Finite Group Databasebeta

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#34304277

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

1312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 185576);