Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D261 |
| unambiguous semidirect product | (C9×D7)⋊D29 |
| unambiguous semidirect product | (D7×C29)⋊D9 |
| Fitting, derived, Hall | C7×C9×C29 ⋊ C22 |
| Hall | C9×C29 ⋊ C2×D7 |
| Hall | C7×C29 ⋊ C2×D9 |
| Hall | C7×C9 ⋊ C2×D29 |
| Sylow | C29 ⋊ D7×D9 |
| Sylow | C9 ⋊ D7×D29 |
| Sylow | C7 ⋊ C2×D261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C7×C9×C29 | C22 |
| Frattini | C3 | D7×D87 |
| socle | C3×C7×C29 | C2×D3 |
| LCS | G ▷ C7×C9×C29 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
660 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D7×D261, D7×D1305, D35×D261, … |
| maximal normal subgroup of | C5×D7×D261 |
| maximal quotient of | C5×D7×D261, D7×D1305, D35×D261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 40);