Finite Group Databasebeta

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#13273402

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

410 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 89174);