Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C22×C33 |
| direct product | C22×C32×A4 |
| Fitting, socle | C24×C32 ⋊ C3 |
| derived | C22 ⋊ C22×C33 |
| Sylow | C24 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32 | A4 |
| commutator, cosocle, hypocenter | C22 | C22×C33 |
| Frattini | C1 | G |
| Fitting, socle | C24×C32 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C22×C32 | |
394 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 108 |
A minimal faithful permutation representation — 3 generators on 14 points:
(3,4)(12,13,14);(1,2)(5,6,7)(11,14)(12,13);(8,9,10)144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 770);