Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C61 ⋊ #13030 |
476 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|a^2=f,b^2=dfg,d^2=g,e^2=g,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,i^a=i^60,d^b=dg,e^b=eg,f^b=fg,g^b=gh,i^b=i^60,d^c=dg,e^c=egh,f^c=fg,g^c=gh1000 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 86753);