Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C5×M32 ⋊ C4 |
| Hall | C3×C5 ⋊ #2159 |
| Sylow | C5 ⋊ #71428 |
| Sylow | C3 ⋊ #10604118 |
312 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|a^2=e,b^2=df,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^2,i^a=i^2,c^b=cg,i^e=i^4132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 40330);