Finite Group DatabasebetaFinite Group Databasebeta| order | 9366 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C223 ⋊ C2×C3 |
| Hall | #17989747 ⋊ C2 |
| Hall | C7×D223 ⋊ C3 |
| Hall | D223 ⋊ ΓL(1,𝔽8) |
| Sylow | C223 ⋊ C2×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ D223⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C223 | C2×C3 |
| LCS | G ▷ C7×C223 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,223|d^a=d^222,c^b=c^2,d^b=d^183269 conjugacy classes — view the full character table.
| maximal subgroup of | #22627314⋊C2, C2×#22627314, ΓL(1,𝔽8)×D223⋊C3, … |
| maximal normal subgroup of | #22627314⋊C2, C2×#22627314, ΓL(1,𝔽8)×D223⋊C3, … |
| maximal quotient of | #34035429, C2×#22627314, #43244458, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9366, 15);