A group is an algebraic structure consisting of a set of elements together with an operation that satisfies four conditions: closure, associativity, identity and invertibility. Group theory studies groups.

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Matrix representations of the generators of the full octahedral group

I want to find matrix representations of the generators of the full octahedral group which has the presentation $\{a,b,c|a^2=1,b^3=1,(ab)^4=1,ac=ca,bc=cb\} $ where a,b and c are the generators of the ...
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Describe the orbits of the action.

So $L$ denotes the set of oriented straight lines through the origin in $\mathbb{R}^{2}$ (that is, straight lines with a preferred direction, indicated by an arrow). The group $$(\mathbb{R},+)\cong ...