Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D61⋊#1308 |
| Sylow | C61 ⋊ C2×#1308 |
526 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=e,b^2=f,e^2=gh,f^2=g,b^a=bd,d^a=dg,f^a=fh,i^a=i^11,d^b=dh,e^b=eg,i^c=i^60,i^e=i^60472 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1086902);