Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C3)⋊C2 |
| automorphism | Aut(G) = C2×#11722315 (order 1728) · Inn(G) = ((C3⋊D3)⋊C3)⋊C2 · Out(G) = C2×D4 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×((C3⋊D3)⋊C3)⋊C2 |
| Fitting | C4×H(3,𝔽3) ⋊ C22 |
| derived, Sylow | H(3,𝔽3) ⋊ C22×C4 |
205 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 205 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 36 |
A minimal faithful permutation representation — 3 generators on 13 points:
(2,8,6,4,5,9)(3,7);(1,2,4)(3,5,8,7,6,9);(10,11,12,13)44 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 300);