Finite Group DatabasebetaFinite Group Databasebeta| order | 32288 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#22549056 |
| Fitting | C4×C1009 ⋊ C8 |
| Sylow | C1009 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4036 |
Polycyclic presentation:
2^5,1009|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^762,f^d=f^469,f^e=f^1008524 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32288, 239);