Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | D61⋊#1839 |
| Sylow | C61 ⋊ C2×#1839 |
1134 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 360 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=g,b^2=ef,c^2=e,g^2=h,b^a=be,c^a=cf,i^a=i^11,i^d=i^60,i^g=i^601072 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1104834);