Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C61 ⋊ #13564 |
494 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 976 |
Polycyclic presentation:
2^8,61|a^2=e,c^2=h,e^2=h,f^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,i^a=i^11,e^b=efh,f^b=fh,g^b=gh,i^b=i^60,e^d=egh,f^d=fh,f^e=fh,i^e=i^60364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1097848);