Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1551 |
| Sylow | C5 ⋊ #71807 |
| Sylow | C3 ⋊ #10605005 |
504 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|a^2=e,c^2=g,d^2=g,e^2=fg,b^a=bd,c^a=cf,d^a=df,h^a=h^2,i^a=i^2,d^b=dg,e^b=efg,i^e=i^4120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 10729);