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Dic₂₁₄₄ #22558427

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^7,67|a^2=g,b^2=g,c^2=de,d^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=cd,d^a=de,e^a=ef,f^a=fg,h^a=h^66,c^b=cd,d^b=de,e^b=ef,f^b=fg,h^b=h^66

Conjugacy classes & character table

2147 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8576, 2728);