Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1289 |
| Sylow | C5 ⋊ #67676 |
| Sylow | C3 ⋊ #10598116 |
456 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=d,b^2=e,c^2=fg,e^2=fg,b^a=bc,c^a=cf,e^a=efg,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, 2743);