Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×D5×M16 |
| Fitting | C3×C5×M16 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×M16 |
| Sylow | C5 ⋊ C2×C3×M16 |
136 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 3 generators on 16 points:
(2,5)(6,8)(9,10,12,13,11)(14,15,16);(1,6,7,2,4,8,3,5);(10,11)(12,13)120 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#64899, C3×#64900, C3×#64901, … |
| maximal normal subgroup of | C3×#64899, C3×#64900, C3×#64901, … |
| maximal quotient of | C3×#64990, C3×D5×#97, C3×#64994, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 699);