Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D5⋊#4535 |
| Hall | C3×C5 ⋊ C2×Q8⋊C8 |
| Sylow | C5 ⋊ C2×#4535 |
| Sylow | C3 ⋊ D5⋊(Q8⋊C8) |
560 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|a^2=e,b^2=f,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^2,i^a=i^2,d^b=df,i^c=i^4,i^e=i^4156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 7226);