Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C5×#5151 |
| Fitting | C2×C3×C5×D8 ⋊ C2 |
| Hall | C3×C5 ⋊ #493 |
| Sylow | C3 ⋊ C5×#493 |
324 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 94 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)(14,17)(15,20)(18,19);(10,12)(13,14)(15,17)(16,19)(18,20);(7,8)(9,10,11,12)180 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#71462, C5×#69202, #14317041, … |
| maximal normal subgroup of | C5×#71462, C5×#69202, #14317041, … |
| maximal quotient of | C5×#71274, C5×#71180, C5×#71359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4845);