Finite Group Databasebeta

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#30636898

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^7,127|a^2=d,b^2=g,c^2=fg,d^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,c^b=cfg,d^b=def,e^b=eg,h^b=h^126,d^c=dfg,e^d=eg

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 2678);