Finite Group DatabasebetaFinite Group Databasebeta| order | 8766 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C2×C3×C487⋊C3 |
| unambiguous semidirect product | (C2×C487)⋊C32 |
| unambiguous semidirect product | (C2×C3×C487)⋊C3 |
| Fitting, socle | C2×C3×C487 ⋊ C3 |
| derived, Sylow | C487 ⋊ C2×C32 |
| Hall | C2×C487 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C487⋊C3 |
| commutator, hypocenter | C487 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C487 | C3 |
| LCS | G ▷ C487 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
990 conjugacy classes — view the full character table.
| maximal subgroup of | C3×(C487⋊C3)⋊C4, C3⋊((C487⋊C3)⋊C4), Dic3×C487⋊C3, … |
| maximal normal subgroup of | C3×(C487⋊C3)⋊C4, C3⋊((C487⋊C3)⋊C4), Dic3×C487⋊C3, … |
| maximal quotient of | C3×C4×C487⋊C3, C22×C3×C487⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8766, 13);