Finite Group Databasebeta

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#10303⋊C₃ #11709142

• solvable
• monolithic
• stem

Aliases

Splittings

Subgroups

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

3,2^8|b^2=h,c^2=h,d^2=i,e^2=h,f^2=i,g^2=hi,b^a=dfi,c^a=bg,d^a=cfgh,e^a=fhi,f^a=gi,g^a=eh,h^a=i,i^a=hi,c^b=ce,d^b=df,e^b=eh,f^b=fi,d^c=dg,e^c=eh,g^c=ghi,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, 1083523);