Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | Aut(G) = C25×AGL(1,ℤ/9) (order 1728) · Inn(G) = C2×D9 · Out(G) = C24×C3 |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×(C2×D9)⋊C4 |
| Fitting | C2×C3×C4×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C22⋊C4 |
118 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 46 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)(4,9,11,10,5,7,6,12,8)(13,16,15,14)(18,20);(5,7)(6,10)(8,9)(11,12)(17,18)(19,20)126 conjugacy classes — view the full character table.
| maximal subgroup of | #11720940, #11720941, #11720942, … |
| maximal normal subgroup of | #11720940, #11720941, #11720942, … |
| maximal quotient of | C3×#63364, C3×#63365, C3×#63368, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 134);