Finite Group Databasebeta

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#31884339

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,71|a^2=d,b^2=e,c^2=fh,d^2=g,e^2=f,f^2=h,g^2=h,b^a=bc,c^a=cf,e^a=ef,f^a=fh,c^b=ch,i^b=i^70

Conjugacy classes & character table

2024 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 56455);