Finite Group DatabasebetaFinite Group Databasebeta| order | 8864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#17984572 |
| Sylow | C277 ⋊ C2×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#11764308 |
| commutator | C2×C277 | C22×C4 |
| Frattini | C2 | C22×#11764308 |
| Fitting | C23×C277 | C4 |
| socle | C22×C277 | C2×C4 |
| hypercenter | C23 | #11764308 |
| hypocenter | C277 | C2×M16 |
| LCS | G ▷ C2×C277 ▷ C277 | |
| UCS | C1 ◁ C22 ◁ C23 | |
68 conjugacy classes of subgroups.
572 conjugacy classes — view the full character table.
| maximal subgroup of | #31800882, #31800883, C4×#17984572, … |
| maximal normal subgroup of | #31800882, #31800883, C4×#17984572, … |
| maximal quotient of | C2×#22579935, C4×#17984572, C2×C22⋊#14555667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8864, 230);