Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#4991 |
| Fitting | C2×C3×C5×C4⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ #394 |
| Sylow | C3 ⋊ C5×#394 |
476 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3,4,5)(6,7,8)(10,12)(17,18,19,20);(13,14,15,16)(18,20);(7,8)(9,10)(11,12)(14,16)210 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#67493, C5×#67456, #14278132, … |
| maximal normal subgroup of | C5×#67493, C5×#67456, #14278132, … |
| maximal quotient of | C5×#69426, C5×#71570, C5×#69429, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4685);