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Order Exponent Nilpotency class Nilpotent
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Results (26 matches)

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Label Name Family name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
24.12 $S_4$ $\ASL(2,2)$ $2^{3} \cdot 3$ $2^{2} \cdot 3$ 5 $C_1$ $S_4$ $A_4$ $C_{2}$ Solvable - 3
216.153 $\PU(3,2)$ $\ASL(2,3)$ $2^{3} \cdot 3^{3}$ $2^{2} \cdot 3$ 10 $C_1$ $\PU(3,2)$ $\PSU(3,2)$ $C_{3}$ Solvable - 4
960.11357 $C_2^4:A_5$ $\ASL(2,4)$ $2^{6} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 9 $C_1$ $C_2^4:A_5$ $C_2^4:A_5$ $C_1$ Non-Solvable - 5
1344.11686 $C_2^3:\GL(3,2)$ $\ASL(3,2)$ $2^{6} \cdot 3 \cdot 7$ $2^{2} \cdot 3 \cdot 7$ 11 $C_1$ $C_2^3:\GL(3,2)$ $C_2^3:\GL(3,2)$ $C_1$ Non-Solvable - 4
3000.a $C_5^2.\SL(2,5)$ $\ASL(2,5)$ $2^{3} \cdot 3 \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ 14 $C_1$ $C_5^2.\SL(2,5)$ $C_5^2.\SL(2,5)$ $C_1$ Non-Solvable - 4
16464.a $C_7^2.\SL(2,7)$ $\ASL(2,7)$ $2^{4} \cdot 3 \cdot 7^{3}$ $2^{3} \cdot 3 \cdot 7$ 18 $C_1$ $C_7^2.\SL(2,7)$ $C_7^2.\SL(2,7)$ $C_1$ Non-Solvable - 4
32256.a $C_2^6.\SL(2,8)$ $\ASL(2,8)$ $2^{9} \cdot 3^{2} \cdot 7$ $2^{2} \cdot 3^{2} \cdot 7$ 17 $C_1$ $C_2^6.\SL(2,8)$ $C_2^6.\SL(2,8)$ $C_1$ Non-Solvable - 7
58320.a $C_3^4.\SL(2,9)$ $\ASL(2,9)$ $2^{4} \cdot 3^{6} \cdot 5$ $2^{3} \cdot 3 \cdot 5$ 22 $C_1$ $C_3^4.\SL(2,9)$ $C_3^4.\SL(2,9)$ $C_1$ Non-Solvable - 6
151632.a $C_3^3.\SL(3,3)$ $\ASL(3,3)$ $2^{4} \cdot 3^{6} \cdot 13$ $2^{3} \cdot 3^{2} \cdot 13$ 22 $C_1$ $C_3^3.\SL(3,3)$ $C_3^3.\SL(3,3)$ $C_1$ Non-Solvable - 4
159720.a $C_{11}^2.\SL(2,11)$ $\ASL(2,11)$ $2^{3} \cdot 3 \cdot 5 \cdot 11^{3}$ $2^{2} \cdot 3 \cdot 5 \cdot 11$ 26 $C_1$ $C_{11}^2.\SL(2,11)$ $C_{11}^2.\SL(2,11)$ $C_1$ Non-Solvable - 4
322560.a $C_2^4.A_8$ $\ASL(4,2)$ $2^{10} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ 25 $C_1$ $C_2^4.A_8$ $C_2^4.A_8$ $C_1$ Non-Solvable - 5
369096.a $C_{13}^2.\SL(2,13)$ $\ASL(2,13)$ $2^{3} \cdot 3 \cdot 7 \cdot 13^{3}$ $2^{2} \cdot 3 \cdot 7 \cdot 13$ 30 $C_1$ $C_{13}^2.\SL(2,13)$ $C_{13}^2.\SL(2,13)$ $C_1$ Non-Solvable - 4
1044480.a $C_2^8.\SL(2,16)$ $\ASL(2,16)$ $2^{12} \cdot 3 \cdot 5 \cdot 17$ $2^{2} \cdot 3 \cdot 5 \cdot 17$ 33 $C_1$ $C_2^8.\SL(2,16)$ $C_2^8.\SL(2,16)$ $C_1$ Non-Solvable - 9
1414944.a $C_{17}^2.\SL(2,17)$ $\ASL(2,17)$ $2^{5} \cdot 3^{2} \cdot 17^{3}$ $2^{4} \cdot 3^{2} \cdot 17$ 38 $C_1$ $C_{17}^2.\SL(2,17)$ $C_{17}^2.\SL(2,17)$ $C_1$ Non-Solvable - 4
2469240.a $C_{19}^2.\SL(2,19)$ $\ASL(2,19)$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 19^{3}$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 19$ 42 $C_1$ $C_{19}^2.\SL(2,19)$ $C_{19}^2.\SL(2,19)$ $C_1$ Non-Solvable - 4
3870720.a $C_2^6.\SL(3,4)$ $\ASL(3,4)$ $2^{12} \cdot 3^{3} \cdot 5 \cdot 7$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ 37 $C_1$ $C_2^6.\SL(3,4)$ $C_2^6.\SL(3,4)$ $C_1$ Non-Solvable - 8
46500000.a $C_5^3.\PSL(3,5)$ $\ASL(3,5)$ $2^{5} \cdot 3 \cdot 5^{6} \cdot 31$ $2^{3} \cdot 3 \cdot 5 \cdot 31$ 44 $C_1$ $C_5^3.\PSL(3,5)$ $C_5^3.\PSL(3,5)$ $C_1$ Non-Solvable - 4
319979520.a $C_2^5.\GL(5,2)$ $\ASL(5,2)$ $2^{15} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 31$ $2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 31$ 52 $C_1$ $C_2^5.\GL(5,2)$ $C_2^5.\GL(5,2)$ $C_1$ Non-Solvable - 6
982575360.a $\ASL(4,3)$ $\ASL(4,3)$ $2^{8} \cdot 3^{10} \cdot 5 \cdot 13$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 13$ 73 $C_1$ $\ASL(4,3)$ $\ASL(4,3)$ $C_1$ Non-Solvable - 6
1931325984.a $\ASL(3,7)$ $\ASL(3,7)$ $2^{5} \cdot 3^{3} \cdot 7^{6} \cdot 19$ $2^{4} \cdot 3 \cdot 7 \cdot 19$ 82 $C_1$ $\ASL(3,7)$ $\ASL(3,7)$ $C_1$ Non-Solvable - 5
8439201792.a $C_2^9.\SL(3,8)$ $\ASL(3,8)$ $2^{18} \cdot 3^{2} \cdot 7^{2} \cdot 73$ $2^{2} \cdot 3^{2} \cdot 7 \cdot 73$ 89 $C_1$ $C_2^9.\SL(3,8)$ $C_2^9.\SL(3,8)$ $C_1$ Non-Solvable - 10
252680601600.a $C_2^8.\PSL(4,4)$ $\ASL(4,4)$ $2^{20} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 17$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17$ 121 $C_1$ $C_2^8.\PSL(4,4)$ $C_2^8.\PSL(4,4)$ $C_1$ Non-Solvable - 9
1290157424640.a $C_2^6.\GL(6,2)$ $\ASL(6,2)$ $2^{21} \cdot 3^{4} \cdot 5 \cdot 7^{2} \cdot 31$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 31$ 112 $C_1$ $C_2^6.\GL(6,2)$ $C_2^6.\GL(6,2)$ $C_1$ Non-Solvable - 7
18135000000000.a $\ASL(4,5)$ $\ASL(4,5)$ $2^{9} \cdot 3^{2} \cdot 5^{10} \cdot 13 \cdot 31$ $2^{3} \cdot 3 \cdot 5 \cdot 13 \cdot 31$ 229 $C_1$ $C_1$ Non-Solvable - 7
57781326620160.a $C_3^5.\SL(5,3)$ $\ASL(5,3)$ $2^{9} \cdot 3^{15} \cdot 5 \cdot 11^{2} \cdot 13$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 13$ 189 $C_1$ $C_3^5.\SL(5,3)$ $C_3^5.\SL(5,3)$ $C_1$ Non-Solvable - 6
30665243413238353920.a $\ASL(6,3)$ $\ASL(6,3)$ $2^{12} \cdot 3^{21} \cdot 5 \cdot 7 \cdot 11^{2} \cdot 13^{2}$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} \cdot 13$ 585 $C_1$ $C_1$ Non-Solvable - 8
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