Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of D3 |
| automorphism | Aut(G) = C22×C3×C4×D3 (order 288) · Inn(G) = D3 · Out(G) = C22×C3×C4 |
| homology | Abelianization (H1) = C9×C16 · Schur multiplier (H2) = C1 |
| direct product | C9×C3⋊C16 |
| unambiguous semidirect product | C3⋊(C9×C16) |
| derived | C3 ⋊ C9×C16 |
| Sylow | C3×C9 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8×C9 | D3 |
| commutator, hypocenter | C3 | C9×C16 |
| Frattini | C3×C8 | C3×D3 |
| Fitting | C3×C8×C9 | C2 |
| socle, prime radical | C2×C32 | C3×C8 |
| cosocle | C32×C8 | C2×C3 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C8×C9 | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 28 points:
(2,3)(4,5,7,6,8,10,9,11,12)(13,20,15,25,16,26,21,28,17,14,22,18,23,19,27,24);(1,2,3)216 conjugacy classes — view the full character table.
| maximal subgroup of | D9×C3⋊C16, (C3⋊D9)⋊C16, #11720230, … |
| maximal normal subgroup of | D9×C3⋊C16, (C3⋊D9)⋊C16, #11720230, … |
| maximal quotient of | C9×C3⋊C32, C2×C9×C3⋊C16, C9×C9⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 29);