Finite Group DatabasebetaFinite Group Databasebeta| order | 8864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C277 ⋊ C2 |
| Sylow | C277 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D277 |
| commutator, socle | C2×C277 | C24 |
| Fitting | #41×C277 | C2 |
| hypercenter | #41 | D277 |
| hypocenter | C277 | H(5,𝔽2) |
| LCS | G ▷ C2×C277 ▷ C277 | |
| UCS | C1 ◁ C2 ◁ #41 | |
166 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,277|b^a=be,d^a=de,c^b=ce,f^c=f^276,f^d=f^2761397 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31800168, #31800171, #31800178, … |
| maximal normal subgroup of | #31800168, #31800171, #31800178, … |
| maximal quotient of | #31800474, #31800476, #31800482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8864, 192);