Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D337⋊#131 |
| Sylow | C337 ⋊ C2×#131 |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5392 |
Polycyclic presentation:
2^6,337|a^2=e,e^2=f,g^a=g^148,c^b=cf,g^d=g^336,g^e=g^336880 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1625);