Understanding C=(2*C5): Elements and Meaning

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SUMMARY

The notation C=(2*C5) refers to a symmetry class within the group C5v, indicating that it contains two elements, specifically the rotations by +72 degrees and -72 degrees. The term 2*C5 signifies that these rotations are part of the same symmetry class, which is confirmed by the relationship C'=(2C5). The discussion clarifies that C' is not standard notation, but the elements C5 and C54 are indeed part of this class.

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  • Understanding of symmetry groups, specifically C5v
  • Familiarity with rotational symmetries and their notations
  • Knowledge of group theory terminology
  • Basic comprehension of mathematical notation in symmetry operations
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  • Study the implications of rotational symmetries in C5v
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Mathematicians, physicists, and students studying group theory and symmetry operations, particularly those interested in the properties of the C5v symmetry group.

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One of the classes of the group C5v is written C=(2*C5). So why do we mean by 2*C5 and how we can know the elements of this class from this writing ?
Thanks
 
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You really mean class or rather symmetry operation? I would guess that 2*C_5 means a rotation by two times 72 degrees.
 
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I mean what means the notation of the class C'=(2C5) ,where C' is a class and 2C5 are the elements of this class.
 
Where did you see this? I don't think the C' is standard notation. The 2 C##_5## means that the class contains two elements, namely the rotations by + or - 72 degrees.
 
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So 2 C5 means : C5, C54.
Thanks you very much that's what I want to know.
 
Yes, the two are in the same class as e.g. ##\sigma_v C_5 \sigma_v=C_5^4##.
 
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