Finite Group DatabasebetaFinite Group Databasebeta| order | 8864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C277 ⋊ C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D277 |
| commutator, socle | C22×C277 | C23 |
| Fitting | C22×C4×C277 | C2 |
| hypercenter | C22×C4 | D277 |
| hypocenter | C277 | C22⋊Q8 |
| LCS | G ▷ C22×C277 ▷ C277 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,277|a^2=d,b^2=d,b^a=bd,c^a=ce,f^a=f^2762222 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31799738, #31799740, #31800153, … |
| maximal normal subgroup of | #31799738, #31799740, #31800153, … |
| maximal quotient of | #31799862, #31799875, #31799886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8864, 125);