Finite Group Databasebeta

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#18009603

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^7,37|a^2=d,b^2=g,c^2=f,d^2=e,e^2=g,b^a=bc,c^a=ce,f^a=fg,h^a=h^6,c^b=cf,d^b=defg,e^b=eg,h^b=h^36,d^c=dg,h^d=h^36

Conjugacy classes & character table

146 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 19517);