Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C61×#444 ⋊ C4 |
| Sylow | C61 ⋊ #20512 |
1014 conjugacy classes of subgroups.
| transitive degree | μt(G) = 976 |
Polycyclic presentation:
2^8,61|a^2=f,b^2=g,c^2=g,d^2=f,e^2=h,f^2=h,b^a=be,e^a=eh,e^b=eh,i^b=i^50,d^c=dh,i^c=i^11,i^g=i^60418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1104083);