Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C61×#3020 ⋊ C2 |
| Sylow | C61 ⋊ #60390 |
4698 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|c^2=h,f^2=h,b^a=bf,c^a=cg,f^a=fh,f^b=fh,g^b=gh,f^c=fh,i^c=i^60,e^d=eh,i^d=i^60,i^e=i^60928 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1036265);