Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #625 |
| automorphism | Aut(G) = C25×D32 (order 1152) · Inn(G) = D32 · Out(G) = C25 |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×(C2×D3)⋊Dic3 |
| unambiguous semidirect product | (C2×D3)⋊(C3×Dic3) |
| Sylow | C33 ⋊ C22⋊C4 |
210 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 48 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,4,3,2)(6,8)(9,10,11)(13,14)(15,16,17);(5,6)(7,8)(12,13,14)(16,17)90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×(C2×D3)⋊Dic3, #11722902, #11722904, … |
| maximal normal subgroup of | D3×(C2×D3)⋊Dic3, #11722902, #11722904, … |
| maximal quotient of | C3×(C2×D3)⋊(C3⋊C8), C3×#63558, C3×#63560, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 426);