Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D5⋊(C3⋊C64) |
| derived, Hall | C3×C5 ⋊ C2×C64 |
| Sylow | C5 ⋊ C2×C3⋊C64 |
| Sylow | C3 ⋊ D5⋊C64 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^2,i^a=i^2,i^b=i^4,i^c=i^4288 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 5482);