Finite Group Databasebeta

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#30636824

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^7,127|a^2=d,b^2=e,c^2=fg,d^2=g,e^2=f,f^2=g,b^a=bc,c^a=cf,e^a=efg,f^a=fg,h^a=h^126

Conjugacy classes & character table

4076 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 2604);