Finite Group DatabasebetaFinite Group Databasebeta| order | 8271 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C919⋊C3 |
| unambiguous semidirect product | C919⋊C32 |
| unambiguous semidirect product | (C3×C919)⋊C3 |
| Fitting, socle | C3×C919 ⋊ C3 |
| derived, Sylow | C919 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C919⋊C3 |
| commutator, hypocenter | C919 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C919 | C3 |
| LCS | G ▷ C919 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
927 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D919⋊C3, C3⋊(D919⋊C3), D3×C919⋊C3, … |
| maximal normal subgroup of | C3×D919⋊C3, C3⋊(D919⋊C3), D3×C919⋊C3, … |
| maximal quotient of | C2×C3×C919⋊C3, C9×C919⋊C3, C3×#22552000, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8271, 4);