Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C181 ⋊ #1363 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23168 |
Polycyclic presentation:
2^7,181|a^2=d,b^2=e,c^2=fg,d^2=ef,f^2=g,b^a=bc,c^a=ce,h^a=h^162,c^b=cf,d^b=def,f^b=fg,h^b=h^180,h^d=h^180659 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 19527);