Finite Group Databasebeta

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#10620013⋊C₂ #13049171

• solvable
• monolithic
• stem

Aliases

Splittings

Subgroups

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

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, 2889);