Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4 |
| unambiguous semidirect product | D61⋊#1910 |
| Fitting | C61×#535 ⋊ C4 |
| Sylow | C61 ⋊ C2×#1910 |
1878 conjugacy classes of subgroups.
| transitive degree | μt(G) = 976 |
Polycyclic presentation:
2^8,61|a^2=g,b^2=egh,e^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,i^a=i^50,f^b=fh,i^b=i^11,e^c=eh,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, 1105335);