Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×C4×D9 |
| Fitting | C2×C3×C4×C9 ⋊ C2 |
| derived | C9 ⋊ C22×C3×C4 |
| Sylow | C3×C9 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C4 | D9 |
| commutator, hypocenter | C9 | C22×C3×C4 |
| Frattini | C2×C3 | C22×C3×D3 |
| Fitting | C2×C3×C4×C9 | C2 |
| socle | C22×C32 | C2×D3 |
| prime radical | C22×C3×D9 | C2 |
| cosocle | C2×C9 | C23×C3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C2×C3×C4 | |
178 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2)(3,4,5)(11,13)(12,16)(14,17)(15,18);(6,7,8,9)(10,15,13,12,17,14,16,11,18);(1,2)144 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×D9)⋊(C3⋊C8), C3×(C2×D9)⋊C8, C2×D9×C3⋊C8, … |
| maximal normal subgroup of | (C2×D9)⋊(C3⋊C8), C3×(C2×D9)⋊C8, C2×D9×C3⋊C8, … |
| maximal quotient of | C3×C4×Dic18, C3×C42×D9, C3×#63434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 342);