Finite Group Databasebeta

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#13398903

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

638 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,7|b^2=f,d^2=e,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,c^b=cg,g^b=gh,i^b=i^6,f^c=fh,i^d=i^6

Conjugacy classes & character table

127 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 214675);