Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D4⋊#14582113 |
| Sylow | C337 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10784 |
Polycyclic presentation:
2^6,337|a^2=d,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^148,c^b=ce,g^d=g^336868 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1396);