Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Hall | C3×C5 ⋊ #3263 |
| Sylow | C5 ⋊ #80626 |
| Sylow | C3 ⋊ #10612630 |
692 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|a^2=g,b^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,h^b=h^2,f^c=fg,i^c=i^4,h^d=h^2,i^d=i^4105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 178869);