Finite Group DatabasebetaFinite Group Databasebeta| order | 4658 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C2×C137⋊C17 |
| unambiguous semidirect product | (C2×C137)⋊C17 |
| Fitting, socle, Hall | C2×C137 ⋊ C17 |
| derived, Sylow | C137 ⋊ C2×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C137⋊C17 |
| commutator, cosocle, hypocenter | C137 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C2×C137 | C17 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 139 |
| transitive degree | μt(G) = 274 |
50 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4658, 2);