Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D32×Dic3 |
| derived, Sylow | C33 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D33 |
| commutator, hypocenter | C33 | C22×C4 |
| Fitting, socle, cosocle | C2×C33 | C23 |
| prime radical | C2×C3×D32 | C2 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C2 | |
270 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 13 points:
(1,2,3,4)(5,6,7)(8,9,10)(12,13);(9,10)(11,12,13);(6,7)54 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×GO+(4,𝔽2), (D32⋊D3)⋊C4, #11724117, … |
| maximal normal subgroup of | Dic3×GO+(4,𝔽2), (D32⋊D3)⋊C4, #11724117, … |
| maximal quotient of | D32×C3⋊C8, D3×#3711, #11722816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 594);