Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C3×C5×#135 ⋊ C22 |
| Hall | C3×C5 ⋊ C2×#577 |
| Sylow | C5 ⋊ D3×#577 |
| Sylow | C3 ⋊ D5×#577 |
2920 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|a^2=g,f^2=g,b^a=bf,f^a=fg,h^a=h^2,f^b=fg,h^b=h^2,d^c=dg,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, 235747);