Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C61×#2229 ⋊ C2 |
| Sylow | C61 ⋊ #33680 |
534 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7808 |
Polycyclic presentation:
2^8,61|a^2=h,b^2=h,d^2=e,f^2=gh,g^2=h,b^a=be,c^a=cf,f^a=fg,g^a=gh,i^a=i^60,d^b=dh,i^b=i^60,f^c=fg,g^c=gh,i^c=i^60,i^d=i^60916 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 324713);