Finite Group Databasebeta

?

← Prev (#10713321) Next (#10713323) →

#10713322

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

306 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 87703);