Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C61×#3125 ⋊ C2 |
| Sylow | C61 ⋊ #60571 |
2088 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=h,d^2=f,g^2=h,b^a=bf,c^a=cg,g^a=gh,e^b=eh,g^c=gh,i^c=i^60,i^d=i^60,i^e=i^601024 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1038139);