Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×#103×C61 ⋊ C2 |
| Sylow | C61 ⋊ #8992 |
500 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=f,b^2=dfg,c^2=g,d^2=g,e^2=h,f^2=h,b^a=bd,c^a=ce,d^b=dg,e^b=eh,f^b=fg,i^b=i^60,d^c=dh,e^c=eh,f^c=fh1732 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 64432);