Finite Group DatabasebetaFinite Group Databasebeta| order | 22688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D709⋊M16 |
| Sylow | C709 ⋊ C2×M16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5672 |
Polycyclic presentation:
2^5,709|a^2=d,d^2=e,b^a=be,f^a=f^96,f^c=f^708,f^d=f^7081436 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22688, 231);