Finite Group DatabasebetaFinite Group Databasebeta| order | 6732 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D33⋊D51 |
| Fitting, socle, derived, Hall | C32×C11×C17 ⋊ C22 |
| Hall | C11×C17 ⋊ D32 |
| Hall | C32×C17 ⋊ C2×D11 |
| Hall | C32×C11 ⋊ C2×D17 |
| Sylow | C17 ⋊ (C3⋊D3)⋊D11 |
| Sylow | C11 ⋊ D3×D51 |
| Sylow | C32 ⋊ D11×D17 |
| 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.
Polycyclic presentation:
2^2,3^2,11,17|c^a=c^2,d^a=d^2,f^a=f^16,d^b=d^2,e^b=e^10471 conjugacy classes — view the full character table.
| maximal subgroup of | (C3⋊AGL(1,𝔽11))⋊D51, C5×D33⋊D51, D33⋊D255, … |
| maximal normal subgroup of | (C3⋊AGL(1,𝔽11))⋊D51, C5×D33⋊D51 |
| maximal quotient of | C5×D33⋊D51, D33⋊D255, #46778138, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6732, 69);