Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C61 ⋊ #12931 |
408 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 127 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=fg,d^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,d^b=dg,e^b=eh,f^b=fh,g^b=gh,i^b=i^60,d^c=dh1000 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 86134);