Finite Group Databasebeta

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#10612⋊C₃ #11709155

• solvable
• monolithic
• stem

Aliases

Splittings

Subgroups

83 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

3,2^8|b^2=ef,c^2=eh,e^2=h,f^2=i,g^2=hi,b^a=cei,c^a=bcde,d^a=dfgi,e^a=eg,f^a=ghi,g^a=fghi,h^a=i,i^a=hi,c^b=ce,d^b=df,e^b=eh,f^b=fh,g^b=gh,d^c=dg,g^c=gi,e^d=eh,f^d=fi,g^d=ghi

Conjugacy classes & character table

22 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1083536);