Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of (C3⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C4×(C3⋊D3)⋊C3 |
| unambiguous semidirect product | (C2×C4×C3⋊D3)⋊C3 |
| Fitting | C2×C4×H(3,𝔽3) ⋊ C2 |
| derived | C32 ⋊ C22×C3×C4 |
| Sylow | H(3,𝔽3) ⋊ C22×C4 |
205 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 205 conjugacy classes of subgroups — too many to draw. Only its 78 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:
(8,13,15,10,11,14)(9,12);(3,4,5,6)(7,8,10)(9,11,14)(12,15,13);(1,2)80 conjugacy classes — view the full character table.
| maximal subgroup of | #11720317, #63647⋊C3, C2×((C3⋊D3)⋊C3)⋊C8, … |
| maximal normal subgroup of | #11720317, #63647⋊C3, C2×((C3⋊D3)⋊C3)⋊C8, … |
| maximal quotient of | C4×#634⋊C3, C42×(C3⋊D3)⋊C3, #64081⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 349);