Finite Group Databasebeta

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#10620012⋊C₂ #13049172

• solvable
• monolithic
• stem

Aliases

Splittings

Subgroups

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,2^3,3^3|b^3=h^2,c^2=e,d^2=e,b^a=b^2h,c^a=cd,d^a=de,f^a=f^2gh^2,g^a=gh^2,h^a=h^2,c^b=d,d^b=cde,f^b=fg,d^c=de,f^c=g^2,g^c=fh,f^d=f^2gh,g^d=fgh,f^e=f^2h^2,g^e=g^2h,g^f=gh

Conjugacy classes & character table

18 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2890);