Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4⋊C4×D15 |
| Fitting | C3×C5×C4⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×C4⋊C4 |
| Sylow | C5 ⋊ D3×C4⋊C4 |
| Sylow | C3 ⋊ D5×C4⋊C4 |
184 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 71 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) = 240 |
A minimal faithful permutation representation — 3 generators on 16 points:
(2,3)(4,5)(7,8);(1,2,4,5,3)(6,7,8)(13,14,15,16);(9,10,11,12)(14,16)90 conjugacy classes — view the full character table.
| maximal subgroup of | #11747330, #11747331, #11747332, … |
| maximal normal subgroup of | #11747330, #11747331, #11747332, … |
| maximal quotient of | #11750748, #11750750, #11750751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 856);