Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#911 |
| Fitting | C3×C5×D8 ⋊ C2 |
| Hall | C3×C5 ⋊ AGL(1,ℤ/8) |
| Sylow | C3 ⋊ C5×AGL(1,ℤ/8) |
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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:
(1,2,3)(4,5)(6,11)(7,8)(9,10)(12,13,14,15,16);(5,9)(6,10)(8,11);(2,3)(5,8)(9,11)90 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#911, #11754047, #11754049, … |
| maximal normal subgroup of | D5×#911, #11754047, #11754049, … |
| maximal quotient of | C5×#4757, C5×#4761, C5×#4762, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 790);