Finite Group DatabasebetaFinite Group Databasebeta| order | 8864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C277 ⋊ C2 |
| Sylow | C277 ⋊ C22⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×D277 |
| commutator | C2×C277 | C2×C8 |
| Fitting | C2×C8×C277 | C2 |
| socle | C22×C277 | C2×C4 |
| hypercenter | C2×C8 | D277 |
| hypocenter | C277 | C22⋊C8 |
| LCS | G ▷ C2×C277 ▷ C277 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C8 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,277|a^2=d,d^2=e,b^a=bc,f^b=f^2762228 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C8×D277, C2×#22579792, #31799964, … |
| maximal normal subgroup of | C22⋊C8×D277, C2×#22579792, #31799964, … |
| maximal quotient of | #31799725, #31799727, #31799729, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8864, 58);