Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1385 |
| Sylow | C5 ⋊ #67820 |
| Sylow | C3 ⋊ #10598222 |
248 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=d,b^2=e,c^2=f,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,h^a=h^2,d^b=dg,i^b=i^4192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 4626);