Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #10384 |
438 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 75 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=d,b^2=dg,e^2=gh,b^a=bd,c^a=ce,e^a=eh,f^a=fgh,i^a=i^60,c^b=cf,e^b=eh,f^b=fg,d^c=dg,e^c=egh991 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 72786);