Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C3⋊D9)⋊Q8 |
| Sylow | C3×C9 ⋊ C2×Q8 |
130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3)(4,9,11,10,5,7,6,12,8)(13,16,17,20)(14,18,15,19);(5,7)(6,10)(8,9)(11,12)(13,15,17,14)(16,18,20,19);(2,3)(13,14,17,15)(16,19,20,18)Polycyclic presentation:
2^4,3^3|a^2=d,b^2=d,c^2=d,e^3=g^2,c^a=cd,f^a=f^2,c^b=cd,e^b=e^2g,g^b=g^251 conjugacy classes — view the full character table.
| maximal subgroup of | #11720817, #11720825, #11720829, … |
| maximal normal subgroup of | #11720817, #11720825, #11720829, … |
| maximal quotient of | #11720902, #11720903, #11720904, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 283);