Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C23 |
| direct product | C3×(C2×AGL(1,𝔽5))⋊C8 |
| unambiguous semidirect product | (C2×AGL(1,𝔽5))⋊(C3×C8) |
| Fitting | C2×C3×C5×C8 ⋊ C4 |
| Hall | C3×C5 ⋊ #336 |
| Sylow | C5 ⋊ C3×#336 |
236 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 240 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,3)(4,5,6,8,7)(10,12)(13,14,15,17,16,18,19,20);(5,6,7,8)(9,10)(11,12)168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 864);