Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| automorphism | Aut(G) = C22×C3×D3×D4 (order 576) · Inn(G) = C22×D3 · Out(G) = C23×C3 |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| direct product | D3×D4×C9 |
| Fitting | C3×D4×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×D4 |
178 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 16 points:
(2,4)(5,6,7)(8,9,11,10,12,14,13,15,16);(1,2)(3,4);(6,7)135 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3672, D3×#3673, #11721168, … |
| maximal normal subgroup of | D3×#3672, D3×#3673, #11721168, … |
| maximal quotient of | C9×#878, D3×C9×C22⋊C4, C9×#67⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 358);