Finite Group DatabasebetaFinite Group Databasebeta| order | 7731 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C859⋊C3 |
| unambiguous semidirect product | C859⋊C32 |
| unambiguous semidirect product | (C3×C859)⋊C3 |
| Fitting, socle | C3×C859 ⋊ C3 |
| derived, Sylow | C859 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C859⋊C3 |
| commutator, hypocenter | C859 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C859 | C3 |
| LCS | G ▷ C859 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
867 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D859⋊C3, C3⋊(D859⋊C3), D3×C859⋊C3, … |
| maximal normal subgroup of | C3×D859⋊C3, C3⋊(D859⋊C3), D3×C859⋊C3, … |
| maximal quotient of | C2×C3×C859⋊C3, C9×C859⋊C3, C3×C859⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7731, 3);