Finite Group DatabasebetaFinite Group Databasebeta| order | 8864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×D277⋊C8 |
| unambiguous semidirect product | D277⋊(C2×C8) |
| derived, Sylow | C277 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11764308 |
| commutator, hypocenter | C277 | C22×C8 |
| Frattini | C2 | C22×#11764308 |
| Fitting | C2×C4×C277 | C4 |
| socle | C22×C277 | C2×C4 |
| LCS | G ▷ C277 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
584 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#11764308)⋊C8, #31800875, #31800877, … |
| maximal normal subgroup of | (C2×#11764308)⋊C8, #31800875, #31800877, … |
| maximal quotient of | C2×C4×#14555667, C4×D277⋊C8, D277⋊(C22⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8864, 229);