Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | Dic9×C29⋊C7 |
| unambiguous semidirect product | C9⋊(C4×C29⋊C7) |
| unambiguous semidirect product | (C29×Dic9)⋊C7 |
| derived, Hall | C9×C29 ⋊ C4×C7 |
| Hall | C9×C29⋊C7 ⋊ C4 |
| Hall | C29×Dic9 ⋊ C7 |
| Sylow | C29 ⋊ C7×Dic9 |
| Sylow | C9 ⋊ C4×C29⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×C29⋊C7 |
| commutator, hypocenter | C9×C29 | C4×C7 |
| Frattini | C2×C3 | D3×C29⋊C7 |
| Fitting | C2×C9×C29 | C2×C7 |
| socle | C2×C3×C29 | D3×C7 |
| LCS | G ▷ C9×C29 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
132 conjugacy classes — view the full character table.
| maximal subgroup of | C5×Dic9×C29⋊C7, Dic45×C29⋊C7, C9⋊AGL(1,𝔽5)×C29⋊C7 |
| maximal normal subgroup of | C5×Dic9×C29⋊C7 |
| maximal quotient of | C5×Dic9×C29⋊C7, Dic45×C29⋊C7, C9⋊AGL(1,𝔽5)×C29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 3);