Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
| unambiguous semidirect product | D61⋊#2974 |
| Sylow | C61 ⋊ C2×#2974 |
2654 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|a^2=g,g^2=h,b^a=bf,d^a=df,i^a=i^11,c^b=cfh,i^e=i^60,i^g=i^60700 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1115283);