Finite Group DatabasebetaFinite Group Databasebeta| order | 22768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊Dic1423 |
| Sylow | C1423 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11384 |
Polycyclic presentation:
2^4,1423|a^2=d,b^a=bc,e^a=e^14225698 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22768, 18);