Finite Group Databasebeta

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#13134010

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^6,3^3|a^2=f,b^2=c,c^2=ef,d^2=ef,e^2=f,g^3=h,h^3=i,b^a=bd,c^a=ce,d^a=de,e^a=ef,g^a=g^2h^2i^2,h^a=h^2i^2,i^a=i^2,d^b=df

Conjugacy classes & character table

276 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 73);