Finite Group Databasebeta

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#10714541

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 88922);