Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of GO+(4,𝔽2) |
| automorphism | Aut(G) = C23×GO+(4,𝔽2) (order 576) · Inn(G) = GO+(4,𝔽2) · Out(G) = C23 |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×D32⋊C4 |
| unambiguous semidirect product | D32⋊(C3×C4) |
| Sylow | C33 ⋊ C22⋊C4 |
132 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 26 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) = 24 |
A minimal faithful permutation representation — 2 generators on 13 points:
(1,2,3)(4,6)(5,8,9)(10,13,12,11);(4,5)(6,9)(7,8)54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D32⋊C4, (D32⋊D3)⋊C4, #11724113, … |
| maximal normal subgroup of | D3×D32⋊C4, (D32⋊D3)⋊C4, #11724113, … |
| maximal quotient of | C3×D32⋊C8, C3×#63727, C3×#63728, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 574);