Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×D5⋊#104 |
| unambiguous semidirect product | D5⋊(C3×#104) |
| Fitting | C3×C5×#41 ⋊ C4 |
| Hall | C3×C5 ⋊ C2×#104 |
| Sylow | C5 ⋊ C2×C3×#104 |
340 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 340 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) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 3 generators on 16 points:
(1,2,3)(4,5,6,8,7)(9,10)(11,15)(12,14)(13,16);(10,14)(13,15);(5,6,7,8)(10,13,14,15)114 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽5)×#104, #14295624, C3×#10604002, … |
| maximal normal subgroup of | C3×AGL(1,𝔽5)×#104, #14295624, C3×#10604002, … |
| maximal quotient of | C3×D5⋊(D4⋊C8), C3×D5⋊(Q8⋊C8), C3×#10605000, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6520);