Finite Group Databasebeta

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#36557004

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

1118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

1994 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 172144);