Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×C5×#533 ⋊ C2 |
| Hall | C3×C5 ⋊ #2031 |
| Sylow | C5 ⋊ #71842 |
| Sylow | C3 ⋊ #10602635 |
488 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|a^2=d,b^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,d^c=dg,e^c=eg,f^c=fg,h^c=h^2,i^c=i^4222 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 34715);