Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C61 ⋊ #7531 |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|a^2=d,c^2=fg,d^2=h,e^2=gh,f^2=h,b^a=bc,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^a=i^60,c^b=cfgh,d^b=def,e^b=egh,f^b=fh,d^c=dfg,e^d=egh,f^d=fh1165 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 57430);