Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#4983 |
| Hall | C3×C5 ⋊ #398 |
| Sylow | C3 ⋊ C5×#398 |
300 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 960 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7,8)(10,12)(13,14)(15,16)(17,19,20,23)(18,22,21,24);(13,14,15,16)(18,21)(22,24);(7,8)(9,10)(11,12)(13,14,15,16)(17,18)(19,22)(20,21)(23,24)210 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#71166, C5×#71174, #14288340, … |
| maximal normal subgroup of | C5×#71166, C5×#71174, #14288340, … |
| maximal quotient of | C5×#71566, C5×#69409, C5×#69413, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4677);