Finite Group DatabasebetaFinite Group Databasebeta| order | 6732 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C2 |
| direct product | D3×C17×D33 |
| unambiguous semidirect product | (C3×D3)⋊(C17×D11) |
| unambiguous semidirect product | (D3×C11)⋊(D3×C17) |
| Fitting, socle, Hall | C32×C11×C17 ⋊ C22 |
| derived, Hall | C32×C11 ⋊ C22×C17 |
| Hall | C11×C17 ⋊ D32 |
| Hall | C32×C17 ⋊ C2×D11 |
| Sylow | C11 ⋊ D32×C17 |
| Sylow | C32 ⋊ C2×C17×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D3×D33 |
| commutator, hypocenter | C32×C11 | C22×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C17 | C22 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C17 | |
88 conjugacy classes of subgroups.
918 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C17×C3⋊AGL(1,𝔽11), C5×D3×C17×D33, D3×C17×D165, … |
| maximal normal subgroup of | D3×C17×C3⋊AGL(1,𝔽11), C5×D3×C17×D33 |
| maximal quotient of | C5×D3×C17×D33, D3×C17×D165, C17×D15×D33, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6732, 64);