Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C61 ⋊ #12867 |
470 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 155 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,c^2=dh,e^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,i^a=i^60,e^c=eg,g^c=gh,i^c=i^602458 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 85861);