Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#64864 |
| Fitting | C3×C5×C22⋊C4 ⋊ C4 |
| Hall | C3×C5 ⋊ AΣL(1,𝔽16) |
| Sylow | C5 ⋊ C3×AΣL(1,𝔽16) |
188 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 36 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)(4,5,6,8,7)(10,13,14,15)(11,16);(5,6,7,8)(9,10)(11,15,16,13)(12,14)69 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#64864, C3×D5⋊AΣL(1,𝔽16), D3×#64864, … |
| maximal normal subgroup of | C2×C3×#64864, C3×D5⋊AΣL(1,𝔽16), D3×#64864, … |
| maximal quotient of | C3×#10598702, C3×#10598704, C3×#10598495, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 836);