Finite Group Databasebeta

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#36611977

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

876 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,89|a^2=fh,c^2=f,e^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=cg,e^b=eh,g^b=gh,g^c=gh,i^c=i^88,e^d=eh

Conjugacy classes & character table

1979 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 227117);