Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88421 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3×C9 ⋊ SD16 |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,3)(5,7)(6,10)(8,9)(11,12)(13,14,16,18)(15,20,19,17);(2,3)(4,5,8,10,12,11,6,9,7)(14,17)(15,19)(18,20)Polycyclic presentation:
2^4,3^3|b^2=d,c^2=d,e^3=g^2,b^a=bc,c^a=cd,f^a=f^2,c^b=cd,e^b=e^2g,g^b=g^248 conjugacy classes — view the full character table.
| maximal subgroup of | #11720817, #11720819, #11720824, … |
| maximal normal subgroup of | #11720817, #11720819, #11720824, … |
| maximal quotient of | #11720265, #11720268, #11720294, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 70);