Finite Group Databasebeta

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#10712435

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 86816);