Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D33 |
| unambiguous semidirect product | (D3×C3⋊D3)⋊C22 |
| Fitting, socle | C2×C33 ⋊ C23 |
| derived, Sylow | C33 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D33 |
| commutator, cosocle, hypocenter | C33 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C2×C33 | C23 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C2 | |
642 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 4 generators on 11 points:
(1,2)(4,5)(6,7,8)(9,10,11);(3,4,5)(7,8);(10,11);(1,2)54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D32⋊C4, #11724112, #11724113, … |
| maximal normal subgroup of | D3×D32⋊C4, #11724112, #11724113, … |
| maximal quotient of | D32×Dic6, D3×#3795, D3×#3796, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 759);