Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×C5×D8 ⋊ C4 |
| Hall | C3×C5 ⋊ #1879 |
| Sylow | C5 ⋊ #72037 |
| Sylow | C3 ⋊ #10604799 |
876 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|a^2=f,b^2=dfg,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,h^a=h^2,i^a=i^3,d^b=dg,e^b=eg,f^b=fg,h^b=h^2,i^b=i^2,d^c=dg,e^c=eg,f^c=fg,i^f=i^4108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 26723);