Finite Group DatabasebetaFinite Group Databasebeta| order | 6402 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1067 |
| unambiguous semidirect product | C11⋊(C3×D97) |
| Fitting, socle, Hall | C3×C11×C97 ⋊ C2 |
| derived, Hall | C11×C97 ⋊ C2×C3 |
| Hall | C3×C97 ⋊ D11 |
| Sylow | C97 ⋊ C3×D11 |
| Hall | C3×C11 ⋊ D97 |
| Sylow | C11 ⋊ C3×D97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1067 |
| commutator, hypocenter | C11×C97 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C97 | C2 |
| LCS | G ▷ C11×C97 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
1605 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D11×D97, D3×D1067, D33⋊D97, … |
| maximal normal subgroup of | C3×D11×D97, D3×D1067, D33⋊D97, … |
| maximal quotient of | C3×Dic1067, C2×C3×D1067, C9×D1067, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6402, 5);