Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×#131×C61 ⋊ C4 |
| Sylow | C61 ⋊ #20338 |
2036 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|a^2=f,b^2=g,e^2=h,b^a=be,g^a=gh,i^a=i^50,f^b=fh,i^b=i^11,d^c=dh,i^f=i^60,i^g=i^60682 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1103415);