Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | Aut(G) = C22×C3×D3×D4 (order 576) · Inn(G) = C2×D3 · Out(G) = C24×C3 |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C22 |
| direct product | C9×#235 |
| Fitting | C2×C3×C4×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ #41 |
136 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3)(4,5,7,6,8,10,9,11,12)(14,18)(17,20);(13,15,16,19)(14,17,18,20);(2,3)(13,14)(15,17)(16,18)(19,20)162 conjugacy classes — view the full character table.
| maximal subgroup of | #11720300, #11720301, C9×#805, … |
| maximal normal subgroup of | #11720300, #11720301, C9×#805, … |
| maximal quotient of | C4×C9×Dic6, C9×#870, C9×#872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 347);