Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#19129199 |
| unambiguous semidirect product | (C2×#19129199)⋊C2 |
| Fitting | C22×C337 ⋊ C16 |
| Sylow | C337 ⋊ C22⋊C16 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1348 |
Polycyclic presentation:
2^6,337|a^2=d,d^2=e,e^2=f,b^a=bc,g^a=g^191,g^d=g^85,g^e=g^148,g^f=g^336124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1675);