Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C61×#2166 ⋊ C2 |
| Sylow | C61 ⋊ #33428 |
528 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|a^2=f,c^2=e,f^2=g,g^2=h,b^a=be,c^a=cg,e^a=eh,d^b=dh,f^b=fh,d^c=dh,f^c=fh,i^c=i^60,i^d=i^601024 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 322710);