I was calculating the Sylow 2-Subgroups of Mathieu group M(12) through GAP. I am facing a problem, some of the Sylow 2-Subgroups are represented as C_8:(C_2×C_2) with colon(" : "). I don't know about the meaning of this. If we see the group order it is 32 of this group. In the same way every Sylow 2-Subgroups of this representation is having order of multiples like this 8x2x2=32.
2026-03-30 07:11:35.1774854695
What is the meaning of symbol " : " in demonstrating the group in GAP? For example C_8:(C_2×C_2).
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It means a semidirect product. In general, we can write $G = N:Q$ for $G = N\rtimes Q$, (or $G=Q\ltimes N$) for a semidirect product, where $N$ is normal in $G$.