Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#4062 |
| Fitting | C3×C5×SD16 ⋊ C2 |
| Hall | C3×C5 ⋊ #135 |
| Sylow | C5 ⋊ C3×#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:
(1,2,4,5,3)(6,16,10,8)(7,14,11,12)(9,15,17,18)(13,21,19,20)(22,23,24);(7,11)(8,15)(9,17)(12,20)(14,21)(16,18);(2,3)(4,5)(6,7)(8,14)(9,13)(10,11)(12,16)(15,20)(17,19)(18,21)84 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#65736, C3×#65737, #11752395, … |
| maximal normal subgroup of | C3×#65736, C3×#65737, #11752395, … |
| maximal quotient of | C3×#65045, C3×#65052, C3×#65057, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 709);