Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D61⋊(D4⋊C16) |
| Sylow | C61 ⋊ C2×D4⋊C16 |
470 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=e,d^2=f,e^2=g,g^2=h,b^a=bd,d^a=df,i^a=i^11,d^b=df,i^c=i^60,i^e=i^60712 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1093924);