Finite Group DatabasebetaFinite Group Databasebeta| order | 9366 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#17989746 |
| Fitting, socle, Hall | C2×C7×C223 ⋊ C3 |
| derived, Hall | C7×C223 ⋊ C2×C3 |
| Hall | C2×C223 ⋊ ΓL(1,𝔽8) |
| Sylow | C223 ⋊ C2×ΓL(1,𝔽8) |
| Hall | C2×C7 ⋊ C223⋊C3 |
| Sylow | C7 ⋊ C2×C223⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #17989746 |
| commutator, hypocenter | C7×C223 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C223 | C3 |
| LCS | G ▷ C7×C223 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
1046 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#17989746, #34035430, #34035434, … |
| maximal normal subgroup of | C4×#17989746, #34035430, #34035434, … |
| maximal quotient of | C4×#17989746, C22×#17989746, C2×#28380796, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9366, 5);