Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×C5×M16 ⋊ C4 |
| Hall | C3×C5 ⋊ C2×#344 |
| Sylow | C5 ⋊ C2×#4556 |
| Sylow | C3 ⋊ #10604763 |
776 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|a^2=e,b^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^2,i^a=i^2,e^b=eg,i^c=i^4,i^e=i^4144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 20521);