Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C23×C4 |
| unambiguous semidirect product | D61⋊#2164 |
| Sylow | C61 ⋊ C2×#2164 |
610 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=f,c^2=e,f^2=g,g^2=h,b^a=be,i^a=i^11,c^b=ch,i^d=i^60,i^f=i^60712 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1113700);