Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C181 ⋊ #1733 |
404 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5792 |
Polycyclic presentation:
2^7,181|a^2=e,b^2=f,d^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^180,c^b=cg,h^b=h^1803644 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 4221);