Finite Group Databasebeta

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#13257614

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

506 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 73386);