Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#4837 |
| Fitting | C3×C5×C4⋊C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #423 |
| Sylow | C3 ⋊ C5×#423 |
252 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 252 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) = 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)(13,14,15,18,16,17,19,20);(9,10,11,12);(7,8)(14,17)(18,20)240 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#68172, #14282084, C5×#68236, … |
| maximal normal subgroup of | C5×#68172, #14282084, C5×#68236, … |
| maximal quotient of | C5×#68529, C5×#68569, C5×#68530, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4531);