cdot 3^{6} \cdot 5 \cdot 7$	$2^{3}$		$2160$	$20$	$40$	$40$	?	?	?	Non-Solvable - 5
148925952.a	$\Unitary(3,8)$	$\Unitary(3,8)$	$2^{9} \cdot 3^{7} \cdot 7 \cdot 19$	$2^{2} \cdot 3^{3} \cdot 7 \cdot 19$	$-1$	$1$	$4$	$2$	666				$C_9$	$\PU(3,8)$	$\SU(3,8)$	$C_{9}$	$2^{10} \cdot 3^{8} \cdot 7 \cdot 19$	$2 \cdot 3^{3}$		$4617$	$57$	?	$342$	?	?	?	Non-Solvable - 4
425736000.a	$\Unitary(3,9)$	$\Unitary(3,9)$	$2^{6} \cdot 3^{6} \cdot 5^{3} \cdot 73$	$2^{4} \cdot 3 \cdot 5 \cdot 73$	$-1$	$1$	$3$	$2$	920				$C_{10}$	$\SU(3,9)$	$\SU(3,9)$	$C_{10}$	$2^{9} \cdot 3^{6} \cdot 5^{2} \cdot 73$	$2^{4}$		$737$	$72$	?	$288$	?	?	?	Non-Solvable - 3
2552964480.a	$\Unitary(3,11)$	$\Unitary(3,11)$	$2^{7} \cdot 3^{4} \cdot 5 \cdot 11^{3} \cdot 37$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 37$	$-1$	$1$	$5$	$2$	1608				$C_{12}$			$C_{12}$	$2^{7} \cdot 3^{4} \cdot 5 \cdot 11^{3} \cdot 37$	$2^{2} \cdot 3$		$4000$	$111$	?	?	?	?	?	Non-Solvable - 5
5091840000.a	$\Unitary(4,4)$	$\Unitary(4,4)$	$2^{12} \cdot 3^{2} \cdot 5^{4} \cdot 13 \cdot 17$	$2^{2} \cdot 3 \cdot 5 \cdot 13 \cdot 17$	$-1$	$1$	$2$	$2$	470				$C_5$	$\SU(4,4)$	$\SU(4,4)$	$C_{5}$	$2^{16} \cdot 3^{2} \cdot 5^{3} \cdot 13 \cdot 17$	$2^{4}$		$330$	$51$	$102$	$204$	?	?	?	Non-Solvable - 2
11357822112.a	$\Unitary(3,13)$	$\Unitary(3,13)$	$2^{5} \cdot 3 \cdot 7^{3} \cdot 13^{3} \cdot 157$	$2^{3} \cdot 3 \cdot 7 \cdot 13 \cdot 157$	$-1$	$1$	$3$	$2$	2576				$C_{14}$			$C_{14}$	$2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13^{3} \cdot 157$	$2^{2} \cdot 3$		$2207$	?	?	?	?	?	?	Non-Solvable - 3
72746987520.a	$\Unitary(3,16)$	$\Unitary(3,16)$	$2^{12} \cdot 3 \cdot 5 \cdot 17^{3} \cdot 241$	$2^{2} \cdot 3 \cdot 5 \cdot 17 \cdot 241$	$-1$	$1$	$2$	$2$	4658				$C_{17}$			$C_{17}$	$2^{19} \cdot 3 \cdot 5 \cdot 17^{2} \cdot 241$	$2^{7}$		$4114$	?	?	?	?	?	?	Non-Solvable - 2
82771476480.a	$\Unitary(6,2)$	$\Unitary(6,2)$	$2^{15} \cdot 3^{8} \cdot 5 \cdot 7 \cdot 11$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11$	$-1$	$1$	$3$	$2$	324				$C_3$	$\PU(6,2)$	$\SU(6,2)$	$C_{3}$				$2016$	$21$	?	?	?	?	?	Non-Solvable - 3
125154626688.a	$\Unitary(3,17)$	$\Unitary(3,17)$	$2^{7} \cdot 3^{7} \cdot 7 \cdot 13 \cdot 17^{3}$	$2^{5} \cdot 3^{3} \cdot 7 \cdot 13 \cdot 17$	$-1$	$1$	$5$	$2$	5544				$C_{18}$			$C_{18}$	$2^{7} \cdot 3^{7} \cdot 7 \cdot 13 \cdot 17^{3}$	$2 \cdot 3^{2}$			?	?	?	?	?	?	Non-Solvable - 5
176904000000.a	$\Unitary(4,5)$	$\Unitary(4,5)$	$2^{9} \cdot 3^{5} \cdot 5^{6} \cdot 7 \cdot 13$	$2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$	$-1$	$1$	$4$	$2$	1002				$C_6$			$C_{6}$	$2^{11} \cdot 3^{4} \cdot 5^{6} \cdot 7 \cdot 13$	$2^{3}$			$104$	?	?	?	?	?	Non-Solvable - 4
338779728000.a	$\Unitary(3,19)$	$\Unitary(3,19)$	$2^{7} \cdot 3^{2} \cdot 5^{3} \cdot 7^{3} \cdot 19^{3}$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{3} \cdot 19$	$-1$	$1$	$4$	$2$	7640				$C_{20}$			$C_{20}$	$2^{9} \cdot 3^{2} \cdot 5^{2} \cdot 7^{3} \cdot 19^{3}$	$2^{4}$			?	?	?	?	?	?	Non-Solvable - 4
1032762286080.a	$\Unitary(5,3)$	$\Unitary(5,3)$	$2^{13} \cdot 3^{10} \cdot 5 \cdot 7 \cdot 61$	$2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 61$	$-1$	$1$	$3$	$2$	600				$C_4$			$C_{4}$	$2^{13} \cdot 3^{10} \cdot 5 \cdot 7 \cdot 61$	$2^{2}$		$2444$	$60$	?	?	?	?	?	Non-Solvable - 3
37298309529600.a	$\Unitary(4,7)$	$\Unitary(4,7)$	$2^{15} \cdot 3^{2} \cdot 5^{2} \cdot 7^{6} \cdot 43$	$2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 43$	$-1$	$1$	$6$	$2$	3320				$C_8$			$C_{8}$	$2^{16} \cdot 3^{2} \cdot 5^{2} \cdot 7^{6} \cdot 43$	$2^{4}$			?	?	?	?	?	?	Non-Solvable - 6
312244108001280.a	$\Unitary(4,8)$	$\Unitary(4,8)$	$2^{18} \cdot 3^{9} \cdot 5 \cdot 7^{2} \cdot 13 \cdot 19$	$2^{2} \cdot 3^{3} \cdot 5 \cdot 7 \cdot 13 \cdot 19$	$-1$	$1$	$3$	$2$	5418				$C_9$			$C_{9}$					?	?	?	?	?	?	Non-Solvable - 3
683361309818880.a	$\Unitary(7,2)$	$\Unitary(7,2)$	$2^{21} \cdot 3^{9} \cdot 5 \cdot 7 \cdot 11 \cdot 43$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 43$	$-1$	$1$	$2$	$2$	717				$C_3$	$\SU(7,2)$	$\SU(7,2)$	$C_{3}$	$2^{23} \cdot 3^{8} \cdot 5 \cdot 7 \cdot 11 \cdot 43$	$2^{2}$		$2712$	$42$	?	?	?	?	?	Non-Solvable - 2
1336098816000000.a	$\Unitary(5,4)$	$\Unitary(5,4)$	$2^{20} \cdot 3^{2} \cdot 5^{6} \cdot 13 \cdot 17 \cdot 41$	$2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \cdot 17 \cdot 41$	$-1$	$1$	$3$	$2$	1935				$C_5$			$C_{5}$	$2^{22} \cdot 3^{2} \cdot 5^{6} \cdot 13 \cdot 17 \cdot 41$	$2^{2} \cdot 5$			?	?	?	?	?	?	Non-Solvable - 3
182699779456696320.a	$\Unitary(6,3)$	$\Unitary(6,3)$	$2^{16} \cdot 3^{15} \cdot 5 \cdot 7^{2} \cdot 13 \cdot 61$	$2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \cdot 61$	$-1$	$1$	$4$	$2$	1888				$C_4$			$C_{4}$	$2^{17} \cdot 3^{15} \cdot 5 \cdot 7^{2} \cdot 13 \cdot 61$	$2^{3}$			?	?	?	?	?	?	Non-Solvable - 4
22304913152488243200.a	$\Unitary(8,2)$	$\Unitary(8,2)$	$2^{28} \cdot 3^{10} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 17 \cdot 43$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 17 \cdot 43$	$-1$	$1$	$2$	$2$	1560				$C_3$			$C_{3}$	$2^{30} \cdot 3^{9} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 17 \cdot 43$	$2^{2}$			?	?	?	?	?	?	Non-Solvable - 2

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