Finite Group Databasebeta

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#12172513

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

700 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,5|a^2=e,b^2=h,c^2=e,d^2=efh,g^2=h,b^a=be,c^a=cf,d^a=de,i^a=i^4,c^b=cg,g^b=gh,g^c=gh,i^d=i^4

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 242781);