Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C61×Q8⋊C8 ⋊ C4 |
| Sylow | C61 ⋊ #8903 |
392 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 88 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=f,b^2=f,c^2=g,d^2=g,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^50,d^b=dg,e^b=eh,i^b=i^11,d^c=dh,e^c=eh,i^f=i^60472 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1089278);