Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C3 |
| direct product | #157×C29⋊C7 |
| unambiguous semidirect product | (C29×#157)⋊C7 |
| Fitting, socle, derived, Hall | C32×C29 ⋊ C4×C7 |
| Hall | C32×C29⋊C7 ⋊ C4 |
| Hall | C29×#157 ⋊ C7 |
| Sylow | C29 ⋊ C7×#157 |
| Sylow | C32 ⋊ C4×C29⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C29 | C4×C7 |
| LCS | G ▷ C32×C29 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
66 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#157×C29⋊C7, #4380×C29⋊C7, #4379×C29⋊C7 |
| maximal normal subgroup of | C5×#157×C29⋊C7 |
| maximal quotient of | C5×#157×C29⋊C7, #4380×C29⋊C7, #4379×C29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 90);