Finite Group Databasebeta

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#37548749

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^7,181|a^2=d,b^2=c,c^2=e,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^162,d^b=dg,h^b=h^180,h^d=h^180

Conjugacy classes & character table

1472 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 19538);