Finite Group DatabasebetaFinite Group Databasebeta| order | 31568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#21463563 |
| unambiguous semidirect product | (C2×#21463563)⋊C2 |
| Fitting | C22×C1973 ⋊ C4 |
| Sylow | C1973 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7892 |
Polycyclic presentation:
2^4,1973|a^2=d,b^a=bc,e^a=e^259,e^d=e^19721982 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31568, 45);