Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C61 ⋊ #11297 |
578 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 136 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=g,b^2=e,c^2=d,d^2=h,e^2=h,g^2=h,b^a=bd,c^a=ce,i^a=i^11,c^b=cf,d^b=dh,f^b=fh,g^b=gh,e^c=eh,f^c=fh,g^c=gh,i^g=i^60382 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1093097);