Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1500 |
| Sylow | C5 ⋊ #68308 |
| Sylow | C3 ⋊ #10600224 |
476 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=e,c^2=f,d^2=g,b^a=bd,d^a=df,d^b=dg,e^b=efg,h^b=h^2,i^b=i^4,h^c=h^2177 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 8470);