Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#4039 |
| Fitting | C3×C5×C4⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ C4×D4 |
| Sylow | C5 ⋊ C3×C4×D4 |
188 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 86 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:
(1,2,4,5,3)(6,9,8,7)(11,13)(14,15,16);(10,13,12,11);(2,3)(4,5)(11,13)120 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#64871, #11746742, #11747216, … |
| maximal normal subgroup of | C3×#64871, #11746742, #11747216, … |
| maximal quotient of | C3×#64943, C3×#64954, C3×#64955, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 686);