Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 20736 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C3×C4×C9 |
| multiplicative | (ℤ/665)ˣ, (ℤ/741)ˣ, (ℤ/777)ˣ, (ℤ/855)ˣ, (ℤ/945)ˣ, (ℤ/988)ˣ, (ℤ/1036)ˣ, (ℤ/1330)ˣ, (ℤ/1332)ˣ, (ℤ/1404)ˣ, (ℤ/1482)ˣ, (ℤ/1554)ˣ, (ℤ/1710)ˣ, (ℤ/1890)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C23×C32 |
| socle, prime radical | C23×C32 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
270 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 432 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3,4)(9,10,11,12,13,14,15,16,17);(5,6)(18,19,20);(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, 400);