Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D61⋊#1370 |
| Sylow | C61 ⋊ C2×#1370 |
286 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7808 |
Polycyclic presentation:
2^8,61|a^2=e,b^2=df,d^2=f,e^2=g,g^2=h,b^a=bd,d^a=df,i^a=i^11,i^c=i^60,i^e=i^601072 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1095323);