Finite Group Databasebeta

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#36657659

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

660 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

1454 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 272799);