Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C8 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×C3⋊C8 |
| unambiguous semidirect product | (C2×C3)⋊(C32×C8) |
| derived | C3 ⋊ C2×C32×C8 |
| Sylow | C33 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C4 | D3 |
| commutator, hypocenter | C3 | C2×C32×C8 |
| Frattini | C4 | C2×C32×D3 |
| Fitting | C2×C33×C4 | C2 |
| socle, prime radical | C22×C33 | C4 |
| cosocle | C3×C4 | C22×C32 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C32×C4 | |
196 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 19 points:
(4,5)(6,7,8)(12,13,14,16,15,17,18,19);(1,2)(3,4,5)(9,10,11)216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic3×C3⋊C8, C3×#63553, C3×#63554, … |
| maximal normal subgroup of | C3×Dic3×C3⋊C8, C3×#63553, C3×#63554, … |
| maximal quotient of | C32×C4×C3⋊C8, C32×C4⋊(C3⋊C8), C2×C32×C3⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 469);