Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C7⋊C9×#1181 |
| unambiguous semidirect product | (C7×#1181)⋊C9 |
| derived, Hall | C7×C29 ⋊ C4×C9 |
| Hall | C29×C7⋊C9 ⋊ C4 |
| Hall | C7×#1181 ⋊ C9 |
| Sylow | C29 ⋊ C4×C7⋊C9 |
| Sylow | C7 ⋊ C9×#1181 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)×#1181 |
| commutator, hypocenter | C7×C29 | C4×C9 |
| Fitting, socle | C3×C7×C29 | C3×C4 |
| LCS | G ▷ C7×C29 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
165 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C7⋊C9×#1181, C7⋊C9×#10596814, C7⋊C9×#10596815, … |
| maximal normal subgroup of | C5×C7⋊C9×#1181 |
| maximal quotient of | C5×C7⋊C9×#1181, C7⋊C9×#10596814, C7⋊C9×#10596815, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 27);