Finite Group DatabasebetaFinite Group Databasebeta| order | 8864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C277 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×D277 |
| commutator, socle | C2×C277 | C2×C8 |
| Fitting | C2×C8×C277 | C2 |
| hypercenter | C2×C8 | D277 |
| hypocenter | C277 | M32 |
| LCS | G ▷ C2×C277 ▷ C277 | |
| UCS | C1 ◁ C8 ◁ C2×C8 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,277|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^2762228 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31799779, #31799780, #31799783, … |
| maximal normal subgroup of | #31799779, #31799780, #31799783, … |
| maximal quotient of | #31799778, C22⋊#17984538, C4⋊#17984538, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8864, 86);