Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#4061 |
| Fitting | C3×C5×SD16 ⋊ C2 |
| Hall | C3×C5 ⋊ #137 |
| Sylow | C5 ⋊ C3×#137 |
120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 120 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:
(1,2,4,5,3)(7,12)(8,14)(9,17)(11,18)(15,16)(19,21)(22,23,24);(6,16,10,8)(7,19,12,11)(9,15,17,14)(13,18,20,21);(2,3)(4,5)(6,7)(8,11)(9,13)(10,12)(14,21)(15,18)(16,19)(17,20)75 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4061, #11754070, #11754074, … |
| maximal normal subgroup of | D3×#4061, #11754070, #11754074, … |
| maximal quotient of | C3×#65046, C3×#65048, C3×#65054, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 708);