Finite Group Databasebeta

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#10702937

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

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, 77318);