Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C61×#1888 ⋊ C2 |
| Sylow | C61 ⋊ #25438 |
892 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=f,b^2=ef,d^2=eh,e^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,i^a=i^60,c^b=cg,g^b=gh,i^b=i^60,d^c=dh,g^c=gh,i^c=i^60,i^d=i^601000 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 221010);