Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Hall | C3×C5 ⋊ C4×C32 |
| Sylow | C5 ⋊ C4×C3⋊C32 |
| Sylow | C3 ⋊ #10598652 |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1920 |
Polycyclic presentation:
2^7,3,5|a^2=c,b^2=d,c^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, 4889);