Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#806 |
| Fitting | C3×C5×C22⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ #99 |
| Sylow | C3 ⋊ C5×#99 |
104 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 38 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 — 2 generators on 16 points:
(1,2,3)(4,6)(5,8,9,10)(7,11)(12,13,14,15,16);(2,3)(4,5)(6,10)(7,9)(8,11)105 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#806, #11747128, #11747129, … |
| maximal normal subgroup of | D5×#806, #11747128, #11747129, … |
| maximal quotient of | C5×#4451, C5×#4452, C5×#4467, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 125);