Finite Group Databasebeta

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SU(3,𝔽₂)⋊C₄ #11722229

• solvable

Aliases

Splittings

Subgroups

79 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^5,3^3|a^2=c,b^2=d,c^2=e,b^a=bcde,f^a=f^2g^2,g^a=f^2h^2,h^a=h^2,c^b=ce,f^b=fg^2h^2,g^b=g^2,h^b=h^2,f^c=f^2g,g^c=fgh^2,f^e=f^2,g^e=g^2h^2,g^f=gh

Conjugacy classes & character table

28 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(864, 2196);