Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C5×#100 ⋊ C22 |
| Hall | C3×C5 ⋊ #3288 |
| Sylow | C5 ⋊ #80932 |
| Sylow | C3 ⋊ #10612670 |
928 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^2,i^a=i^4,d^b=de,e^b=eg,h^b=h^2,i^b=i^4,f^c=fg,h^c=h^2,i^c=i^4,e^d=eg,i^d=i^496 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 183453);