Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C61×#2061 ⋊ C2 |
| Sylow | C61 ⋊ #24314 |
1034 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=e,b^2=e,c^2=h,d^2=e,f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,g^a=gh,c^b=cg,f^b=fh,f^c=fh,i^c=i^60,i^d=i^60826 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 205806);