Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #2103 |
| Sylow | C5 ⋊ #69016 |
| Sylow | C3 ⋊ #10599809 |
296 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=d,b^2=de,c^2=d,d^2=g,f^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^2,i^a=i^4,c^b=cf,d^b=dg,e^b=eg,f^b=fg,h^c=h^2,i^c=i^4180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 38167);