Finite Group Databasebeta

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#10712748

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,3|a^2=f,b^2=df,e^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^2,d^b=dg,e^b=eh,f^b=fg,g^b=gh,i^b=i^2,d^c=dh,e^c=eh,f^c=fh,f^d=fh

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 87129);