Finite Group DatabasebetaFinite Group Databasebeta| order | 22112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C691 ⋊ #137 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11056 |
Polycyclic presentation:
2^5,691|b^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,d^b=de,f^b=f^6903461 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22112, 176);