Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D3×#687 |
| Hall | C3×C5 ⋊ C2×SD16 |
| Sylow | C5 ⋊ D3×SD16 |
| Sylow | C3 ⋊ C2×#687 |
136 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 44 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)(7,10)(8,13)(11,12)(14,15,16);(2,3)(4,5)(6,7,9,12)(8,10,13,11);(15,16)51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4057, D3×#4058, #11754057, … |
| maximal normal subgroup of | D3×#4057, D3×#4058, #11754057, … |
| maximal quotient of | #11747147, #11747179, #11747199, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 561);