Finite Group Databasebeta

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#31782659

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^7,137|a^2=e,b^2=g,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,d^b=df,f^b=fg,h^b=h^136,h^c=h^136

Conjugacy classes & character table

1528 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17536, 6380);