Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C3)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×((C3⋊D3)⋊C3)⋊C4 |
| derived, Sylow | H(3,𝔽3) ⋊ C22×C4 |
205 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 205 conjugacy classes of subgroups — too many to draw. Only its 61 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:
(1,2)(3,4,5,6)(8,14,12,10,11,15)(9,13);(7,8,10)(9,11,14,13,12,15);(1,2)44 conjugacy classes — view the full character table.
| maximal subgroup of | C4×((C3⋊D3)⋊C3)⋊C4, #11721119, #11721120, … |
| maximal normal subgroup of | C4×((C3⋊D3)⋊C3)⋊C4, #11721119, #11721120, … |
| maximal quotient of | C2×((C3⋊D3)⋊C3)⋊C8, #11721053, #11721054, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 317);