Finite Group DatabasebetaFinite Group Databasebeta| order | 22688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#19150893 |
| Sylow | C709 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11344 |
Polycyclic presentation:
2^5,709|a^2=d,d^2=e,b^a=bc,f^a=f^96,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, 202);