Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23 |
| direct product | C3×#65014 |
| Fitting | C3×C5×C22⋊C8 ⋊ C2 |
| Hall | C3×C5 ⋊ C8×D4 |
| Sylow | C5 ⋊ C3×C8×D4 |
268 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3)(4,5,7,8,6)(10,12)(13,14,15,17,16,18,19,20);(9,10)(11,12);(5,6)(7,8)(10,12)240 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10603903, #14314983, C3×#10603904, … |
| maximal normal subgroup of | C3×#10603903, #14314983, C3×#10603904, … |
| maximal quotient of | C3×#10598941, C3×#10599005, C3×#10598942, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3817);