Finite Group DatabasebetaFinite Group Databasebeta| order | 9324 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#15690924 |
| derived, Hall | C7×C37 ⋊ C32×C4 |
| Hall | C3×#11715913 ⋊ C4 |
| Hall | Dic7×C37 ⋊ C32 |
| Sylow | C37 ⋊ C3×ΓL(1,𝔽8)⋊C4 |
| Hall | Dic7 ⋊ C3×C37⋊C3 |
| Sylow | C7 ⋊ C3×C4×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #13095535 |
| commutator, hypocenter | C7×C37 | C32×C4 |
| Frattini | C2 | C3×#13095535 |
| Fitting, socle | C2×C3×C7×C37 | C2×C3 |
| LCS | G ▷ C7×C37 | |
| UCS | C1 ◁ C2×C3 | |
72 conjugacy classes of subgroups.
402 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9324, 98);