Finite Group DatabasebetaFinite Group Databasebeta| order | 6732 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×D11×D17 |
| unambiguous semidirect product | (C17×D11)⋊(C2×C32) |
| unambiguous semidirect product | (C11×D17)⋊(C2×C32) |
| unambiguous semidirect product | D187⋊(C2×C32) |
| Fitting, socle, Hall | C32×C11×C17 ⋊ C22 |
| derived, Hall | C11×C17 ⋊ C22×C32 |
| Hall | C32×C17 ⋊ C2×D11 |
| Hall | C32×C11 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×C32×D11 |
| Sylow | C11 ⋊ C2×C32×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D11×D17 |
| commutator, hypocenter | C11×C17 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C17 | C22 |
| LCS | G ▷ C11×C17 | |
| UCS | C1 ◁ C32 | |
120 conjugacy classes of subgroups.
630 conjugacy classes — view the full character table.
| maximal subgroup of | C32×D17×AGL(1,𝔽11), C32×C5×D11×D17, C32×D17×D55, … |
| maximal normal subgroup of | C32×D17×AGL(1,𝔽11), C32×C5×D11×D17 |
| maximal quotient of | C32×C5×D11×D17, C32×D17×D55, C32×D11×D85, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6732, 44);