Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | D29×C3⋊D21 |
| unambiguous semidirect product | (C3×D29)⋊D21 |
| unambiguous semidirect product | (C7×D29)⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C7×C29 ⋊ C22 |
| 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, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C7×C29 | C22 |
| LCS | G ▷ C32×C7×C29 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
528 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D29×C3⋊D21, D29×C3⋊D105, C3⋊D21×D145, … |
| maximal normal subgroup of | C5×D29×C3⋊D21 |
| maximal quotient of | C5×D29×C3⋊D21, D29×C3⋊D105, C3⋊D21×D145, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 131);