Finite Group Databasebeta

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#36368633

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^7,173|a^2=d,b^2=e,c^2=f,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,h^a=h^80,d^b=dg,h^d=h^172

Conjugacy classes & character table

1408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22144, 19580);