Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of D3×D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | Dic3×Dic33 |
| derived, Hall | C32×C11 ⋊ C42 |
| Sylow | C11 ⋊ Dic32 |
| Sylow | C32 ⋊ C4×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D3×D33 |
| commutator, hypocenter | C32×C11 | C42 |
| Fitting, socle, prime radical, cosocle | C22×C32×C11 | C22 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C22 | |
136 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 528 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 252);