Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C3×C5×#125 ⋊ C22 |
| Hall | C3×C5 ⋊ C2×#539 |
| Sylow | C5 ⋊ D3×#539 |
| Sylow | C3 ⋊ D5×#539 |
2288 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|b^2=g,c^2=f,b^a=bf,c^a=cg,d^a=df,h^a=h^2,c^b=cf,h^b=h^2,h^d=h^2,h^e=h^2,i^e=i^4138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 206649);