Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#4070 |
| Hall | C3×C5 ⋊ C22⋊Q8 |
| Sylow | C5 ⋊ C3×C22⋊Q8 |
148 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 74 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)(18,19,20);(10,17,13,12)(11,16,15,14);(2,3)(4,5)(6,7)(8,9)(10,15,13,11)(12,14,17,16)138 conjugacy classes — view the full character table.
| maximal subgroup of | #11745960, #11745961, C3×#64672, … |
| maximal normal subgroup of | #11745960, #11745961, C3×#64672, … |
| maximal quotient of | C3×#65217, C3×#65218, C3×#65222, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 717);