Finite Group DatabasebetaFinite Group Databasebeta| order | 8864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4⋊C4×C277 ⋊ C2 |
| Sylow | C277 ⋊ #126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D277 |
| commutator, socle | C22×C277 | C23 |
| Fitting | C4⋊C4×C277 | C2 |
| hypercenter | C4⋊C4 | D277 |
| hypocenter | C277 | #126 |
| LCS | G ▷ C22×C277 ▷ C277 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,277|b^2=de,c^2=d,b^a=bd,c^a=ce,f^a=f^276,f^c=f^2761394 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #126×D277, C2×#22579875, #31800529, … |
| maximal normal subgroup of | #126×D277, C2×#22579875, #31800529, … |
| maximal quotient of | #31799869, #31799883, #31799885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8864, 141);