Finite Group DatabasebetaFinite Group Databasebeta| order | 8864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#14555660 |
| Sylow | C277 ⋊ C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×D277 |
| commutator | C2×C277 | C2×C8 |
| Fitting | C42×C277 | C2 |
| socle | C22×C277 | C2×C4 |
| hypercenter | C42 | D277 |
| hypocenter | C277 | C4⋊C8 |
| LCS | G ▷ C2×C277 ▷ C277 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,277|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^2762228 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊#14555660, #31799731, Q8⋊#14555660, … |
| maximal normal subgroup of | D4⋊#14555660, #31799731, Q8⋊#14555660, … |
| maximal quotient of | #31799753, #31799755, #31799757, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8864, 76);