Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C3×C5×#137 ⋊ C22 |
| Hall | C3×C5 ⋊ #3586 |
| Sylow | C5 ⋊ #87211 |
| Sylow | C3 ⋊ #10619102 |
2824 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|b^2=g,f^2=g,b^a=bf,e^a=eg,f^a=fg,h^a=h^2,i^a=i^4,f^b=fg,d^c=dg,i^c=i^4,i^d=i^4,h^e=h^2129 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236155);