Finite Group Databasebeta

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#26214872

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,47|a^2=f,b^2=g,c^2=g,d^2=f,e^2=h,f^2=h,b^a=be,c^a=ch,e^a=eh,i^a=i^46,e^b=eh,d^c=dh,i^d=i^46

Conjugacy classes & character table

1376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 168162);