Finite Group Databasebeta

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#31797880

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^7,137|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,b^a=bf,d^a=dg,h^a=h^96,c^b=cg,h^b=h^100,h^c=h^37,h^d=h^136,h^e=h^136

Conjugacy classes & character table

316 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17536, 21601);