Finite Group Databasebeta

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#36469403

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,89|a^2=e,b^2=f,c^2=h,d^2=h,b^a=bd,d^a=dg,f^a=fh,g^a=gh,c^b=ch,e^b=egh,i^b=i^88,e^d=eh

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, 84543);