Finite Group Databasebeta

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#13270396

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

426 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,7|a^2=f,b^2=f,c^2=h,d^2=gh,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,g^a=gh,i^a=i^6,d^b=dg,e^b=eg,g^b=gh,d^c=dg,e^c=eg,g^c=gh,i^c=i^6

Conjugacy classes & character table

190 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 86168);