Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#4096 |
| Fitting | C3×C5×#41 ⋊ C2 |
| Hall | C3×C5 ⋊ #135 |
| Sylow | C5 ⋊ C3×#135 |
124 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 124 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)(9,17)(11,18)(13,14)(15,21)(19,20)(22,23,24);(6,16,10,8)(7,20,14,11)(9,21,17,15)(12,19,13,18);(2,3)(4,5)(6,7)(8,11)(9,12)(10,14)(13,17)(15,18)(16,20)(19,21)102 conjugacy classes — view the full character table.
| maximal subgroup of | #11749436, #11749437, #11749440, … |
| maximal normal subgroup of | #11749436, #11749437, #11749440, … |
| maximal quotient of | C3×#65285, C3×#65287, C3×#65291, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 743);