Finite Group Databasebeta

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(Q₈⋊C₂₇)⋊C₈ #13134129

• solvable

Aliases

Splittings

Subgroups

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^3,3^3,2^3|a^2=b,b^2=c,d^3=e,e^3=f,g^2=i,h^2=i,d^a=d^2e^2f^2,e^a=e^2f^2,f^a=f^2,g^a=gh,h^a=hi,g^d=h,h^d=ghi,h^g=hi

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 192);