Meaning of colon in group theory, if not subgroup index?

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SUMMARY

The colon notation in group theory, as seen in expressions like "(Z_5 X A_4):Z_2" and "(G_1 x G_2):G_3", signifies the semi-direct product rather than the index of a subgroup. This notation is utilized in the context of computational algebra systems, specifically GAP (Groups, Algorithms, Programming). The discussion clarifies that while the colon may suggest division, it is distinct from the traditional index notation G:H or quotient group G/H.

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I am reading a paper where the author uses colons in the description of groups. Example (not verbatim): "This subgroup is isomorphic to (Z_5 X A_4):Z_2". Several subgroups are described in the same way (as (G_1 x G_2):G_3) throughout the paper.

I have seen the colon in G:H to indicate the index of a subgroup H, in G, but that doesn't seem to make sense in this context. Does anyone know what this means?
 
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Perhaps /, as in quotient group G/H? (they both suggest some sort of division)
 
Evidently, it turns out that it's semi-direct product. The notation comes from the computational algebra system GAP.
 

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