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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 (14 matches)

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Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
7920.a $M_{11}$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 11$ $2^{3} \cdot 3 \cdot 5 \cdot 11$ 10 $C_1$ $M_{11}$ $M_{11}$ $C_1$ Simple
95040.a $M_{12}$ $2^{6} \cdot 3^{3} \cdot 5 \cdot 11$ $2^{3} \cdot 3 \cdot 5 \cdot 11$ 15 $C_1$ $M_{12}$ $M_{12}$ $C_1$ Simple
175560.a $J_1$ $2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 19$ $2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 19$ 15 $C_1$ $J_1$ $J_1$ $C_1$ Simple
443520.a $M_{22}$ $2^{7} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11$ $2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11$ 12 $C_1$ $M_{22}$ $M_{22}$ $C_1$ Simple
604800.a $J_2$ $2^{7} \cdot 3^{3} \cdot 5^{2} \cdot 7$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ 21 $C_1$ $J_2$ $J_2$ $C_1$ Simple
10200960.a $M_{23}$ $2^{7} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 23$ $2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 23$ 17 $C_1$ $M_{23}$ $M_{23}$ $C_1$ Simple
44352000.a $\HS$ $2^{9} \cdot 3^{2} \cdot 5^{3} \cdot 7 \cdot 11$ $2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11$ 24 $C_1$ $\HS$ $\HS$ $C_1$ Simple
50232960.a $J_3$ $2^{7} \cdot 3^{5} \cdot 5 \cdot 17 \cdot 19$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 17 \cdot 19$ 21 $C_1$ $J_3$ $J_3$ $C_1$ Simple
244823040.a $M_{24}$ $2^{10} \cdot 3^{3} \cdot 5 \cdot 7 \cdot 11 \cdot 23$ $2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 23$ 26 $C_1$ $M_{24}$ $M_{24}$ $C_1$ Simple
898128000.a $\McL$ $2^{7} \cdot 3^{6} \cdot 5^{3} \cdot 7 \cdot 11$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11$ 24 $C_1$ $\McL$ $\McL$ $C_1$ Simple
4030387200.a $\He$ $2^{10} \cdot 3^{3} \cdot 5^{2} \cdot 7^{3} \cdot 17$ $2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 17$ 33 $C_1$ $\He$ $\He$ $C_1$ Simple
145926144000.a $\Ru$ $2^{14} \cdot 3^{3} \cdot 5^{3} \cdot 7 \cdot 13 \cdot 29$ $2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 29$ 36 $C_1$ $\Ru$ $\Ru$ $C_1$ Simple
495766656000.a $\Co_3$ $2^{10} \cdot 3^{7} \cdot 5^{3} \cdot 7 \cdot 11 \cdot 23$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 23$ not computed $C_1$ $\Co_3$ $\Co_3$ $C_1$ Simple
42305421312000.a $\Co_2$ $2^{18} \cdot 3^{6} \cdot 5^{3} \cdot 7 \cdot 11 \cdot 23$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 23$ 60 $C_1$ $\Co_2$ $\Co_2$ $C_1$ Simple
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