Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C61×#368 ⋊ C4 |
| Sylow | C61 ⋊ #13171 |
274 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 86 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=f,c^2=eg,d^2=h,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,g^a=gh,i^a=i^50,d^b=dh,i^b=i^11,i^f=i^60382 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1097474);