Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #7242 |
190 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 66 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=d,b^2=e,c^2=fgh,d^2=gh,e^2=fg,f^2=h,b^a=bc,c^a=cf,e^a=efgh,f^a=fh,i^a=i^11,d^b=dg,i^d=i^601012 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1084078);