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Order Exponent Nilpotency class Nilpotent
Center Commutator Central quotient Abelianization
Abelian Cyclic Solvable Simple
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 (17 matches)

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Label Name Family name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
36.10 $S_3^2$ $\POmegaPlus(4,2)$ $2^{2} \cdot 3^{2}$ $2 \cdot 3$ 9 $C_1$ $S_3^2$ $C_3^2$ $C_{2}^{2}$ Solvable - 2
144.184 $A_4^2$ $\POmegaPlus(4,3)$ $2^{4} \cdot 3^{2}$ $2 \cdot 3$ 16 $C_1$ $A_4^2$ $C_2^4$ $C_{3}^{2}$ Solvable - 2
3600.a $A_5^2$ $\POmegaPlus(4,4), \POmegaPlus(4,5)$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $2 \cdot 3 \cdot 5$ 25 $C_1$ $A_5^2$ $A_5^2$ $C_1$ Non-Solvable - 2
20160.a $A_8$ $\POmegaPlus(6,2)$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ 14 $C_1$ $A_8$ $A_8$ $C_1$ Simple
28224.a $\GL(3,2)^2$ $\POmegaPlus(4,7)$ $2^{6} \cdot 3^{2} \cdot 7^{2}$ $2^{2} \cdot 3 \cdot 7$ 36 $C_1$ $\GL(3,2)^2$ $\GL(3,2)^2$ $C_1$ Non-Solvable - 2
129600.a $A_6^2$ $\POmegaPlus(4,9)$ $2^{6} \cdot 3^{4} \cdot 5^{2}$ $2^{2} \cdot 3 \cdot 5$ 49 $C_1$ $A_6^2$ $A_6^2$ $C_1$ Non-Solvable - 2
254016.a $\SL(2,8)^2$ $\POmegaPlus(4,8)$ $2^{6} \cdot 3^{4} \cdot 7^{2}$ $2 \cdot 3^{2} \cdot 7$ 81 $C_1$ $\SL(2,8)^2$ $\SL(2,8)^2$ $C_1$ Non-Solvable - 2
435600.a $\PSL(2,11)^2$ $\POmegaPlus(4,11)$ $2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2}$ $2 \cdot 3 \cdot 5 \cdot 11$ 64 $C_1$ $\PSL(2,11)^2$ $\PSL(2,11)^2$ $C_1$ Non-Solvable - 2
1192464.a $\PSL(2,13)^2$ $\POmegaPlus(4,13)$ $2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 13^{2}$ $2 \cdot 3 \cdot 7 \cdot 13$ 81 $C_1$ $\PSL(2,13)^2$ $\PSL(2,13)^2$ $C_1$ Non-Solvable - 2
6065280.a $\PSL(4,3)$ $\POmegaPlus(6,3)$ $2^{7} \cdot 3^{6} \cdot 5 \cdot 13$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 13$ 29 $C_1$ $\PSL(4,3)$ $\PSL(4,3)$ $C_1$ Simple
16646400.a $\SL(2,16)^2$ $\POmegaPlus(4,16)$ $2^{8} \cdot 3^{2} \cdot 5^{2} \cdot 17^{2}$ $2 \cdot 3 \cdot 5 \cdot 17$ 289 $C_1$ $\SL(2,16)^2$ $\SL(2,16)^2$ $C_1$ Non-Solvable - 2
174182400.a $\OmegaPlus(8,2)$ $\POmegaPlus(8,2)$ $2^{12} \cdot 3^{5} \cdot 5^{2} \cdot 7$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ 53 $C_1$ $\OmegaPlus(8,2)$ $\OmegaPlus(8,2)$ $C_1$ Simple
987033600.a $\SL(4,4)$ $\POmegaPlus(6,4)$ $2^{12} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 17$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17$ 84 $C_1$ $\SL(4,4)$ $\SL(4,4)$ $C_1$ Simple
7254000000.a $\PSL(4,5)$ $\POmegaPlus(6,5)$ $2^{7} \cdot 3^{2} \cdot 5^{6} \cdot 13 \cdot 31$ $2^{3} \cdot 3 \cdot 5 \cdot 13 \cdot 31$ 49 $C_1$ $\PSL(4,5)$ $\PSL(4,5)$ $C_1$ Simple
2317591180800.a $\PSL(4,7)$ $\POmegaPlus(6,7)$ $2^{9} \cdot 3^{4} \cdot 5^{2} \cdot 7^{6} \cdot 19$ $2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19$ 217 $C_1$ $\PSL(4,7)$ $\PSL(4,7)$ $C_1$ Simple
4952179814400.a $\POmegaPlus(8,3)$ $\POmegaPlus(8,3)$ $2^{12} \cdot 3^{12} \cdot 5^{2} \cdot 7 \cdot 13$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ 114 $C_1$ $\POmegaPlus(8,3)$ $\POmegaPlus(8,3)$ $C_1$ Simple
34558531338240.a $\SL(4,8)$ $\POmegaPlus(6,8)$ $2^{18} \cdot 3^{4} \cdot 5 \cdot 7^{3} \cdot 13 \cdot 73$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \cdot 73$ 584 $C_1$ $\SL(4,8)$ $\SL(4,8)$ $C_1$ Simple
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