Finite Group Databasebeta

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#31907247

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,71|a^2=e,d^2=f,e^2=g,f^2=h,g^2=h,b^a=bd,d^a=df,f^a=fh,i^a=i^70,c^b=ch,d^b=dfh,e^b=eh,f^b=fh

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, 79363);