Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×(C2×D3)⋊C4 |
| unambiguous semidirect product | (C2×D3)⋊(C32×C4) |
| Fitting | C2×C33×C4 ⋊ C2 |
| Sylow | C33 ⋊ C22⋊C4 |
268 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 102 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 — 2 generators on 17 points:
(4,5,6)(7,8,9)(10,13,12,11)(15,17);(1,2,3)(8,9)(14,15)(16,17)162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#63852, C3×#63853, C3×#63854, … |
| maximal normal subgroup of | C3×#63852, C3×#63853, C3×#63854, … |
| maximal quotient of | C32×#805, C32×#806, C32×#809, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 474);