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show/hide this revision's text 3 added reference to Mathieu groups, alternating and cyclic groups

There is a useful convention to decorate some of the groups with an index which is the smallest $n$ for which the group can act transitively on $n$ points, i.e. embeds in $S_n$ (edit:) as a transitive subgroup. Your The notation for $S_n, A_n, D_n, Q_8C_n$, ...$ suggest that you are using ityour $Q_8$ and for example Mathieu groups $M_{11}, M_{12}, M_{22}$ (although not other sporadic simple groups) follow this pattern.

Of course, there is also another convention to use the size of the group instead...
show/hide this revision's text 2 I meant transitive, thank you

There is a useful convention to decorate some of the groups with an index which is the smallest $n$ for which the group embeds in $S_n$. S_n$ (edit:) as a transitive subgroup. Your $S_n, D_n, Q_8, ...$ suggest that you are using it. Of course, there is also another convention to use the size of the group instead...
show/hide this revision's text 1 [made Community Wiki]

There is a useful convention to decorate some of the groups with an index which is the smallest $n$ for which the group embeds in $S_n$. Your $S_n, D_n, Q_8, ...$ suggest that you are using it. Of course, there is also another convention to use the size of the group instead...