Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88521 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C3×C8×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ D8 |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3)(13,14,18,20,16,19,15,17);(2,3)(5,7)(6,10)(8,9)(11,12)(14,17)(15,18)(19,20);(4,5,8,10,12,11,6,9,7)Polycyclic presentation:
2^4,3^3|b^2=cd,c^2=d,e^3=g^2,b^a=bc,c^a=cd,e^a=e^2g,f^a=f^2,g^a=g^2111 conjugacy classes — view the full character table.
| maximal subgroup of | #11720232, #11720234, #11720239, … |
| maximal normal subgroup of | #11720232, #11720234, #11720239, … |
| maximal quotient of | #11720507, #11720508, #11720509, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 172);