Finite Group Databasebeta

?

← Prev (#10700726) Next (#10700728) →

#10700727

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

1186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 75108);