Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88543 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C3×C9 ⋊ Q16 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 432 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(13,15,17,23)(14,18,20,27)(16,25,26,22)(19,28,24,21);(2,3)(5,7)(6,10)(8,9)(11,12)(13,14,17,20)(15,21,23,28)(16,24,26,19)(18,25,27,22);(4,5,8,10,12,11,6,9,7)Polycyclic presentation:
2^4,3^3|a^2=d,b^2=d,c^2=d,e^3=g^2,b^a=bc,c^a=cd,e^a=e^2g,f^a=f^2,g^a=g^2,c^b=cd72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3674, #11721203, #11721206, … |
| maximal normal subgroup of | D3×#3674, #11721203, #11721206, … |
| maximal quotient of | #11720525, #11720527, #11720582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 194);