Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#3828 |
| Fitting | C2×C33×C4 ⋊ C2 |
| Sylow | C33 ⋊ #41 |
304 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 72 |
A minimal faithful permutation representation — 3 generators on 17 points:
(2,6)(5,8)(9,10,11)(15,16,17);(1,7,4,3)(2,8,6,5)(12,13,14);(1,2)(3,5)(4,6)(7,8)(13,14)(16,17)126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#63570, #11722045, #11722046, … |
| maximal normal subgroup of | C3×#63570, #11722045, #11722046, … |
| maximal quotient of | C3×C4×#634, C3×#64079, C3×#64081, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 713);