Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#896 |
| Fitting | C3×C5×C4⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ C22⋊Q8 |
| Sylow | C3 ⋊ C5×C22⋊Q8 |
148 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 148 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)(12,15)(16,17,18,19,20);(5,7)(8,10,11,14)(9,12,13,15);(2,3)(5,7)(8,9)(10,12)(11,13)(14,15)120 conjugacy classes — view the full character table.
| maximal subgroup of | #11753319, #11753320, #11753339, … |
| maximal normal subgroup of | #11753319, #11753320, #11753339, … |
| maximal quotient of | C5×#4646, C5×#4652, C5×#4657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 775);