Finite Group DatabasebetaFinite Group Databasebeta| order | 22112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D691)⋊C4 |
| Fitting | C22⋊C4×C691 ⋊ C2 |
| Sylow | C691 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11056 |
Polycyclic presentation:
2^5,691|a^2=e,c^2=e,b^a=bd,f^c=f^6903470 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22112, 106);