Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#4057 |
| Fitting | C3×C5×D8 ⋊ C2 |
| Hall | C3×C5 ⋊ AGL(1,ℤ/8) |
| Sylow | C5 ⋊ C3×AGL(1,ℤ/8) |
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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:
(1,2,4,5,3)(6,7)(8,13)(9,10)(11,12)(14,15,16);(7,11)(8,12)(10,13);(2,3)(4,5)(7,10)(11,13)75 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4057, #11754047, #11754049, … |
| maximal normal subgroup of | D3×#4057, #11754047, #11754049, … |
| maximal quotient of | C3×#65046, C3×#65050, C3×#65051, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 704);