Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×C4×C5×C8 ⋊ C22 |
| Hall | C3×C5 ⋊ #3297 |
| Sylow | C5 ⋊ #79441 |
| Sylow | C3 ⋊ #10611340 |
840 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=eg,b^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,i^a=i^4,d^b=de,i^b=i^4,f^c=fg,h^c=h^2,i^d=i^4195 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 184732);