Finite Group DatabasebetaFinite Group Databasebeta| order | 8862 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#17984522 |
| Fitting, socle, Hall | C2×C7×C211 ⋊ C3 |
| derived, Hall | C7×C211 ⋊ C2×C3 |
| Hall | C2×C211 ⋊ ΓL(1,𝔽8) |
| Sylow | C211 ⋊ C2×ΓL(1,𝔽8) |
| Hall | C2×C7 ⋊ C211⋊C3 |
| Sylow | C7 ⋊ C2×C211⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #17984522 |
| commutator, hypocenter | C7×C211 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C211 | C3 |
| LCS | G ▷ C7×C211 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
990 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#17984522, #31799388, #31799392, … |
| maximal normal subgroup of | C4×#17984522, #31799388, #31799392, … |
| maximal quotient of | C4×#17984522, C22×#17984522, C2×#27210813, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8862, 5);