Finite Group DatabasebetaFinite Group Databasebeta| order | 8864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C277 ⋊ C2 |
| Sylow | C277 ⋊ #135 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D277 |
| commutator | C4×C277 | C23 |
| Frattini | C4 | C22×D277 |
| Fitting | Q16×C277 | C2 |
| socle | C2×C277 | C2×D4 |
| hypercenter | Q16 | D277 |
| hypocenter | C277 | #135 |
| LCS | G ▷ C4×C277 ▷ C2×C277 ▷ C277 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,277|c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^276,d^b=de,f^b=f^276,f^c=f^276980 conjugacy classes — view the full character table.
| maximal subgroup of | #31800433, #31800435, #31800439, … |
| maximal normal subgroup of | #31800433, #31800435, #31800439, … |
| maximal quotient of | #31799997, #31800039, #31800084, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8864, 169);