Finite Group Databasebeta

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#34289753

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

1668 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,79|a^2=g,b^2=eg,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=dh,f^a=fh,i^a=i^78,e^b=eh,g^b=gh,i^b=i^78,f^c=fh

Conjugacy classes & character table

1774 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 171052);