Finite Group Databasebeta

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#31795944

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^7,137|a^2=d,c^2=efg,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^100,c^b=ceg,d^b=dg,e^b=ef,f^b=fg,h^d=h^136

Conjugacy classes & character table

400 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17536, 19665);