Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D5⋊#806 |
| Hall | C3×C5 ⋊ C2×#99 |
| Sylow | C5 ⋊ C2×#806 |
| Sylow | C3 ⋊ D5⋊#99 |
420 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^6,3,5|a^2=d,b^a=be,e^a=ef,h^a=h^2,c^b=cf,d^b=df,g^b=g^2,h^d=h^460 conjugacy classes — view the full character table.
| maximal subgroup of | #14295409, AGL(1,𝔽5)×#806, #14297149, … |
| maximal normal subgroup of | #14295409, AGL(1,𝔽5)×#806, #14297149, … |
| maximal quotient of | D5⋊#4468, D5⋊#4469, #14280886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6200);