Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C3×C5×Q64 ⋊ C2 |
| Hall | C3×C5 ⋊ SD128 |
| Sylow | C5 ⋊ #67609 |
| Sylow | C3 ⋊ #10598100 |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 72 |
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|a^2=g,c^2=de,d^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=cd,d^a=de,e^a=ef,f^a=fg,c^b=cd,d^b=de,e^b=ef,f^b=fg,h^b=h^2,i^b=i^4168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 5514);