Finite Group DatabasebetaFinite Group Databasebeta| order | 22112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic691⋊C8 |
| Sylow | C691 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22112 |
Polycyclic presentation:
2^5,691|a^2=d,b^2=c,d^2=e,b^a=bc,f^b=f^6905540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22112, 75);