Finite Group Databasebeta

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#30771129

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

412 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,67|a^2=e,b^2=f,c^2=e,d^2=g,e^2=h,f^2=gh,g^2=h,b^a=bd,d^a=dg,f^a=fg,g^a=gh,c^b=cg,e^b=eh,i^b=i^66,d^c=dh,f^c=fh

Conjugacy classes & character table

1498 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 84866);