Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| unambiguous semidirect product | D61⋊#1905 |
| Fitting | C2×#137×C61 ⋊ C4 |
| Sylow | C61 ⋊ C2×#1905 |
1678 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|a^2=g,b^2=eg,c^2=h,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^50,f^b=fh,i^b=i^11,e^c=eh,f^c=fh,g^c=gh,i^d=i^60,i^g=i^60388 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1105315);