Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D5⋊#833 |
| Hall | C3×C5 ⋊ C2×#100 |
| Sylow | C5 ⋊ C2×#833 |
| Sylow | C3 ⋊ D5⋊#100 |
372 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 89 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^2=f,d^2=f,c^a=ce,e^a=ef,g^a=g^2,h^a=h^3,c^b=cf,d^c=df,h^d=h^472 conjugacy classes — view the full character table.
| maximal subgroup of | #14279052, #14279065, #100×ΓL(1,𝔽16), … |
| maximal normal subgroup of | #14279052, #14279065, #100×ΓL(1,𝔽16), … |
| maximal quotient of | D5⋊#4525, #14280902, #14280904, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6632);