Finite Group Databasebeta

?

← Prev (#10596404) Next (#10596406) →

AGL(1,𝔽₉)⋊Q₈ #10596405

• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

117 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^6,3^2|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bdf,g^a=g^2h^2,h^a=g^2,c^b=ce,d^b=df,g^b=gh^2,h^b=h^2,g^d=g^2h,h^d=gh,g^f=g^2,h^f=h^2

Conjugacy classes & character table

27 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 8287);