Finite Group Databasebeta

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#33003064

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,73|a^2=f,b^2=dfgh,c^2=h,d^2=gh,e^2=gh,f^2=gh,g^2=h,b^a=bd,c^a=ce,i^a=i^72,d^b=dg,e^b=eg,f^b=fg,g^b=gh,i^b=i^72,d^c=dg,e^c=eg,f^c=fg,g^c=gh

Conjugacy classes & character table

1642 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 86648);