Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of C3⋊D3×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C3×C4 |
| direct product | C3⋊Dic3×Dic11 |
| derived, Hall | C32×C11 ⋊ C42 |
| Sylow | C11 ⋊ C4×C3⋊Dic3 |
| Sylow | C32 ⋊ C4×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | C3⋊D3×D11 |
| commutator, hypocenter | C32×C11 | C42 |
| Fitting, socle, prime radical, cosocle | C22×C32×C11 | C22 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C22 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1584 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 211);