Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | Aut(G) = C2×C3×D3×#120 (order 1152) · Inn(G) = C2×D3 · Out(G) = C22×C3×D4 |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| direct product | C2×C9×#67 |
| Fitting | C23×C3×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×D4 |
194 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 18 points:
(3,4,5)(7,9)(10,14,18,12,17,13,15,11,16);(4,5)(6,7)(8,9);(1,2)162 conjugacy classes — view the full character table.
| maximal subgroup of | #11720332, C9×#806, #11721262, … |
| maximal normal subgroup of | #11720332, C9×#806, #11721262, … |
| maximal quotient of | C2×C9×Dic3⋊C4, C9×#924, C2×C9×(C2×D3)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 375);