Finite Group DatabasebetaFinite Group Databasebeta| order | 4585 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C131⋊C5 |
| unambiguous semidirect product | C131⋊(C5×C7) |
| unambiguous semidirect product | (C7×C131)⋊C5 |
| Fitting, socle, Hall | C7×C131 ⋊ C5 |
| derived, Sylow | C131 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C131⋊C5 |
| commutator, cosocle, hypocenter | C131 | C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C131 | C5 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 138 |
| transitive degree | μt(G) = 917 |
217 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4585, 1);