Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C61 ⋊ #9095 |
546 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=f,b^2=df,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^50,d^b=dg,e^b=eg,f^b=fg,i^b=i^11,d^c=dg,e^c=eg,f^c=fg,i^f=i^60394 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1089802);