Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of D3×#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×D3×#157 |
| Fitting, socle | C2×C33 ⋊ C2×C4 |
| derived, Sylow | C33 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×#157 |
| commutator, hypocenter | C33 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C33 | C2×C4 |
| prime radical | C2×D3×C3⋊D3 | C2 |
| cosocle | C3×C3⋊D3 | C23 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C2 | |
192 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 42 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 — 3 generators on 11 points:
(3,4,5)(6,7)(8,9,10,11);(1,2)(4,5)(6,10,8);(1,2)36 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×D3)⋊AGL(1,𝔽9), D3×D32⋊C4, D3×#3773, … |
| maximal normal subgroup of | (C2×D3)⋊AGL(1,𝔽9), D3×D32⋊C4, D3×#3773, … |
| maximal quotient of | Dic6×#157, #11724245, #11724246, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 753);