Finite Group Databasebeta

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#34258992

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

590 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,79|a^2=f,b^2=g,c^2=fg,e^2=g,f^2=h,b^a=be,c^a=ch,d^a=dh,e^a=eg,i^a=i^78,d^b=dh,e^b=eg,i^c=i^78

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 140291);