Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#937 |
| Fitting | C2×C3×C5×D4 ⋊ C2 |
| Hall | C3×C5 ⋊ #120 |
| Sylow | C3 ⋊ C5×#120 |
260 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 74 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)(5,7)(9,11)(12,13,14,15,16);(8,9)(10,11);(2,3)(4,5)(6,7)120 conjugacy classes — view the full character table.
| maximal subgroup of | #11745996, #11745997, C5×#4471, … |
| maximal normal subgroup of | #11745996, #11745997, C5×#4471, … |
| maximal quotient of | C5×#4946, C5×#4947, C5×#4955, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 816);