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×#491 ⋊ C4 |
| Sylow | C61 ⋊ #9376 |
430 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 76 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=dfg,d^2=gh,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,i^a=i^50,d^b=dh,e^b=eg,f^b=fh,i^b=i^11,d^c=dg,e^c=eh,f^c=fg,i^c=i^60,i^f=i^60277 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1090523);