Finite Group Databasebeta

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#10690389

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

476 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,3|a^2=f,b^2=dfg,c^2=g,d^2=g,e^2=g,f^2=h,b^a=bd,c^a=ce,e^a=egh,i^a=i^2,d^b=dg,e^b=eh,f^b=fg,i^b=i^2,d^c=dh,e^c=eg,f^c=fh

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 64770);