Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D181⋊#443 |
| Fitting | #135×C181 ⋊ C4 |
| Sylow | C181 ⋊ C2×#443 |
472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2896 |
Polycyclic presentation:
2^7,181|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,e^a=eg,h^a=h^19,e^b=eg,h^c=h^162,h^d=h^180,h^f=h^180686 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 21276);