Finite Group DatabasebetaFinite Group Databasebeta| order | 8864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C42×D277 |
| Fitting | C42×C277 ⋊ C2 |
| derived, Sylow | C277 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D277 |
| commutator, hypocenter | C277 | C2×C42 |
| Frattini | C22 | C22×D277 |
| Fitting | C42×C277 | C2 |
| socle | C22×C277 | C23 |
| LCS | G ▷ C277 | |
| UCS | C1 ◁ C42 | |
108 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C8×D277, #97×D277, C4×#17984546, … |
| maximal normal subgroup of | C4×C8×D277, #97×D277, C4×#17984546, … |
| maximal quotient of | C42×Dic277, #95×D277, #31799847, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8864, 94);