Finite Group Databasebeta

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#12000576

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,5|a^2=gh,b^2=gh,c^2=g,d^2=g,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^4,c^b=cf,d^b=dg,e^b=eh,i^b=i^4,d^c=dh,e^c=eh,i^c=i^4

Conjugacy classes & character table

158 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 70844);