Finite Group Databasebeta

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#10624482⋊C₂ #13090512

• supersolvable
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

75 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3^6|b^3=g,c^3=g,d^3=g^2,b^a=c^2g^2,c^a=b^2g^2,d^a=d^2efg,e^a=f,f^a=e,g^a=g^2,c^b=cd,d^b=de,e^b=eg,f^b=fg,d^c=df,e^c=eg,f^c=fg

Conjugacy classes & character table

42 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 586);