Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Hall | C3×C5 ⋊ #2932 |
| Sylow | C5 ⋊ #79480 |
| Sylow | C3 ⋊ #10617310 |
968 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|a^2=f,c^2=f,f^2=g,b^a=be,c^a=cg,d^a=dg,h^a=h^2,i^a=i^3,d^b=dg,h^c=h^2,i^c=i^3,h^d=h^2,i^d=i^4,i^f=i^496 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 141104);