Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Sylow | C181 ⋊ #1747 |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5792 |
Polycyclic presentation:
2^7,181|a^2=e,b^2=f,c^2=d,d^2=g,b^a=bd,f^a=fg,h^a=h^180,e^b=eg,h^b=h^180,h^c=h^1802024 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 4266);