Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#4088 |
| Fitting | C2×C3×C5×Q8 ⋊ C2 |
| Hall | C3×C5 ⋊ #137 |
| Sylow | C5 ⋊ C3×#137 |
120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 58 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)(6,19,10,9)(7,21,14,12)(8,18,16,15)(11,20,13,17)(22,23,24);(6,16,10,8)(7,13,14,11)(9,15,19,18)(12,17,21,20);(2,3)(4,5)(6,7)(8,11)(9,17)(10,14)(12,18)(13,16)(15,21)(19,20)93 conjugacy classes — view the full character table.
| maximal subgroup of | #11749375, #11749376, #11749377, … |
| maximal normal subgroup of | #11749375, #11749376, #11749377, … |
| maximal quotient of | C3×#65253, C3×#65255, C3×#65256, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 735);