Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×(C3⋊D3)⋊D29 |
| unambiguous semidirect product | (C3⋊D3)⋊(C7×D29) |
| Fitting, socle, Hall | C32×C7×C29 ⋊ C22 |
| derived, Hall | C32×C29 ⋊ C22×C7 |
| Hall | C7×C29 ⋊ D32 |
| Hall | C32×C7 ⋊ C2×D29 |
| Sylow | C29 ⋊ D32×C7 |
| Sylow | C32 ⋊ C2×C7×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | (C3⋊D3)⋊D29 |
| commutator, hypocenter | C32×C29 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C29 | C22 |
| LCS | G ▷ C32×C29 | |
| UCS | C1 ◁ C7 | |
88 conjugacy classes of subgroups.
651 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C7×(C3⋊D3)⋊D29, C7×D87⋊D15, C7×(C3⋊D3)⋊D145 |
| maximal normal subgroup of | C5×C7×(C3⋊D3)⋊D29 |
| maximal quotient of | C5×C7×(C3⋊D3)⋊D29, C7×D87⋊D15, C7×(C3⋊D3)⋊D145 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 138);