Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#916 |
| Fitting | C3×C5×SD16 ⋊ C2 |
| Hall | C3×C5 ⋊ #135 |
| Sylow | C3 ⋊ C5×#135 |
124 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 124 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) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,6,8,14)(5,10,9,12)(7,16,15,13)(11,18,17,19)(20,21,22,23,24);(5,9)(6,13)(7,15)(10,18)(12,19)(14,16);(2,3)(4,5)(6,12)(7,11)(8,9)(10,14)(13,18)(15,17)(16,19)105 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#916, #11754073, #11754075, … |
| maximal normal subgroup of | D5×#916, #11754073, #11754075, … |
| maximal quotient of | C5×#4756, C5×#4763, C5×#4768, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 795);