↑

Learn more

Refine search

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
Order statistics Family Order factorization Commutator length
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
Almost simple Quasisimple A-group Z-group
Frattini subgroup Derived length Rank Schur multiplier
Supersolvable Monomial Rational
Num. of char. subgroups Num. of aut. classes Number of divisions
Sort order Select

Results (19 matches)

  displayed columns for results
Label Name Family name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
36.10 $S_3^2$ $\SpinPlus(4,2)$ $2^{2} \cdot 3^{2}$ $2 \cdot 3$ 9 $C_1$ $S_3^2$ $C_3^2$ $C_{2}^{2}$ Solvable - 2
576.5128 $\SL(2,3)^2$ $\SpinPlus(4,3)$ $2^{6} \cdot 3^{2}$ $2^{2} \cdot 3$ 49 $C_2^2$ $A_4^2$ $Q_8^2$ $C_{3}^{2}$ Solvable - 3
3600.a $A_5^2$ $\SpinPlus(4,4)$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $2 \cdot 3 \cdot 5$ 25 $C_1$ $A_5^2$ $A_5^2$ $C_1$ Non-Solvable - 2
14400.b $\SL(2,5)^2$ $\SpinPlus(4,5)$ $2^{6} \cdot 3^{2} \cdot 5^{2}$ $2^{2} \cdot 3 \cdot 5$ 81 $C_2^2$ $A_5^2$ $\SL(2,5)^2$ $C_1$ Non-Solvable - 4
20160.a $A_8$ $\SpinPlus(6,2)$ $2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ 14 $C_1$ $A_8$ $A_8$ $C_1$ Simple
112896.b $\SL(2,7)^2$ $\SpinPlus(4,7)$ $2^{8} \cdot 3^{2} \cdot 7^{2}$ $2^{3} \cdot 3 \cdot 7$ 121 $C_2^2$ $\GL(3,2)^2$ $\SL(2,7)^2$ $C_1$ Non-Solvable - 4
254016.a $\SL(2,8)^2$ $\SpinPlus(4,8)$ $2^{6} \cdot 3^{4} \cdot 7^{2}$ $2 \cdot 3^{2} \cdot 7$ 81 $C_1$ $\SL(2,8)^2$ $\SL(2,8)^2$ $C_1$ Non-Solvable - 2
518400.b $\SL(2,9)^2$ $\SpinPlus(4,9)$ $2^{8} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 3 \cdot 5$ 169 $C_2^2$ $A_6^2$ $\SL(2,9)^2$ $C_1$ Non-Solvable - 4
1742400.b $\SL(2,11)^2$ $\SpinPlus(4,11)$ $2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2}$ $2^{2} \cdot 3 \cdot 5 \cdot 11$ 225 $C_2^2$ $\PSL(2,11)^2$ $\SL(2,11)^2$ $C_1$ Non-Solvable - 4
4769856.b $\SpinPlus(4,13)$ $\SpinPlus(4,13)$ $2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13^{2}$ $2^{2} \cdot 3 \cdot 7 \cdot 13$ 289 $C_2^2$ $\PSL(2,13)^2$ $\SpinPlus(4,13)$ $C_1$ Non-Solvable - 4
12130560.a $\SL(4,3)$ $\SpinPlus(6,3)$ $2^{8} \cdot 3^{6} \cdot 5 \cdot 13$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 13$ 51 $C_2$ $\PSL(4,3)$ $\SL(4,3)$ $C_1$ Non-Solvable - 2
16646400.a $\SL(2,16)^2$ $\SpinPlus(4,16)$ $2^{8} \cdot 3^{2} \cdot 5^{2} \cdot 17^{2}$ $2 \cdot 3 \cdot 5 \cdot 17$ 289 $C_1$ $\SL(2,16)^2$ $\SL(2,16)^2$ $C_1$ Non-Solvable - 2
174182400.a $\OmegaPlus(8,2)$ $\SpinPlus(8,2)$ $2^{12} \cdot 3^{5} \cdot 5^{2} \cdot 7$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ 53 $C_1$ $\OmegaPlus(8,2)$ $\OmegaPlus(8,2)$ $C_1$ Simple
987033600.a $\SL(4,4)$ $\SpinPlus(6,4)$ $2^{12} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 17$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17$ 84 $C_1$ $\SL(4,4)$ $\SL(4,4)$ $C_1$ Simple
29016000000.a $\SL(4,5)$ $\SpinPlus(6,5)$ $2^{9} \cdot 3^{2} \cdot 5^{6} \cdot 13 \cdot 31$ $2^{3} \cdot 3 \cdot 5 \cdot 13 \cdot 31$ 185 $C_4$ $\PSL(4,5)$ $\SL(4,5)$ $C_1$ Non-Solvable - 3
4635182361600.a $\SL(4,7)$ $\SpinPlus(6,7)$ $2^{10} \cdot 3^{4} \cdot 5^{2} \cdot 7^{6} \cdot 19$ $2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19$ 423 $C_2$ $\PSL(4,7)$ $\SL(4,7)$ $C_1$ Non-Solvable - 2
19808719257600.b $\SpinPlus(8,3)$ $\SpinPlus(8,3)$ $2^{14} \cdot 3^{12} \cdot 5^{2} \cdot 7 \cdot 13$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ 354 $C_2^2$ $\POmegaPlus(8,3)$ $\SpinPlus(8,3)$ $C_1$ Non-Solvable - 3
23499295948800.a $\OmegaPlus(10,2)$ $\SpinPlus(10,2)$ $2^{20} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 17 \cdot 31$ $2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 \cdot 31$ 97 $C_1$ $\OmegaPlus(10,2)$ $\OmegaPlus(10,2)$ $C_1$ Simple
34558531338240.a $\SL(4,8)$ $\SpinPlus(6,8)$ $2^{18} \cdot 3^{4} \cdot 5 \cdot 7^{3} \cdot 13 \cdot 73$ $2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \cdot 73$ 584 $C_1$ $\SL(4,8)$ $\SL(4,8)$ $C_1$ Simple
  displayed columns for results