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Order Exponent Nilpotency class Nilpotent
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Results (24 matches)

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Label Name Family name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
6.1 $S_3$ $\Orth(3,2)$ $2 \cdot 3$ $2 \cdot 3$ 3 $C_1$ $S_3$ $C_3$ $C_{2}$ Solvable - 2
48.48 $C_2\times S_4$ $\Orth(3,3)$ $2^{4} \cdot 3$ $2^{2} \cdot 3$ 10 $C_2$ $S_4$ $A_4$ $C_{2}^{2}$ Solvable - 3
60.5 $A_5$ $\Orth(3,4)$ $2^{2} \cdot 3 \cdot 5$ $2 \cdot 3 \cdot 5$ 5 $C_1$ $A_5$ $A_5$ $C_1$ Simple
240.189 $C_2\times S_5$ $\Orth(3,5)$ $2^{4} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 14 $C_2$ $S_5$ $A_5$ $C_{2}^{2}$ Non-Solvable - 3
504.156 $\SL(2,8)$ $\Orth(3,8)$ $2^{3} \cdot 3^{2} \cdot 7$ $2 \cdot 3^{2} \cdot 7$ 9 $C_1$ $\SL(2,8)$ $\SL(2,8)$ $C_1$ Simple
672.1254 $C_2\times \PGL(2,7)$ $\Orth(3,7)$ $2^{5} \cdot 3 \cdot 7$ $2^{3} \cdot 3 \cdot 7$ 18 $C_2$ $\PGL(2,7)$ $\PSL(2,7)$ $C_{2}^{2}$ Non-Solvable - 3
720.763 $S_6$ $\Orth(5,2)$ $2^{4} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 11 $C_1$ $S_6$ $A_6$ $C_{2}$ Non-Solvable - 2
1440.5843 $C_2\times \PGL(2,9)$ $\Orth(3,9)$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{3} \cdot 3 \cdot 5$ 22 $C_2$ $\PGL(2,9)$ $A_6$ $C_{2}^{2}$ Non-Solvable - 3
2640.a $C_2\times \PGL(2,11)$ $\Orth(3,11)$ $2^{4} \cdot 3 \cdot 5 \cdot 11$ $2^{2} \cdot 3 \cdot 5 \cdot 11$ 26 $C_2$ $\PGL(2,11)$ $\PSL(2,11)$ $C_{2}^{2}$ Non-Solvable - 3
4080.a $\SL(2,16)$ $\Orth(3,16)$ $2^{4} \cdot 3 \cdot 5 \cdot 17$ $2 \cdot 3 \cdot 5 \cdot 17$ 17 $C_1$ $\SL(2,16)$ $\SL(2,16)$ $C_1$ Simple
4368.a $C_2\times \PGL(2,13)$ $\Orth(3,13)$ $2^{4} \cdot 3 \cdot 7 \cdot 13$ $2^{2} \cdot 3 \cdot 7 \cdot 13$ 30 $C_2$ $\PGL(2,13)$ $\PSL(2,13)$ $C_{2}^{2}$ Non-Solvable - 3
9792.a $C_2\times \PGL(2,17)$ $\Orth(3,17)$ $2^{6} \cdot 3^{2} \cdot 17$ $2^{4} \cdot 3^{2} \cdot 17$ 38 $C_2$ $\PGL(2,17)$ $\PSL(2,17)$ $C_{2}^{2}$ Non-Solvable - 3
13680.a $C_2\times \PGL(2,19)$ $\Orth(3,19)$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 19$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 19$ 42 $C_2$ $C_{2}^{2}$ Non-Solvable - 3
24288.a $C_2\times \PGL(2,23)$ $\Orth(3,23)$ $2^{5} \cdot 3 \cdot 11 \cdot 23$ $2^{3} \cdot 3 \cdot 11 \cdot 23$ 50 $C_2$ $\PGL(2,23)$ $\PSL(2,23)$ $C_{2}^{2}$ Non-Solvable - 3
103680.a $C_2\times \SO(5,3)$ $\Orth(5,3)$ $2^{8} \cdot 3^{4} \cdot 5$ $2^{3} \cdot 3^{2} \cdot 5$ 50 $C_2$ $\SO(5,3)$ $\SU(4,2)$ $C_{2}^{2}$ Non-Solvable - 3
979200.a $\Sp(4,4)$ $\Orth(5,4)$ $2^{8} \cdot 3^{2} \cdot 5^{2} \cdot 17$ $2^{2} \cdot 3 \cdot 5 \cdot 17$ 27 $C_1$ $\Sp(4,4)$ $\Sp(4,4)$ $C_1$ Simple
1451520.a $\Sp(6,2)$ $\Orth(7,2)$ $2^{9} \cdot 3^{4} \cdot 5 \cdot 7$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ 30 $C_1$ $\Sp(6,2)$ $\Sp(6,2)$ $C_1$ Simple
18720000.a $\Orth(5,5)$ $\Orth(5,5)$ $2^{8} \cdot 3^{2} \cdot 5^{4} \cdot 13$ $2^{3} \cdot 3 \cdot 5 \cdot 13$ 94 $C_2$ $\SO(5,5)$ $\PSp(4,5)$ $C_{2}^{2}$ Non-Solvable - 3
553190400.a $\Orth(5,7)$ $\Orth(5,7)$ $2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 7^{4}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ 154 $C_2$ $\SO(5,7)$ $\PSp(4,7)$ $C_{2}^{2}$ Non-Solvable - 3
1056706560.a $\Sp(4,8)$ $\Orth(5,8)$ $2^{12} \cdot 3^{4} \cdot 5 \cdot 7^{2} \cdot 13$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ 83 $C_1$ $\Sp(4,8)$ $\Sp(4,8)$ $C_1$ Simple
18341406720.a $\Orth(7,3)$ $\Orth(7,3)$ $2^{11} \cdot 3^{9} \cdot 5 \cdot 7 \cdot 13$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ 196 $C_2$ $\SO(7,3)$ $\Omega(7,3)$ $C_{2}^{2}$ Non-Solvable - 3
47377612800.a $\Sp(8,2)$ $\Orth(9,2)$ $2^{16} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 17$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17$ 81 $C_1$ $\Sp(8,2)$ $\Sp(8,2)$ $C_1$ Simple
4106059776000.a $\Sp(6,4)$ $\Orth(7,4)$ $2^{18} \cdot 3^{4} \cdot 5^{3} \cdot 7 \cdot 13 \cdot 17$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \cdot 17$ 120 $C_1$ $\Sp(6,4)$ $\Sp(6,4)$ $C_1$ Simple
263139026617958400.a $\Orth(9,3)$ $\Orth(9,3)$ $2^{16} \cdot 3^{16} \cdot 5^{2} \cdot 7 \cdot 13 \cdot 41$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \cdot 41$ 728 $C_2$ $C_{2}^{2}$ Non-Solvable - 3
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