Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of D11×(C22⋊C9)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| direct product | D11×(C22⋊C9)⋊C2 |
| unambiguous semidirect product | (C11×(C22⋊C9)⋊C2)⋊C2 |
| unambiguous semidirect product | (C11⋊((C22⋊C9)⋊C2))⋊C2 |
| unambiguous semidirect product | (D11×C22⋊C9)⋊C2 |
| derived | C11×C22⋊C9 ⋊ C22 |
| Sylow | C11 ⋊ C2×(C22⋊C9)⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C11×C22⋊C9 | C22 |
| Frattini | C3 | D11×S4 |
| Fitting, socle | C22×C3×C11 | C2×D3 |
| LCS | G ▷ C11×C22⋊C9 | |
| UCS | C1 | |
112 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 19 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 198 |
63 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 364);