Finite Group Databasebeta

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#1658⋊C₉ #11919329

• solvable
• monomial

Aliases

Splittings

Subgroups

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3^2,2^6|b^3=c,d^2=h,e^2=hi,f^2=i,g^2=h,b^a=bh,d^a=df,e^a=eg,f^a=fi,g^a=gh,d^b=eh,e^b=de,f^b=g,g^b=fghi,h^b=hi,i^b=h,f^d=fi,g^d=ghi,f^e=fhi,g^e=gh

Conjugacy classes & character table

36 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 153340);