Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×ΓL(1,𝔽8)×Dic29 |
| unambiguous semidirect product | (C7×Dic29)⋊C32 |
| unambiguous semidirect product | (C3×C7×Dic29)⋊C3 |
| derived, Hall | C7×C29 ⋊ C32×C4 |
| Hall | C3×ΓL(1,𝔽8)×C29 ⋊ C4 |
| Hall | C7×Dic29 ⋊ C32 |
| Sylow | C29 ⋊ C3×C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C32×Dic29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | ΓL(1,𝔽8)×D29 |
| commutator, hypocenter | C7×C29 | C32×C4 |
| Frattini | C2 | C3×ΓL(1,𝔽8)×D29 |
| Fitting, socle | C2×C3×C7×C29 | C2×C3 |
| LCS | G ▷ C7×C29 | |
| UCS | C1 ◁ C2×C3 | |
72 conjugacy classes of subgroups.
480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 62);