Finite Group DatabasebetaFinite Group Databasebeta| order | 8864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×D277 |
| Fitting | C2×Q8×C277 ⋊ C2 |
| Sylow | C277 ⋊ C22×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D277 |
| commutator | C2×C277 | C24 |
| Frattini | C2 | C23×D277 |
| Fitting | C2×Q8×C277 | C2 |
| socle | C22×C277 | C23 |
| hypercenter | C2×Q8 | D277 |
| hypocenter | C277 | C22×Q8 |
| LCS | G ▷ C2×C277 ▷ C277 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
156 conjugacy classes of subgroups.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #101×D277, #103×D277, #31800009, … |
| maximal normal subgroup of | #101×D277, #103×D277, #31800009, … |
| maximal quotient of | C2×C4⋊C4×D277, C4×Q8×D277, C2×#22579845, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8864, 185);