Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2177280 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C24×C3×C9 |
| multiplicative | (ℤ/1064)ˣ, (ℤ/1368)ˣ, (ℤ/1512)ˣ, (ℤ/1596)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C24×C32 |
| socle, prime radical | C24×C32 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
670 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 432 |
A minimal faithful permutation representation — 4 generators on 20 points:
(1,2)(9,10,11,12,13,14,15,16,17);(3,4)(18,19,20);(5,6);(7,8)432 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 562);