Finite Group DatabasebetaFinite Group Databasebeta| order | 6732 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D561 |
| unambiguous semidirect product | (C3×D3)⋊D187 |
| unambiguous semidirect product | (D3×C11)⋊D51 |
| unambiguous semidirect product | (D3×C17)⋊D33 |
| Fitting, socle, derived, Hall | C32×C11×C17 ⋊ C22 |
| Hall | C11×C17 ⋊ D32 |
| Hall | C32×C17 ⋊ C2×D11 |
| Hall | C32×C11 ⋊ C2×D17 |
| Sylow | C17 ⋊ D3×D33 |
| Sylow | C11 ⋊ D3×D51 |
| Sylow | C32 ⋊ C2×D187 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C11×C17 | C22 |
| LCS | G ▷ C32×C11×C17 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
846 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C3⋊(C17⋊AGL(1,𝔽11)), C5×D3×D561, D3×D2805, … |
| maximal normal subgroup of | D3×C3⋊(C17⋊AGL(1,𝔽11)), C5×D3×D561 |
| maximal quotient of | C5×D3×D561, D3×D2805, D15×D561, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6732, 65);