Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C61×#419 ⋊ C4 |
| Sylow | C61 ⋊ #11131 |
852 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|a^2=g,b^2=d,d^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^11,c^b=cf,e^b=eh,d^c=dh,f^c=fh,i^c=i^60,i^g=i^60376 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1092891);