Finite Group DatabasebetaFinite Group Databasebeta| order | 8864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C23×Dic277 |
| derived, Sylow | C277 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D277 |
| commutator, hypocenter | C277 | C23×C4 |
| Frattini | C2 | C23×D277 |
| Fitting, socle | C24×C277 | C2 |
| LCS | G ▷ C277 | |
| UCS | C1 ◁ C24 | |
236 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#22579787, C22⋊C4×Dic277, #31799860, … |
| maximal normal subgroup of | C2×#22579787, C22⋊C4×Dic277, #31799860, … |
| maximal quotient of | C22×C4×Dic277, C22×C22⋊Dic277, C22×C4⋊Dic277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8864, 181);