Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | Aut(G) = C25×C3×D3 (order 576) · Inn(G) = C2×D3 · Out(G) = C24×C3 |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C22 |
| direct product | C9×(C2×D3)⋊C4 |
| unambiguous semidirect product | (C2×D3)⋊(C4×C9) |
| Fitting | C2×C3×C4×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C22⋊C4 |
118 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,3)(4,5,7,6,8,10,9,11,12)(13,14,15,16)(18,20);(2,3)(17,18)(19,20)162 conjugacy classes — view the full character table.
| maximal subgroup of | #11720956, #11720957, #11720958, … |
| maximal normal subgroup of | #11720956, #11720957, #11720958, … |
| maximal quotient of | C9×#805, C9×#806, C9×#809, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 135);