Finite Group Databasebeta

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#10682128

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,3|a^2=d,b^2=e,c^2=f,d^2=g,e^2=fg,f^2=h,g^2=h,b^a=bc,c^a=cf,e^a=ef,f^a=fh,d^b=dh,i^b=i^2

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 56509);