Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#4075 |
| Fitting | C22×C3×C4×C5 ⋊ C2 |
| Hall | C3×C5 ⋊ #123 |
| Sylow | C5 ⋊ C3×#123 |
156 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,4,5,3)(7,9)(10,16,13,12)(11,17,14,15)(18,19,20);(11,14)(15,17);(2,3)(4,5)(6,7)(8,9)(10,11)(12,15)(13,14)(16,17)138 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#64916, #11746787, #11748939, … |
| maximal normal subgroup of | C3×#64916, #11746787, #11748939, … |
| maximal quotient of | C3×#65222, C3×#65229, C3×#65241, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 722);