Finite Group DatabasebetaFinite Group Databasebeta| order | 33568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×#16862310)⋊C4 |
| Fitting | C2×C4×C1049 ⋊ C4 |
| Sylow | C1049 ⋊ #95 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8392 |
Polycyclic presentation:
2^5,1049|a^2=d,b^2=e,b^a=bc,f^a=f^623,f^d=f^10482116 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33568, 197);