Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#3797 |
| Sylow | C33 ⋊ C2×Q8 |
198 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 68 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 — 3 generators on 17 points:
(1,8,5,4)(2,7,3,6)(9,10,11)(12,13,14)(15,16,17);(1,2,5,3)(4,7,8,6)(13,14);(1,3,5,2)(4,6,8,7)(16,17)72 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#63728, C3×#63730, #11722756, … |
| maximal normal subgroup of | C3×#63728, C3×#63730, #11722756, … |
| maximal quotient of | C3×#63838, C3×#63839, C3×#63843, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 645);