Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #11524 |
288 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 288 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) = 1952 |
Polycyclic presentation:
2^8,61|a^2=e,c^2=f,d^2=h,e^2=g,g^2=h,b^a=bd,c^a=cg,d^a=df,f^a=fh,i^a=i^11,c^b=ch,d^b=dh,e^b=efh,e^c=eh,i^c=i^60,e^d=eh,i^e=i^60460 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1093712);