Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×D3×SD16 |
| Fitting | C3×C5×SD16 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×SD16 |
| Sylow | C3 ⋊ C2×C5×SD16 |
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 3 generators on 16 points:
(2,5)(3,8)(6,7)(9,10,11)(12,13,14,15,16);(1,2,4,7)(3,5,8,6);(10,11)105 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D5×SD16, D3×#4060, D3×#4061, … |
| maximal normal subgroup of | D3×D5×SD16, D3×#4060, D3×#4061, … |
| maximal quotient of | C5×#4758, C5×#4760, C5×#4761, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 792);