Finite Group Databasebeta

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#31912673

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,71|a^2=e,b^2=f,c^2=eh,d^2=gh,f^2=g,g^2=h,b^a=bd,d^a=dg,f^a=fgh,g^a=gh,i^a=i^70,c^b=ch,i^c=i^70

Conjugacy classes & character table

1604 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 84789);