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	$C_3\times S_3$	$\GUnitary(2,2)$	$2 \cdot 3^{2}$	$2 \cdot 3$	$-1$	$2$	$3$	$2$	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
192.963	$\GL(2,3):C_4$	$\GUnitary(2,3)$	$2^{6} \cdot 3$	$2^{3} \cdot 3$	$-1$	$4$	$7$	$2$	32	$215$	$64$	$15$	$C_8$	$S_4$	$\SL(2,3)$	$C_{2} \times C_{4}$	$2^{6} \cdot 3$	$2^{3}$	$32$	$32$	$2$	$4$	$8$	$2$	$4$	$8$	Solvable - 4
648.533	$\Unitary(3,2)$	$\GUnitary(3,2)$	$2^{3} \cdot 3^{4}$	$2^{2} \cdot 3^{2}$	$-1$	$5$	$7$	$2$	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
900.88	$C_{15}\times A_5$	$\GUnitary(2,4)$	$2^{2} \cdot 3^{2} \cdot 5^{2}$	$2 \cdot 3 \cdot 5$	$-1$	$1$	$3$	$2$	75	$344$	$46$	$8$	$C_{15}$	$A_5$	$A_5$	$C_{15}$	$2^{6} \cdot 3 \cdot 5$	$2^{4}$	$75$	$13$	$3$	$6$	$24$	$3$	$5$	$10$	Non-Solvable - 3
2880.b	$C_{24}.S_5$	$\GUnitary(2,5)$	$2^{6} \cdot 3^{2} \cdot 5$	$2^{3} \cdot 3 \cdot 5$	$-1$	$1$	$6$	$2$	144				$C_{24}$	$S_5$	$\SL(2,5)$	$C_{2} \times C_{12}$	$2^{7} \cdot 3 \cdot 5$	$2^{4}$		$51$	$4$	$8$	$32$	?	?	?	Non-Solvable - 6
16128.a	$\GL(2,7):C_8$	$\GUnitary(2,7)$	$2^{8} \cdot 3^{2} \cdot 7$	$2^{4} \cdot 3 \cdot 7$	$-1$	$1$	$7$	$2$	384	$10000$	$424$	$32$	$C_{48}$	$\PGL(2,7)$	$\SL(2,7)$	$C_{2} \times C_{24}$	$2^{9} \cdot 3 \cdot 7$	$2^{5}$	$384$	$131$	$6$	$12$	$96$	$6$	$12$	$50$	Non-Solvable - 7
31752.a	$C_9\times \GL(2,8)$	$\GUnitary(2,8)$	$2^{3} \cdot 3^{4} \cdot 7^{2}$	$2 \cdot 3^{2} \cdot 7$	$-1$	$1$	$4$	$2$	567	$3910$	$113$	$12$	$C_{63}$	$\SL(2,8)$	$\SL(2,8)$	$C_{63}$	$2^{5} \cdot 3^{5} \cdot 7$	$2^{2} \cdot 3^{3}$	$567$	$25$	$7$	?	$252$	?	?	?	Non-Solvable - 4
48384.a	$C_8\times \SU(3,3)$	$\GUnitary(3,3)$	$2^{8} \cdot 3^{3} \cdot 7$	$2^{3} \cdot 3 \cdot 7$	$-1$	$1$	$4$	$2$	112	$52058$	$304$	$8$	$C_8$	$\SU(3,3)$	$\SU(3,3)$	$C_{8}$	$2^{8} \cdot 3^{3} \cdot 7$	$2^{3}$	$224$	$36$	$6$	$12$	$24$	$6$	$9$	$11$	Non-Solvable - 4
57600.b	$\GL(2,9):C_{10}$	$\GUnitary(2,9)$	$2^{8} \cdot 3^{2} \cdot 5^{2}$	$2^{4} \cdot 3 \cdot 5$	$-1$	$1$	$7$	$2$	800	$21152$	$490$	$32$	$C_{80}$	$\PGL(2,9)$	$\SL(2,9)$	$C_{2} \times C_{40}$	$2^{11} \cdot 3^{2} \cdot 5$	$2^{7}$	$800$	$165$	$8$	?	$256$	?	?	?	Non-Solvable - 7
77760.a	$\Unitary(4,2)$	$\GUnitary(4,2)$	$2^{6} \cdot 3^{5} \cdot 5$	$2^{2} \cdot 3^{2} \cdot 5$	$-1$	$1$	$2$	$2$	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
158400.a	$\GL(2,11):C_{12}$	$\GUnitary(2,11)$	$2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 11$	$2^{3} \cdot 3 \cdot 5 \cdot 11$	$-1$	$1$	$7$	$2$	1440	$61076$	$862$	$48$	$C_{120}$	$\PGL(2,11)$	$\SL(2,11)$	$C_{2} \times C_{60}$	$2^{9} \cdot 3 \cdot 5 \cdot 11$	$2^{6}$	$1440$	$104$	$10$	?	?	?	?	?	Non-Solvable - 7
366912.a	$\GUnitary(2,13)$	$\GUnitary(2,13)$	$2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13$	$2^{3} \cdot 3 \cdot 7 \cdot 13$	$-1$	$1$	$7$	$2$	2352	$96356$	$960$	$48$	$C_{168}$	$\PGL(2,13)$	$\SL(2,13)$	$C_{2} \times C_{84}$	$2^{8} \cdot 3^{2} \cdot 7 \cdot 13$	$2^{5} \cdot 3$	$2352$	$122$	$12$	?	?	?	?	?	Non-Solvable - 7
936000.a	$C_{15}\times \SU(3,4)$	$\GUnitary(3,4)$	$2^{6} \cdot 3^{2} \cdot 5^{3} \cdot 13$	$2^{2} \cdot 3 \cdot 5 \cdot 13$	$-1$	$1$	$3$	$2$	330	$308900$	$282$	$8$	$C_{15}$	$\SU(3,4)$	$\SU(3,4)$	$C_{15}$	$2^{11} \cdot 3 \cdot 5^{2} \cdot 13$	$2^{5}$	$975$	$73$	$12$	$24$	$96$	?	?	?	Non-Solvable - 3
1040400.a	$C_{255}\times \SL(2,16)$	$\GUnitary(2,16)$	$2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 17^{2}$	$2 \cdot 3 \cdot 5 \cdot 17$	$-1$	$1$	$4$	$2$	4335	$47832$	$304$	$16$	$C_{255}$	$\SL(2,16)$	$\SL(2,16)$	$C_{255}$	$2^{13} \cdot 3 \cdot 5 \cdot 17$	$2^{9}$	$4335$	$42$	?	?	?	?	?	?	Non-Solvable - 4
1410048.a	$\GL(2,17).C_{18}$	$\GUnitary(2,17)$	$2^{10} \cdot 3^{4} \cdot 17$	$2^{5} \cdot 3^{2} \cdot 17$	$-1$	$1$	$9$	$2$	5184			$60$	$C_{288}$	$\PGL(2,17)$	$\SL(2,17)$	$C_{2} \times C_{144}$	$2^{11} \cdot 3^{3} \cdot 17$	$2^{6} \cdot 3$	$5184$	$585$	?	?	?	?	?	?	Non-Solvable - 9
2462400.a	$\GL(2,19).C_{20}$	$\GUnitary(2,19)$	$2^{6} \cdot 3^{4} \cdot 5^{2} \cdot 19$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$	$-1$	$1$	$8$	$2$	7200			$72$	$C_{360}$	$\PGL(2,19)$	$\SL(2,19)$	$C_{2} \times C_{180}$	$2^{9} \cdot 3^{3} \cdot 5 \cdot 19$	$2^{6} \cdot 3$	$7200$	$174$	?	?	?	?	?	?	Non-Solvable - 8
6412032.a	$\GL(2,23).C_{24}$	$\GUnitary(2,23)$	$2^{8} \cdot 3^{2} \cdot 11^{2} \cdot 23$	$2^{4} \cdot 3 \cdot 11 \cdot 23$	$-1$	$1$	$8$	$2$	12672			$64$	$C_{528}$	$\PGL(2,23)$	$\SL(2,23)$	$C_{2} \times C_{264}$	$2^{10} \cdot 3 \cdot 5 \cdot 11 \cdot 23$	$2^{6} \cdot 5$	$12672$	$398$	?	?	?	?	?	?	Non-Solvable - 8
9072000.a	$\GUnitary(3,5)$	$\GUnitary(3,5)$	$2^{7} \cdot 3^{4} \cdot 5^{3} \cdot 7$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 7$	$-1$	$1$	$6$	$2$	768			$16$	$C_{24}$	$\PU(3,5)$	$\SU(3,5)$	$C_{24}$	$2^{7} \cdot 3^{4} \cdot 5^{3} \cdot 7$	$2^{3} \cdot 3$	$3024$	$386$	$21$	?	$168$	?	?	?	Non-Solvable - 6
9734400.a	$\GL(2,25).C_{26}$	$\GUnitary(2,25)$	$2^{8} \cdot 3^{2} \cdot 5^{2} \cdot 13^{2}$	$2^{4} \cdot 3 \cdot 5 \cdot 13$	$-1$	$1$	$8$	$2$	16224			$64$	$C_{624}$	$\PGL(2,25)$	$\SL(2,25)$	$C_{2} \times C_{312}$	$2^{12} \cdot 3^{2} \cdot 5^{2} \cdot 13$	$2^{8} \cdot 3$		$432$	?	?	?	?	?	?	Non-Solvable - 8
14309568.a	$\GL(2,27).C_{28}$	$\GUnitary(2,27)$	$2^{6} \cdot 3^{3} \cdot 7^{2} \cdot 13^{2}$	$2^{3} \cdot 3 \cdot 7 \cdot 13$	$-1$	$1$	$7$	$2$	20384			$48$	$C_{728}$	$\PGL(2,27)$	$\SL(2,27)$	$C_{2} \times C_{364}$	$2^{9} \cdot 3^{6} \cdot 7 \cdot 13$	$2^{6} \cdot 3^{3}$	$20384$	$244$	?	?	?	?	?	?	Non-Solvable - 7
20462400.a	$\GL(2,29).C_{30}$	$\GUnitary(2,29)$	$2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 29$	$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 29$	$-1$	$1$	$8$	$2$	25200			$96$	$C_{840}$	$\PGL(2,29)$	$\SL(2,29)$	$C_{2} \times C_{420}$	$2^{10} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 29$	$2^{7} \cdot 3$		$255$	?	?	?	?	?	?	Non-Solvable - 8
28569600.a	$\GUnitary(2,31)$	$\GUnitary(2,31)$	$2^{12} \cdot 3^{2} \cdot 5^{2} \cdot 31$	$2^{6} \cdot 3 \cdot 5 \cdot 31$	$-1$	$1$	$10$	$2$	30720				$C_{960}$	$\PGL(2,31)$	$\SL(2,31)$	$C_{2} \times C_{480}$	$2^{15} \cdot 3 \cdot 5 \cdot 31$	$2^{9}$		$2056$	?	?	?	?	?	?	Non-Solvable - 10
33488928.a	$C_{1023}\times \SL(2,32)$	$\GUnitary(2,32)$	$2^{5} \cdot 3^{2} \cdot 11^{2} \cdot 31^{2}$	$2 \cdot 3 \cdot 11 \cdot 31$	$-1$	$1$	$4$	$2$	33759	$313400$	$440$	$16$	$C_{1023}$	$\SL(2,32)$	$\SL(2,32)$	$C_{1023}$	$2^{8} \cdot 3^{2} \cdot 5^{3} \cdot 11 \cdot 31$	$2^{3} \cdot 3 \cdot 5^{3}$	$33759$	$78$	?	?	?	?	?	?	Non-Solvable - 4
41057280.a	$\Unitary(5,2)$	$\GUnitary(5,2)$	$2^{10} \cdot 3^{6} \cdot 5 \cdot 11$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 11$	$-1$	$1$	$2$	$2$	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
104509440.a	$\GUnitary(4,3)$	$\GUnitary(4,3)$	$2^{12} \cdot 3^{6} \cdot 5 \cdot 7$	$2^{4} \cdot 3^{2} \cdot 5 \cdot 7$	$-1$	$1$	$6$	$2$	376				$C_8$	$\PU(4,3)$	$\SU(4,3)$	$C_{2} \times C_{4}$	$2^{13} \cdot 3^{6} \cdot 5 \cdot 7$	$2^{4}$		$2240$	$20$	$40$	$80$	?	?	?	Non-Solvable - 6
271853568.a	$\GUnitary(3,7)$	$\GUnitary(3,7)$	$2^{11} \cdot 3^{2} \cdot 7^{3} \cdot 43$	$2^{4} \cdot 3 \cdot 7 \cdot 43$	$-1$	$1$	$6$	$2$	2784				$C_{48}$	$\SU(3,7)$	$\SU(3,7)$	$C_{48}$	$2^{12} \cdot 3 \cdot 7^{3} \cdot 43$	$2^{5}$		$363$	?	?	?	?	?	?	Non-Solvable - 6
1042481664.a	$\GUnitary(3,8)$	$\GUnitary(3,8)$	$2^{9} \cdot 3^{7} \cdot 7^{2} \cdot 19$	$2^{2} \cdot 3^{3} \cdot 7 \cdot 19$	$-1$	$1$	$5$	$2$	4662				$C_{63}$	$\PU(3,8)$	$\SU(3,8)$	$C_{63}$	$2^{11} \cdot 3^{9} \cdot 7 \cdot 19$	$2^{2} \cdot 3^{4}$		$4624$	?	?	?	?	?	?	Non-Solvable - 5
3405888000.a	$\GUnitary(3,9)$	$\GUnitary(3,9)$	$2^{9} \cdot 3^{6} \cdot 5^{3} \cdot 73$	$2^{4} \cdot 3 \cdot 5 \cdot 73$	$-1$	$1$	$6$	$2$	7360				$C_{80}$	$\SU(3,9)$	$\SU(3,9)$	$C_{80}$	$2^{12} \cdot 3^{6} \cdot 5^{2} \cdot 73$	$2^{7}$		$751$	?	?	?	?	?	?	Non-Solvable - 6
15275520000.a	$\GUnitary(4,4)$	$\GUnitary(4,4)$	$2^{12} \cdot 3^{3} \cdot 5^{4} \cdot 13 \cdot 17$	$2^{2} \cdot 3 \cdot 5 \cdot 13 \cdot 17$	$-1$	$1$	$3$	$2$	1410				$C_{15}$	$\SU(4,4)$	$\SU(4,4)$	$C_{15}$	$2^{17} \cdot 3^{2} \cdot 5^{3} \cdot 13 \cdot 17$	$2^{5}$		$333$	$51$	?	?	?	?	?	Non-Solvable - 3
25529644800.a	$\GUnitary(3,11)$	$\GUnitary(3,11)$	$2^{8} \cdot 3^{4} \cdot 5^{2} \cdot 11^{3} \cdot 37$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 37$	$-1$	$1$	$7$	$2$	16080				$C_{120}$			$C_{120}$	$2^{10} \cdot 3^{4} \cdot 5 \cdot 11^{3} \cdot 37$	$2^{5} \cdot 3$		$4009$	?	?	?	?	?	?	Non-Solvable - 7
82771476480.a	$\Unitary(6,2)$	$\GUnitary(6,2)$	$2^{15} \cdot 3^{8} \cdot 5 \cdot 7 \cdot 11$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11$	$-1$	$1$	$3$	$2$	324				$C_3$	$\PU(6,2)$	$\SU(6,2)$	$C_{3}$				$2016$	$21$	?	?	?	?	?	Non-Solvable - 3
136293865344.a	$\GUnitary(3,13)$	$\GUnitary(3,13)$	$2^{7} \cdot 3^{2} \cdot 7^{3} \cdot 13^{3} \cdot 157$	$2^{3} \cdot 3 \cdot 7 \cdot 13 \cdot 157$	$-1$	$1$	$6$	$2$	30912				$C_{168}$			$C_{168}$	$2^{9} \cdot 3^{2} \cdot 7^{2} \cdot 13^{3} \cdot 157$	$2^{5} \cdot 3$			?	?	?	?	?	?	Non-Solvable - 6
707616000000.a	$\GUnitary(4,5)$	$\GUnitary(4,5)$	$2^{11} \cdot 3^{5} \cdot 5^{6} \cdot 7 \cdot 13$	$2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$	$-1$	$1$	$6$	$2$	4008				$C_{24}$			$C_{2} \times C_{12}$	$2^{13} \cdot 3^{4} \cdot 5^{6} \cdot 7 \cdot 13$	$2^{5}$			?	?	?	?	?	?	Non-Solvable - 6
1091204812800.a	$\GUnitary(3,16)$	$\GUnitary(3,16)$	$2^{12} \cdot 3^{2} \cdot 5^{2} \cdot 17^{3} \cdot 241$	$2^{2} \cdot 3 \cdot 5 \cdot 17 \cdot 241$	$-1$	$1$	$4$	$2$	69870				$C_{255}$			$C_{255}$	$2^{22} \cdot 3 \cdot 5 \cdot 17^{2} \cdot 241$	$2^{10}$			?	?	?	?	?	?	Non-Solvable - 4
2002474027008.a	$\GUnitary(3,17)$	$\GUnitary(3,17)$	$2^{11} \cdot 3^{7} \cdot 7 \cdot 13 \cdot 17^{3}$	$2^{5} \cdot 3^{3} \cdot 7 \cdot 13 \cdot 17$	$-1$	$1$	$9$	$2$	88704				$C_{288}$			$C_{288}$	$2^{11} \cdot 3^{7} \cdot 7 \cdot 13 \cdot 17^{3}$	$2^{5} \cdot 3^{2}$			?	?	?	?	?	?	Non-Solvable - 9
2065524572160.a	$\GUnitary(5,3)$	$\GUnitary(5,3)$	$2^{14} \cdot 3^{10} \cdot 5 \cdot 7 \cdot 61$	$2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 61$	$-1$	$1$	$4$	$2$	1200				$C_8$	$\SU(5,3)$	$\SU(5,3)$	$C_{8}$	$2^{14} \cdot 3^{10} \cdot 5 \cdot 7 \cdot 61$	$2^{3}$		$2448$	$60$	?	?	?	?	?	Non-Solvable - 4
6098035104000.a	$\GUnitary(3,19)$	$\GUnitary(3,19)$	$2^{8} \cdot 3^{4} \cdot 5^{3} \cdot 7^{3} \cdot 19^{3}$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{3} \cdot 19$	$-1$	$1$	$7$	$2$	not computed				$C_{360}$			$C_{360}$					?	?	?	?	?	?	Non-Solvable - 7
223789857177600.a	$\GUnitary(4,7)$	$\GUnitary(4,7)$	$2^{16} \cdot 3^{3} \cdot 5^{2} \cdot 7^{6} \cdot 43$	$2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 43$	$-1$	$1$	$8$	$2$	19920				$C_{48}$			$C_{2} \times C_{24}$					?	?	?	?	?	?	Non-Solvable - 8
683361309818880.a	$\Unitary(7,2)$	$\GUnitary(7,2)$	$2^{21} \cdot 3^{9} \cdot 5 \cdot 7 \cdot 11 \cdot 43$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 43$	$-1$	$1$	$2$	$2$	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
2185708756008960.a	$\GUnitary(4,8)$	$\GUnitary(4,8)$	$2^{18} \cdot 3^{9} \cdot 5 \cdot 7^{3} \cdot 13 \cdot 19$	$2^{2} \cdot 3^{3} \cdot 5 \cdot 7 \cdot 13 \cdot 19$	$-1$	$1$	$4$	$2$	37926				$C_{63}$			$C_{63}$					?	?	?	?	?	?	Non-Solvable - 4
4008296448000000.a	$\GUnitary(5,4)$	$\GUnitary(5,4)$	$2^{20} \cdot 3^{3} \cdot 5^{6} \cdot 13 \cdot 17 \cdot 41$	$2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \cdot 17 \cdot 41$	$-1$	$1$	$4$	$2$	5805				$C_{15}$			$C_{15}$	$2^{23} \cdot 3^{2} \cdot 5^{6} \cdot 13 \cdot 17 \cdot 41$	$2^{3} \cdot 5$			?	?	?	?	?	?	Non-Solvable - 4
365399558913392640.a	$\GUnitary(6,3)$	$\GUnitary(6,3)$	$2^{17} \cdot 3^{15} \cdot 5 \cdot 7^{2} \cdot 13 \cdot 61$	$2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \cdot 61$	$-1$	$1$	$5$	$2$	3776				$C_8$			$C_{2} \times C_{4}$	$2^{18} \cdot 3^{15} \cdot 5 \cdot 7^{2} \cdot 13 \cdot 61$	$2^{4}$			?	?	?	?	?	?	Non-Solvable - 5
22304913152488243200.a	$\Unitary(8,2)$	$\GUnitary(8,2)$	$2^{28} \cdot 3^{10} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 17 \cdot 43$	$2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 17 \cdot 43$	$-1$	$1$	$2$	$2$	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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