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 | C4 | C2×#11764308 |
| commutator, socle | C2×C277 | C2×C8 |
| Fitting | C8×C277 | C4 |
| hypercenter | C8 | #11764308 |
| hypocenter | C277 | M32 |
| LCS | G ▷ C2×C277 ▷ C277 | |
| UCS | C1 ◁ C4 ◁ 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^217,f^b=f^276,f^c=f^276572 conjugacy classes — view the full character table.
| maximal subgroup of | #31800892, #31800893, #31800918, … |
| maximal normal subgroup of | #31800892, #31800893, #31800918, … |
| maximal quotient of | #31800891, #31800897, #31800923, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8864, 221);