Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of D3×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×D3×C3⋊D3 |
| Fitting, socle | C22×C33 ⋊ C22 |
| derived, Sylow | C33 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×C3⋊D3 |
| commutator, cosocle, hypocenter | C33 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C22×C33 | C22 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C22 | |
932 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 188 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) = 72 |
A minimal faithful permutation representation — 4 generators on 13 points:
(1,2)(3,4)(6,7)(9,10)(11,12,13);(5,6,7)(12,13);(3,4)(8,9,10);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3722, #11722904, #11722906, … |
| maximal normal subgroup of | D3×#3722, #11722904, #11722906, … |
| maximal quotient of | C2×D3×#634, C2×#89014, C2×#89015, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 768);