Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C61×#1996 ⋊ C2 |
| Sylow | C61 ⋊ #9275 |
606 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|a^2=f,b^2=df,d^2=gh,e^2=gh,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eg,i^a=i^60,d^b=dh,e^b=eh,f^b=fh,i^b=i^60,d^c=dh,e^c=egh,f^c=fh,i^c=i^601003 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 66130);