Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of D9 |
| automorphism | Aut(G) = C24×AGL(1,ℤ/9) (order 864) · Inn(G) = D9 · Out(G) = C24×C3 |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C3×C8×D9 |
| Fitting | C3×C8×C9 ⋊ C2 |
| derived | C9 ⋊ C2×C3×C8 |
| Sylow | C3×C9 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C8 | D9 |
| commutator, hypocenter | C9 | C2×C3×C8 |
| Frattini | C3×C4 | C2×C3×D3 |
| Fitting | C3×C8×C9 | C2 |
| socle | C2×C32 | C4×D3 |
| prime radical | C2×C3×D9 | C4 |
| cosocle | C4×C9 | C22×C3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C3×C8 | |
74 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,3)(5,7)(6,10)(8,11)(9,12);(4,9,7,6,11,8,10,5,12)(13,17,19,14,16,20,15,18)144 conjugacy classes — view the full character table.
| maximal subgroup of | D9×C3⋊C16, #11720230, C3×C16×D9, … |
| maximal normal subgroup of | D9×C3⋊C16, #11720230, C3×C16×D9, … |
| maximal quotient of | C3×C16×D9, C3×#63357, C3×C8×Dic9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 105);