Finite Group Databasebeta

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#13269221

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

318 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,7|a^2=e,b^2=f,c^2=de,d^2=gh,e^2=g,g^2=h,b^a=bd,c^a=cg,d^a=dh,i^a=i^6,d^b=dg,e^b=egh,g^b=gh,i^b=i^6,d^c=dh,e^c=eh,i^c=i^6

Conjugacy classes & character table

142 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 84993);