Finite Group Databasebeta

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#32994626

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

2068 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 78210);