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Order Exponent Nilpotency class Nilpotent
Center Commutator Central quotient Abelianization
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Perfect Direct product Semidirect product Wreath product
Automorphism group Automorphisms Min. transitive degree Min. permutation degree
Number of subgroups Num. of normal subs Num. of conj. classes
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Min. degree of $\C$-irrep Min. degree of $\Q$-irrep Min. degree of $\C$-rep Min. degree of $\Q$-rep
Outer aut. group Outer automorphisms Metabelian Metacyclic
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Results (15 matches)

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Label Name Family name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
720.763 $S_6$ $\Spin(5,2)$ $2^{4} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 11 $C_1$ $S_6$ $A_6$ $C_{2}$ Non-Solvable - 2
51840.a $\Sp(4,3)$ $\Spin(5,3)$ $2^{7} \cdot 3^{4} \cdot 5$ $2^{3} \cdot 3^{2} \cdot 5$ 34 $C_2$ $\SU(4,2)$ $\Sp(4,3)$ $C_1$ Non-Solvable - 2
979200.a $\Sp(4,4)$ $\Spin(5,4)$ $2^{8} \cdot 3^{2} \cdot 5^{2} \cdot 17$ $2^{2} \cdot 3 \cdot 5 \cdot 17$ 27 $C_1$ $\Sp(4,4)$ $\Sp(4,4)$ $C_1$ Simple
1451520.a $\Sp(6,2)$ $\Spin(7,2)$ $2^{9} \cdot 3^{4} \cdot 5 \cdot 7$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ 30 $C_1$ $\Sp(6,2)$ $\Sp(6,2)$ $C_1$ Simple
9360000.a $\Sp(4,5)$ $\Spin(5,5)$ $2^{7} \cdot 3^{2} \cdot 5^{4} \cdot 13$ $2^{3} \cdot 3 \cdot 5 \cdot 13$ 60 $C_2$ $\PSp(4,5)$ $\Sp(4,5)$ $C_1$ Non-Solvable - 2
276595200.a $\Sp(4,7)$ $\Spin(5,7)$ $2^{9} \cdot 3^{2} \cdot 5^{2} \cdot 7^{4}$ $2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ 94 $C_2$ $\PSp(4,7)$ $\Sp(4,7)$ $C_1$ Non-Solvable - 2
1056706560.a $\Sp(4,8)$ $\Spin(5,8)$ $2^{12} \cdot 3^{4} \cdot 5 \cdot 7^{2} \cdot 13$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ 83 $C_1$ $\Sp(4,8)$ $\Sp(4,8)$ $C_1$ Simple
3443212800.a $\Sp(4,9)$ $\Spin(5,9)$ $2^{9} \cdot 3^{8} \cdot 5^{2} \cdot 41$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 41$ 136 $C_2$ $\PSp(4,9)$ $\Sp(4,9)$ $C_1$ Non-Solvable - 2
9170703360.c $\Spin(7,3)$ $\Spin(7,3)$ $2^{10} \cdot 3^{9} \cdot 5 \cdot 7 \cdot 13$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ 88 $C_2$ $\Omega(7,3)$ $\Spin(7,3)$ $C_1$ Non-Solvable - 2
25721308800.a $\Sp(4,11)$ $\Spin(5,11)$ $2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 11^{4} \cdot 61$ $2^{3} \cdot 3 \cdot 5 \cdot 11 \cdot 61$ 186 $C_2$ $\PSp(4,11)$ $\Sp(4,11)$ $C_1$ Non-Solvable - 2
137037962880.a $\Sp(4,13)$ $\Spin(5,13)$ $2^{7} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13^{4} \cdot 17$ $2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17$ 244 $C_2$ $C_1$ Non-Solvable - 2
1095199948800.a $\Sp(4,16)$ $\Spin(5,16)$ $2^{16} \cdot 3^{2} \cdot 5^{2} \cdot 17^{2} \cdot 257$ $2^{2} \cdot 3 \cdot 5 \cdot 17 \cdot 257$ 291 $C_1$ $\Sp(4,16)$ $\Sp(4,16)$ $C_1$ Simple
2008994088960.a $\Sp(4,17)$ $\Spin(5,17)$ $2^{11} \cdot 3^{4} \cdot 5 \cdot 17^{4} \cdot 29$ $2^{5} \cdot 3^{2} \cdot 5 \cdot 17 \cdot 29$ 384 $C_2$ $C_1$ Non-Solvable - 2
4106059776000.a $\Sp(6,4)$ $\Spin(7,4)$ $2^{18} \cdot 3^{4} \cdot 5^{3} \cdot 7 \cdot 13 \cdot 17$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \cdot 17$ 120 $C_1$ $\Sp(6,4)$ $\Sp(6,4)$ $C_1$ Simple
6114035779200.a $\Sp(4,19)$ $\Spin(5,19)$ $2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 19^{4} \cdot 181$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 19 \cdot 181$ 466 $C_2$ $C_1$ Non-Solvable - 2
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