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Note: Search results may be incomplete due to uncomputed quantities: Outer aut. group order (4830 objects)

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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 Transitive degree Permutation degree
Minimal degree of $\C$-irrep Minimal degree of $\Q$-irrep Minimal degree of $\C$-rep Minimal 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
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Number of subgroups Number of normal subgroups Number of conjugacy classes
Number of characteristic subgroups Number of autjugacy classes Number of divisions
Order statistics Order factorization Commutator length
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Results (39 matches)

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Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
6.1 $S_3$ $2 \cdot 3$ $2 \cdot 3$ $3$ $C_1$ $S_3$ $C_3$ $C_{2}$ Solvable - 2
42.1 $F_7$ $2 \cdot 3 \cdot 7$ $2 \cdot 3 \cdot 7$ $7$ $C_1$ $F_7$ $C_7$ $C_{6}$ Solvable - 2
110.1 $F_{11}$ $2 \cdot 5 \cdot 11$ $2 \cdot 5 \cdot 11$ $11$ $C_1$ $F_{11}$ $C_{11}$ $C_{10}$ Solvable - 2
506.1 $F_{23}$ $2 \cdot 11 \cdot 23$ $2 \cdot 11 \cdot 23$ $23$ $C_1$ $F_{23}$ $C_{23}$ $C_{22}$ Solvable - 2
930.1 $F_{31}$ $2 \cdot 3 \cdot 5 \cdot 31$ $2 \cdot 3 \cdot 5 \cdot 31$ $31$ $C_1$ $F_{31}$ $C_{31}$ $C_{30}$ Solvable - 2
1806.1 $F_{43}$ $2 \cdot 3 \cdot 7 \cdot 43$ $2 \cdot 3 \cdot 7 \cdot 43$ $43$ $C_1$ $F_{43}$ $C_{43}$ $C_{42}$ Solvable - 2
2162.1 $F_{47}$ $2 \cdot 23 \cdot 47$ $2 \cdot 23 \cdot 47$ $47$ $C_1$ $F_{47}$ $C_{47}$ $C_{46}$ Solvable - 2
3422.1 $F_{59}$ $2 \cdot 29 \cdot 59$ $2 \cdot 29 \cdot 59$ $59$ $C_1$ $F_{59}$ $C_{59}$ $C_{58}$ Solvable - 2
4422.18 $F_{67}$ $2 \cdot 3 \cdot 11 \cdot 67$ $2 \cdot 3 \cdot 11 \cdot 67$ $67$ $C_1$ $F_{67}$ $C_{67}$ $C_{66}$ Solvable - 2
4970.18 $F_{71}$ $2 \cdot 5 \cdot 7 \cdot 71$ $2 \cdot 5 \cdot 7 \cdot 71$ $71$ $C_1$ $F_{71}$ $C_{71}$ $C_{70}$ Solvable - 2
6162.30 $F_{79}$ $2 \cdot 3 \cdot 13 \cdot 79$ $2 \cdot 3 \cdot 13 \cdot 79$ $79$ $C_1$ $F_{79}$ $C_{79}$ $C_{78}$ Solvable - 2
6806.1 $F_{83}$ $2 \cdot 41 \cdot 83$ $2 \cdot 41 \cdot 83$ $83$ $C_1$ $F_{83}$ $C_{83}$ $C_{82}$ Solvable - 2
10506.18 $F_{103}$ $2 \cdot 3 \cdot 17 \cdot 103$ $2 \cdot 3 \cdot 17 \cdot 103$ $103$ $C_1$ $F_{103}$ $C_{103}$ $C_{102}$ Solvable - 2
11342.1 $F_{107}$ $2 \cdot 53 \cdot 107$ $2 \cdot 53 \cdot 107$ $107$ $C_1$ $F_{107}$ $C_{107}$ $C_{106}$ Solvable - 2
17030.18 $F_{131}$ $2 \cdot 5 \cdot 13 \cdot 131$ $2 \cdot 5 \cdot 13 \cdot 131$ $131$ $C_1$ $F_{131}$ $C_{131}$ $C_{130}$ Solvable - 2
19182.18 $F_{139}$ $2 \cdot 3 \cdot 23 \cdot 139$ $2 \cdot 3 \cdot 23 \cdot 139$ $139$ $C_1$ $F_{139}$ $C_{139}$ $C_{138}$ Solvable - 2
27722.1 $F_{167}$ $2 \cdot 83 \cdot 167$ $2 \cdot 83 \cdot 167$ $167$ $C_1$ $F_{167}$ $C_{167}$ $C_{166}$ Solvable - 2
31862.1 $F_{179}$ $2 \cdot 89 \cdot 179$ $2 \cdot 89 \cdot 179$ $179$ $C_1$ $F_{179}$ $C_{179}$ $C_{178}$ Solvable - 2
36290.18 $F_{191}$ $2 \cdot 5 \cdot 19 \cdot 191$ $2 \cdot 5 \cdot 19 \cdot 191$ $191$ $C_1$ $F_{191}$ $C_{191}$ $C_{190}$ Solvable - 2
44310.90 $F_{211}$ $2 \cdot 3 \cdot 5 \cdot 7 \cdot 211$ $2 \cdot 3 \cdot 5 \cdot 7 \cdot 211$ $211$ $C_1$ $F_{211}$ $C_{211}$ $C_{210}$ Solvable - 2
49506.30 $F_{223}$ $2 \cdot 3 \cdot 37 \cdot 223$ $2 \cdot 3 \cdot 37 \cdot 223$ $223$ $C_1$ $F_{223}$ $C_{223}$ $C_{222}$ Solvable - 2
51302.1 $F_{227}$ $2 \cdot 113 \cdot 227$ $2 \cdot 113 \cdot 227$ $227$ $C_1$ $F_{227}$ $C_{227}$ $C_{226}$ Solvable - 2
56882.18 $F_{239}$ $2 \cdot 7 \cdot 17 \cdot 239$ $2 \cdot 7 \cdot 17 \cdot 239$ $239$ $C_1$ $F_{239}$ $C_{239}$ $C_{238}$ Solvable - 2
68906.1 $F_{263}$ $2 \cdot 131 \cdot 263$ $2 \cdot 131 \cdot 263$ $263$ $C_1$ $F_{263}$ $C_{263}$ $C_{262}$ Solvable - 2
79806.18 $F_{283}$ $2 \cdot 3 \cdot 47 \cdot 283$ $2 \cdot 3 \cdot 47 \cdot 283$ $283$ $C_1$ $F_{283}$ $C_{283}$ $C_{282}$ Solvable - 2
96410.38 $F_{311}$ $2 \cdot 5 \cdot 31 \cdot 311$ $2 \cdot 5 \cdot 31 \cdot 311$ $311$ $C_1$ $F_{311}$ $C_{311}$ $C_{310}$ Solvable - 2
109230.114 $F_{331}$ $2 \cdot 3 \cdot 5 \cdot 11 \cdot 331$ $2 \cdot 3 \cdot 5 \cdot 11 \cdot 331$ $331$ $C_1$ $F_{331}$ $C_{331}$ $C_{330}$ Solvable - 2
120062.1 $F_{347}$ $2 \cdot 173 \cdot 347$ $2 \cdot 173 \cdot 347$ $347$ $C_1$ $F_{347}$ $C_{347}$ $C_{346}$ Solvable - 2
128522.1 $F_{359}$ $2 \cdot 179 \cdot 359$ $2 \cdot 179 \cdot 359$ $359$ $C_1$ $F_{359}$ $C_{359}$ $C_{358}$ Solvable - 2
134322.30 $F_{367}$ $2 \cdot 3 \cdot 61 \cdot 367$ $2 \cdot 3 \cdot 61 \cdot 367$ $367$ $C_1$ $F_{367}$ $C_{367}$ $C_{366}$ Solvable - 2
146306.1 $F_{383}$ $2 \cdot 191 \cdot 383$ $2 \cdot 191 \cdot 383$ $383$ $C_1$ $F_{383}$ $C_{383}$ $C_{382}$ Solvable - 2
175142.18 $F_{419}$ $2 \cdot 11 \cdot 19 \cdot 419$ $2 \cdot 11 \cdot 19 \cdot 419$ $419$ $C_1$ $F_{419}$ $C_{419}$ $C_{418}$ Solvable - 2
185330.18 $F_{431}$ $2 \cdot 5 \cdot 43 \cdot 431$ $2 \cdot 5 \cdot 43 \cdot 431$ $431$ $C_1$ $F_{431}$ $C_{431}$ $C_{430}$ Solvable - 2
192282.30 $F_{439}$ $2 \cdot 3 \cdot 73 \cdot 439$ $2 \cdot 3 \cdot 73 \cdot 439$ $439$ $C_1$ $F_{439}$ $C_{439}$ $C_{438}$ Solvable - 2
195806.18 $F_{443}$ $2 \cdot 13 \cdot 17 \cdot 443$ $2 \cdot 13 \cdot 17 \cdot 443$ $443$ $C_1$ $F_{443}$ $C_{443}$ $C_{442}$ Solvable - 2
213906.90 $F_{463}$ $2 \cdot 3 \cdot 7 \cdot 11 \cdot 463$ $2 \cdot 3 \cdot 7 \cdot 11 \cdot 463$ $463$ $C_1$ $F_{463}$ $C_{463}$ $C_{462}$ Solvable - 2
217622.1 $F_{467}$ $2 \cdot 233 \cdot 467$ $2 \cdot 233 \cdot 467$ $467$ $C_1$ $F_{467}$ $C_{467}$ $C_{466}$ Solvable - 2
228962.1 $F_{479}$ $2 \cdot 239 \cdot 479$ $2 \cdot 239 \cdot 479$ $479$ $C_1$ $F_{479}$ $C_{479}$ $C_{478}$ Solvable - 2
248502.18 $F_{499}$ $2 \cdot 3 \cdot 83 \cdot 499$ $2 \cdot 3 \cdot 83 \cdot 499$ $499$ $C_1$ $F_{499}$ $C_{499}$ $C_{498}$ Solvable - 2
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