4
$\begingroup$

Wiki says that this is a Cayley table of Dih4:

Cayley table of Dih4 group

Can somebody explain what are these numbers/colors mean?
Wiki page on Cayley table uses letters and does not mention any numbers.

Also what are these small tables with red squares on top/left mean?
There are other examples of such a schemes like here:
https://en.wikipedia.org/wiki/Dihedral_group_of_order_6

Update: I recently figured out that 'small tables with red squares' are actually a permutation matrices corresponding to the group's elements.
But the question about numbers and colors is still open.

Update2: as Nex pointed out the numbers come from Caley table of S4 group. Symmetric group S4 page contains explanation of the colors:

Even permutations are white:
- the identity
- eight 3-cycles
- three double-transpositions (in bold typeface)
Odd permutations are colored:
- six transpositions (green)
- six 4-cycles (orange)

$\endgroup$
  • 6
    $\begingroup$ That has got to be one of the most confusing diagrams I've ever seen, of Cayley tables or otherwise. $\endgroup$ – Zev Chonoles Dec 17 '16 at 19:15
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    $\begingroup$ the black dot is probably the identity $\endgroup$ – Jorge Fernández Hidalgo Dec 17 '16 at 19:31
  • $\begingroup$ Do the numbers make any sense in binary? I do agree that this is, at best, confusing. I know wiki articles can be somewhat hard to learn from, as they are a reference, but this is quite unhelpful. $\endgroup$ – Josh B. Sep 22 '17 at 19:49
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    $\begingroup$ I think the numbers come from seeing this group as a subgroup of commons.wikimedia.org/wiki/User:Watchduck#/media/… $\endgroup$ – Nex Sep 24 '17 at 12:11

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