Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | D61⋊#1828 |
| Fitting | C61×#518 ⋊ C4 |
| Sylow | C61 ⋊ C2×#1828 |
1554 conjugacy classes of subgroups.
| transitive degree | μt(G) = 976 |
Polycyclic presentation:
2^8,61|a^2=g,c^2=e,b^a=be,c^a=cf,e^a=eh,i^a=i^11,g^b=gh,f^c=fh,i^d=i^60,i^g=i^60568 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1104675);