Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C5×#137 ⋊ C4 |
| Hall | C3×C5 ⋊ #2956 |
| Sylow | C5 ⋊ #84000 |
| Sylow | C3 ⋊ #10617453 |
916 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,e^a=eg,h^a=h^2,i^a=i^3,e^b=eg,i^b=i^4,d^c=dg,h^c=h^2,i^c=i^2,i^f=i^499 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 143826);