Finite Group DatabasebetaFinite Group Databasebeta| order | 33568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#22554218 |
| unambiguous semidirect product | (C2×#22554218)⋊C2 |
| Fitting | C22×C1049 ⋊ C8 |
| Sylow | C1049 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4196 |
Polycyclic presentation:
2^5,1049|a^2=d,d^2=e,b^a=bc,f^a=f^461,f^d=f^623,f^e=f^1048544 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33568, 238);