Finite Group Databasebeta

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#13136736

• solvable
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

183 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^6,3^3|a^2=c,b^2=ce,c^2=f,b^a=bcd,e^a=ef,g^a=g^2h^2i,h^a=g^2h,c^b=cf,d^b=df,e^b=ef,g^b=gh^2i^2,h^b=g^2h^2,g^c=g^2i,h^c=h^2i^2,h^g=hi

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 2799);