Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#4471 |
| Fitting | C3×C5×#99 ⋊ C2 |
| Hall | C3×C5 ⋊ AΣL(1,𝔽16) |
| Sylow | C3 ⋊ C5×AΣL(1,𝔽16) |
188 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 16 points:
(1,2,3,4,5)(6,7,8)(9,10)(11,15,16,13)(12,14);(7,8)(10,13)(14,15)120 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×AΣL(1,𝔽16), C2×C5×#4471, D5×#4471, … |
| maximal normal subgroup of | C5×D3×AΣL(1,𝔽16), C2×C5×#4471, D5×#4471, … |
| maximal quotient of | C5×#67444, C5×#67446, C5×#67489, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 365);