Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #6189 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D3)⋊Dic9 |
| Sylow | C3×C9 ⋊ C22⋊C4 |
118 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(13,14,15,16)(18,20);(2,3)(4,9,11,10,5,7,6,12,8)(17,18)(19,20)Polycyclic presentation:
2^4,3^3|b^2=c,e^3=g^2,b^a=bd,f^a=f^2,e^b=e^2g,g^b=g^266 conjugacy classes — view the full character table.
| maximal subgroup of | #11720906, #11720954, #11720955, … |
| maximal normal subgroup of | #11720906, #11720954, #11720955, … |
| maximal quotient of | (C2×D3)⋊(C9⋊C8), #11720294, #11720295, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 93);