Finite Group Databasebeta

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#13403333

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,7|a^2=fh,b^2=f,c^2=h,d^2=e,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,i^a=i^6,c^b=cg,i^b=i^6,f^c=fh,g^c=gh,i^c=i^6

Conjugacy classes & character table

172 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 219105);