Finite Group Databasebeta

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#12102410

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

814 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,5|a^2=g,b^2=g,c^2=h,d^2=e,f^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^4,d^b=dh,i^b=i^4,f^c=fh

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 172678);