Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #13489 |
278 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 83 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=eg,c^2=d,e^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,c^b=cf,f^b=fg,g^b=gh,f^c=fg,g^c=gh,i^c=i^601000 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 89403);