Finite Group Databasebeta

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#10624619⋊C₂ #13090776

• supersolvable
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

170 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3^6|b^3=fg^2,c^3=fg,b^a=b^2d^2e^2f^2g,c^a=c^2e^2f^2g^2,d^a=df^2g^2,e^a=eg,f^a=f^2,g^a=g^2,c^b=ce,d^b=df,e^b=ef,e^c=eg

Conjugacy classes & character table

50 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 850);