Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of D3 |
| automorphism | Aut(G) = C2×C3×D3×#120 (order 1152) · Inn(G) = D3 · Out(G) = C2×C3×#120 |
| homology | Abelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C23 |
| direct product | C2×C4×D3×C9 |
| Fitting | C2×C3×C4×C9 ⋊ C2 |
| derived | C3 ⋊ C22×C4×C9 |
| Sylow | C3×C9 ⋊ C22×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)(4,5)(10,17,16,12,11,18,15,14,13);(3,4,5)(6,7,8,9);(1,2)216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 345);