Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C3×#638 |
| Fitting | C23×C33 ⋊ C2 |
| Sylow | C33 ⋊ C2×D4 |
452 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 15 points:
(3,4,5)(9,10,11)(13,15);(1,2)(4,5)(7,8)(12,13)(14,15);(1,2)(6,7,8)126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#63581, #11722063, #11722083, … |
| maximal normal subgroup of | C3×#63581, #11722063, #11722083, … |
| maximal quotient of | C2×C3×#3750, C3×#64133, C2×C3×#3752, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 719);