Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#4035 |
| Hall | C3×C5 ⋊ #125 |
| Sylow | C5 ⋊ C3×#125 |
112 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 62 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) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,4,5,3)(7,11)(10,13)(14,20,17,16)(15,21,19,18)(22,23,24);(6,12,9,8)(7,13,11,10)(16,20)(18,21);(2,3)(4,5)(6,7)(8,10)(9,11)(12,13)(14,19,17,15)(16,21,20,18)102 conjugacy classes — view the full character table.
| maximal subgroup of | #11753308, #11753309, #11753314, … |
| maximal normal subgroup of | #11753308, #11753309, #11753314, … |
| maximal quotient of | C3×#64936, C3×#64939, C3×#64941, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 682);