Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C61 ⋊ #10573 |
494 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15616 |
Polycyclic presentation:
2^8,61|a^2=d,b^2=d,c^2=d,e^2=g,f^2=h,b^a=bd,c^a=ce,e^a=eg,f^a=fh,i^a=i^60,c^b=cf,e^b=eh,f^b=fh,e^c=eg,f^c=fh,i^c=i^601726 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 74006);