Finite Group DatabasebetaFinite Group Databasebeta| order | 8724 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C4×C727⋊C3 |
| unambiguous semidirect product | (C4×C727)⋊C3 |
| Fitting, Hall | C4×C727 ⋊ C3 |
| derived, Sylow | C727 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C727⋊C3 |
| commutator, hypocenter | C727 | C3×C4 |
| Frattini | C2 | C2×C727⋊C3 |
| Fitting | C4×C727 | C3 |
| socle | C2×C727 | C2×C3 |
| LCS | G ▷ C727 | |
| UCS | C1 ◁ C4 | |
12 conjugacy classes of subgroups.
980 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×C727⋊C3, C3×C4×C727⋊C3 |
| maximal normal subgroup of | C3×C4×C727⋊C3 |
| maximal quotient of | C4×C727⋊C9, Dic3×C727⋊C3, C3×C4×C727⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8724, 3);