Finite Group DatabasebetaFinite Group Databasebeta| order | 9324 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C4×#14556423 |
| Fitting, Hall | C4×C7×C37 ⋊ C9 |
| derived, Hall | C7×C37 ⋊ C4×C9 |
| Hall | C4×C37 ⋊ C7⋊C9 |
| Sylow | C37 ⋊ C4×C7⋊C9 |
| Hall | C4×C7 ⋊ #66526 |
| Sylow | C7 ⋊ C4×#66526 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #14556423 |
| commutator, hypocenter | C7×C37 | C4×C9 |
| Frattini | C2 | C2×#14556423 |
| Fitting | C4×C7×C37 | C9 |
| socle | C2×C7×C37 | C2×C9 |
| LCS | G ▷ C7×C37 | |
| UCS | C1 ◁ C4 | |
36 conjugacy classes of subgroups.
172 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9324, 92);