Finite Group DatabasebetaFinite Group Databasebeta| order | 8864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C277 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#11764308 |
| commutator, socle | C2×C277 | C22×C4 |
| Fitting | Q8×C277 | C4 |
| hypercenter | Q8 | #11764308 |
| hypocenter | C277 | #131 |
| LCS | G ▷ C2×C277 ▷ C277 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,277|a^2=d,d^2=e,f^a=f^217,c^b=ce,f^b=f^276,f^c=f^276,f^d=f^276365 conjugacy classes — view the full character table.
| maximal subgroup of | #31801045, #31801046, #31801047, … |
| maximal normal subgroup of | #31801045, #31801046, #31801047, … |
| maximal quotient of | #31800967, #31800977, #31801009, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8864, 234);