Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C5×#5135 |
| Fitting | C2×C3×C5×M16 ⋊ C2 |
| Hall | C3×C5 ⋊ #469 |
| Sylow | C3 ⋊ C5×#469 |
260 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 86 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)(14,19)(17,20);(13,14,18,20,16,19,15,17);(7,8)(9,10)(11,12)(14,17)(15,18)(19,20)180 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#67481, C5×#67534, #14277994, … |
| maximal normal subgroup of | C5×#67481, C5×#67534, #14277994, … |
| maximal quotient of | C5×#70868, C5×#70959, C5×#70873, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4829);