Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C61 ⋊ #13545 |
216 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^8,61|a^2=dg,b^2=de,c^2=d,f^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=eh,f^a=fh,i^a=i^60,c^b=cf,d^b=dh,e^b=eh,f^b=fg,g^b=gh,i^b=i^60,f^c=fgh,g^c=gh994 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 89734);