Finite Group Databasebeta

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#31906386

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

922 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,71|a^2=g,b^2=f,c^2=f,d^2=h,e^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fh,i^a=i^70,c^b=cf,i^b=i^70,d^c=dh,g^c=gh

Conjugacy classes & character table

1592 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 78502);