Finite Group DatabasebetaFinite Group Databasebeta| order | 3568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D223)⋊C4 |
| Fitting | C2×C4×C223 ⋊ C2 |
| Sylow | C223 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1784 |
Polycyclic presentation:
2^4,223|a^2=d,b^a=bc,e^b=e^222898 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3568, 17);