Finite Group Databasebeta

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#13135137

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^6,3^3|a^2=e,b^2=c,c^2=f,e^2=f,h^3=i,b^a=bd,h^a=h^2i^2,i^a=i^2,g^b=g^2

Conjugacy classes & character table

264 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 1200);