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Conjugacy classes may be referred to by describing them, or more briefly by abbreviations such as "6A", meaning "a certain conjugacy class with elements of order 6", and "6B" would be a different conjugacy class with elements of order 6; the conjugacy class 1A is the conjugacy class of the identity which has order 1.
# of pitch classes Lower tetrachord Upper tetrachord Use of key signature usual or unusual 15 equal temperament: 15-tet scale on C. Play ⓘ — — — 15 — — — 16 equal temperament: 16-tet scale on C. Play ⓘ — — — 16 — — — 17 equal temperament: 17-tet scale on C. Play ⓘ — — — 17 — — — 19 equal temperament: 19 ...
The five conjugacy classes have representatives e, (12)(34), (12), (123), (1234) and, of these, the Möbius configuration corresponds to the conjugacy class e. It could be denoted Ke .
D [1] is a musical note a whole tone above C, and is known as Re within the fixed-Do solfege system. Its enharmonic equivalents are C (C-double sharp) and E (E-double flat). It is the third semitone of the solfège.
We can easily distinguish three kinds of permutations of the three blocks, the conjugacy classes of the group: no change (), a group element of order 1; interchanging two blocks: (RG), (RB), (GB), three group elements of order 2; a cyclic permutation of all three blocks: (RGB), (RBG), two group elements of order 3
All the reflections are conjugate to each other whenever n is odd, but they fall into two conjugacy classes if n is even. If we think of the isometries of a regular n-gon: for odd n there are rotations in the group between every pair of mirrors, while for even n only half of the mirrors can be reached from one by these rotations. Geometrically ...
The irreducible complex characters of a finite group form a character table which encodes much useful information about the group G in a concise form. Each row is labelled by an irreducible character and the entries in the row are the values of that character on any representative of the respective conjugacy class of G (because characters are class functions).
By definition, an element is central whenever its conjugacy class contains only the element itself; i.e. Cl(g) = {g}. The center is the intersection of all the centralizers of elements of G: = (). As centralizers are subgroups, this again shows that the center is a subgroup.