Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#4130 |
| Fitting | C2×C3×C4×C5 ⋊ C4 |
| Hall | C3×C5 ⋊ #117 |
| Sylow | C5 ⋊ C3×#117 |
152 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 72 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:
(1,2,3,5,4)(7,11)(10,13)(14,15,16);(6,12,9,8)(7,13,11,10);(2,5,4,3)(6,7)(8,10)(9,11)(12,13)84 conjugacy classes — view the full character table.
| maximal subgroup of | #11746518, #11746519, #11746522, … |
| maximal normal subgroup of | #11746518, #11746519, #11746522, … |
| maximal quotient of | C3×#65678, C3×#65680, C3×#65683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1052);