Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#886 |
| Fitting | C3×C5×C22⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ #123 |
| Sylow | C3 ⋊ C5×#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:
(1,2,3)(4,5,6,7)(9,13)(10,15)(16,17,18,19,20);(8,10)(9,12)(11,15)(13,14);(2,3)(5,7)(8,9)(10,14)(11,13)(12,15)120 conjugacy classes — view the full character table.
| maximal subgroup of | #11747135, C5×#4742, #11752790, … |
| maximal normal subgroup of | #11747135, C5×#4742, #11752790, … |
| maximal quotient of | C5×#4653, C5×#4659, C5×#4661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 765);