Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C61 ⋊ #8473 |
732 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7808 |
Polycyclic presentation:
2^8,61|a^2=f,b^2=g,c^2=g,d^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,i^a=i^11,d^b=dh,e^b=eh,f^b=fgh,d^c=dh,f^c=fg,i^f=i^60550 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1088144);