Finite Group DatabasebetaFinite Group Databasebeta| order | 8864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D277⋊C16 |
| derived, Sylow | C277 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #11764308 |
| commutator, hypocenter | C277 | C2×C16 |
| Frattini | C4 | C2×#11764308 |
| Fitting | C8×C277 | C4 |
| socle | C2×C277 | C2×C8 |
| LCS | G ▷ C277 | |
| UCS | C1 ◁ C8 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,277|a^2=c,c^2=d,d^2=e,f^a=f^217,f^b=f^276,f^c=f^276584 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#11764308, #31800889, #31800914, … |
| maximal normal subgroup of | C16×#11764308, #31800889, #31800914, … |
| maximal quotient of | #31800888, #31800897, #31800923, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8864, 219);