Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #8838 |
386 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7808 |
Polycyclic presentation:
2^8,61|a^2=f,b^2=f,c^2=g,d^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^50,c^b=ch,d^b=dg,e^b=eg,i^b=i^11,d^c=dg,i^f=i^60382 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1089128);