Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | D5×ΓL(1,𝔽25) |
| Fitting | C3×C5×C8 ⋊ C22 |
| Hall | C3×C5 ⋊ C2×M16 |
| Sylow | C5 ⋊ C2×ΓL(1,𝔽25) |
| Sylow | C3 ⋊ D5×M16 |
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)(4,5,6,9,7,8,10,11)(12,13,15,16,14);(2,3)(5,8)(9,11);(13,14)(15,16)72 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×ΓL(1,𝔽25), #11751650, #11751653, … |
| maximal normal subgroup of | AGL(1,𝔽5)×ΓL(1,𝔽25), #11751650, #11751653, … |
| maximal quotient of | #11747567, D5×Dic3⋊C8, #11747579, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 320);