Finite Group DatabasebetaFinite Group Databasebeta| order | 22768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊Dic1423 |
| Sylow | C1423 ⋊ C4⋊C4 |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22768 |
Polycyclic presentation:
2^4,1423|a^2=d,b^2=c,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, 20);