Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#4038 |
| Fitting | C3×C5×C4⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ #117 |
| Sylow | C5 ⋊ C3×#117 |
152 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 82 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)(6,9,8,7)(11,15)(12,16)(18,19,20);(10,16,13,12)(11,17,15,14);(2,3)(4,5)(10,11)(12,14)(13,15)(16,17)120 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#64875, #11746746, #11747166, … |
| maximal normal subgroup of | C3×#64875, #11746746, #11747166, … |
| maximal quotient of | C3×#64937, C3×#64940, C3×#64944, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 685);