Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#3752 |
| Fitting | C2×C33×C4 ⋊ C2 |
| Sylow | C33 ⋊ C22⋊C4 |
268 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 144 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,4,3,2)(6,8)(9,10,11)(15,16,17);(5,6)(7,8)(13,14)(16,17);(12,13,14)126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#63836, C3×#63848, C3×#63850, … |
| maximal normal subgroup of | C3×#63836, C3×#63848, C3×#63850, … |
| maximal quotient of | C3×#63632, C3×#63633, C3×#63636, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 490);