Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #6226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C4⋊(C3⋊Dic9) |
| Sylow | C3×C9 ⋊ C4⋊C4 |
130 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)(17,18,19,20);(2,3)(5,7)(6,10)(8,9)(11,12)(13,14,15,16)(18,20);(4,9,11,10,5,7,6,12,8)Polycyclic presentation:
2^4,3^3|a^2=c,b^2=d,e^3=g^2,b^a=bd,e^a=e^2g,f^a=f^2,g^a=g^2114 conjugacy classes — view the full character table.
| maximal subgroup of | #11720262, #11720264, #11720276, … |
| maximal normal subgroup of | #11720262, #11720264, #11720276, … |
| maximal quotient of | C4⋊(C3⋊(C9⋊C8)), #11720535, #11720540, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 182);