Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D21×D29 |
| unambiguous semidirect product | (C3×D29)⋊(C3×D7) |
| Fitting, socle, Hall | C32×C7×C29 ⋊ C22 |
| derived | C3×C7×C29 ⋊ C22×C3 |
| Hall | C32×C29 ⋊ C2×D7 |
| Hall | C7×C29 ⋊ C2×C3×D3 |
| Hall | C32×C7 ⋊ C2×D29 |
| Sylow | C29 ⋊ C2×C3×D21 |
| Sylow | C32 ⋊ D7×D29 |
| Sylow | C7 ⋊ C3×D3×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D21×D29 |
| commutator, hypocenter | C3×C7×C29 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C29 | C22 |
| LCS | G ▷ C3×C7×C29 | |
| UCS | C1 ◁ C3 | |
88 conjugacy classes of subgroups.
576 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×D21×D29, C3×D29×D105, C3×D21×D145, … |
| maximal normal subgroup of | C3×C5×D21×D29 |
| maximal quotient of | C3×C5×D21×D29, C3×D29×D105, C3×D21×D145, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 123);