Finite Group Databasebeta

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#10815004

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

754 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 189385);