Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #3156 |
| Sylow | C5 ⋊ #83403 |
| Sylow | C3 ⋊ #10615706 |
1064 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|a^2=g,b^2=eg,c^2=f,e^2=g,b^a=be,c^a=cf,e^a=eg,i^a=i^4,h^b=h^2,i^b=i^4,d^c=dg,i^c=i^4138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 165405);