Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of D33⋊S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D33⋊S4 |
| unambiguous semidirect product | (C3⋊S4)⋊D11 |
| unambiguous semidirect product | (C11⋊S4)⋊D3 |
| Fitting, socle | C22×C3×C11 ⋊ C2×D3 |
| derived | C3×C11×A4 ⋊ C22 |
| Sylow | C11 ⋊ D3×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C11×A4 | C22 |
| Fitting, socle | C22×C3×C11 | C2×D3 |
| LCS | G ▷ C3×C11×A4 | |
| UCS | C1 | |
140 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 132 |
Polycyclic presentation:
2^2,3^2,11,2^2|d^a=d^2,e^a=e^10,c^b=c^2,d^b=d^2,f^b=fg,f^c=g,g^c=fg60 conjugacy classes — view the full character table.
| maximal subgroup of | #72268710, D3×D11×S4 |
| maximal normal subgroup of | #72268710, D3×D11×S4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 664);