Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C181 ⋊ #1726 |
328 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23168 |
Polycyclic presentation:
2^7,181|a^2=d,b^2=e,c^2=f,d^2=g,h^a=h^162,c^b=cg,h^d=h^180980 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 20167);