Finite Group DatabasebetaFinite Group Databasebeta| order | 4718 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C2×C337⋊C7 |
| unambiguous semidirect product | (C2×C337)⋊C7 |
| Fitting, socle, Hall | C2×C337 ⋊ C7 |
| derived, Sylow | C337 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C337⋊C7 |
| commutator, cosocle, hypocenter | C337 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C337 | C7 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 339 |
| transitive degree | μt(G) = 674 |
110 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4718, 2);