Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×D5×SD16 |
| Fitting | C3×C5×SD16 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×SD16 |
| Sylow | C5 ⋊ C2×C3×SD16 |
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 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)(3,8)(6,7)(9,10,12,13,11)(14,15,16);(1,7,4,2)(3,6,8,5);(10,11)(12,13)84 conjugacy classes — view the full character table.
| maximal subgroup of | C3×SD16×AGL(1,𝔽5), C3×#65735, SD16×ΓL(1,𝔽16), … |
| maximal normal subgroup of | C3×SD16×AGL(1,𝔽5), C3×#65735, SD16×ΓL(1,𝔽16), … |
| maximal quotient of | C3×#65047, C3×#65049, C3×#65050, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 706);