Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C61×#578 ⋊ C4 |
| Sylow | C61 ⋊ #60183 |
2612 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|a^2=g,c^2=g,f^2=h,g^2=h,b^a=bf,f^a=fh,i^a=i^50,f^b=fh,i^b=i^60,i^c=i^11,e^d=eh,i^g=i^60418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1115049);