Finite Group Databasebeta

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#16821721

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^7,29|a^2=g,b^2=e,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,h^a=h^28,h^b=h^28,h^c=h^28

Conjugacy classes & character table

346 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 6739);