Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#4097 |
| 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)(7,12)(8,15)(9,17)(11,18)(13,14)(19,20)(22,23,24);(6,8)(7,11)(9,16)(10,15)(12,20)(13,18)(14,19)(17,21);(2,3)(4,5)(6,14,10,7)(8,19,15,11)(9,13,17,12)(16,18,21,20)93 conjugacy classes — view the full character table.
| maximal subgroup of | #11749416, #11749424, #11749450, … |
| maximal normal subgroup of | #11749416, #11749424, #11749450, … |
| maximal quotient of | C3×#65284, C3×#65285, C3×#65293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 744);