Finite Group Databasebeta

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#7837⋊C₃ #11709107

• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

99 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

3,2^8|b^2=ghi,c^2=g,d^2=i,e^2=g,f^2=i,b^a=be,c^a=dgi,d^a=cdhi,e^a=fh,f^a=efg,g^a=i,h^a=hi,i^a=gi,c^b=ce,d^b=df,e^b=eg,f^b=fi,e^c=eg,f^c=fh,e^d=eh,f^d=fi

Conjugacy classes & character table

23 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1083488);