Finite Group Databasebeta

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#10823901

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

1102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,3|a^2=ef,b^2=e,c^2=h,d^2=h,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,g^a=gh,i^a=i^2,c^b=cg,d^b=dh,i^b=i^2,d^c=dh,e^c=eh,f^c=fh,g^c=gh,i^c=i^2

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, 198282);