Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×#101×C61 ⋊ C4 |
| Sylow | C61 ⋊ #10963 |
978 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|a^2=f,b^2=g,c^2=efh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,g^a=gh,i^a=i^50,d^b=dh,e^b=eh,f^b=fh,d^c=dh,e^c=eh,f^c=fh,i^c=i^11,i^f=i^60394 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1092661);