Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #625 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#3722 |
| Sylow | C33 ⋊ C22⋊C4 |
210 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,4,3)(6,8)(9,10,11)(13,14)(15,16,17);(1,3,4,2)(5,8,7,6)(12,13,14)(16,17)90 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#63738, #11722770, D3×#3722, … |
| maximal normal subgroup of | C3×#63738, #11722770, D3×#3722, … |
| maximal quotient of | C3×#63557, C3×#63559, C3×#63561, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 427);