Finite Group Databasebeta

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#31797890

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

58 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^7,137|a^2=d,b^2=c,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,h^a=h^127,h^b=h^136,h^d=h^100,h^e=h^136

Conjugacy classes & character table

328 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17536, 21611);