Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C61×#2921 ⋊ C2 |
| Sylow | C61 ⋊ #9036 |
566 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 115 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=f,b^2=dfg,c^2=g,d^2=g,f^2=gh,b^a=bd,c^a=ce,e^a=eh,i^a=i^60,d^b=dg,e^b=eh,f^b=fg,d^c=dh,f^c=fh1366 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 64672);