Finite Group Databasebeta

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#10691753

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

93 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 66134);