Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4 |
| unambiguous semidirect product | D181⋊#431 |
| Sylow | C181 ⋊ C2×#431 |
528 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5792 |
Polycyclic presentation:
2^7,181|a^2=f,c^2=e,f^2=g,b^a=be,h^a=h^162,h^d=h^180,h^f=h^1801520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 21174);