Finite Group Databasebeta

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#36472988

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,89|a^2=f,b^2=def,c^2=e,d^2=g,e^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=eh,i^a=i^88,d^b=dg,f^b=fgh,g^b=gh,i^b=i^88

Conjugacy classes & character table

1982 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 88128);