Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C61×#382 ⋊ C4 |
| Sylow | C61 ⋊ #9460 |
512 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=f,b^2=df,c^2=g,d^2=gh,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=egh,i^a=i^50,d^b=dh,e^b=egh,f^b=fh,i^b=i^11,d^c=dgh,f^c=fgh,i^f=i^60457 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1090707);