Finite Group Databasebeta

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#10690006

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

680 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 64387);