Finite Group Databasebeta

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#33002863

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,73|a^2=f,b^2=df,d^2=h,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^72,d^b=dh,e^b=eh,f^b=fh,i^b=i^72,d^c=dh,e^c=eh,f^c=fh

Conjugacy classes & character table

2092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 86447);