Finite Group Databasebeta

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#13149873

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

117 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 15936);