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The Sage documentation page:

points to the PARI documentation page:

Note that it is after a previous similar question here:

that the link to the PARI documentation was added in Sage:

There is an open ticket to make it easier to extract information about a PARI group:

Forwarding this answer received from Alexander Hulpke:

The names (for degrees up to 15) are from the paper:

Basically they describe the particular permutation action, not just the abstract isomorphism type. The group in the question is abstractly a C(10) (cyclic), but the [x] (brackets indicate permutational actions) indicates that it is the product action of C(5) with C(2) on 10 points (not the intransitive action on 7 points).


[Related notes.]

The Sage documentation page:

points to the PARI documentation page:

Note that it is after a previous similar question here:

that the link to the PARI documentation was added in Sage:

There is an open ticket to make it easier to extract information about a PARI group: