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I'm trying to compute $H^3(point group,\mathbb{Z})$ for all the 32 point groups in 3D which has some applications in physics. Unfortunately, I could not find literature discussing this problem. So I tried to use GAP program to compute it.

I used the following code to do the computation:

gap> CroupCohomology(PointGroup(SpaceGroup(3,x)),3);

which is basically calculating the point group corresponding to the space group No.x. I have to admit it might be a bit inefficient because I'm new to GAP program.

My problem is that when I take $x=207$, because I want to obtain $H^3(O,\mathbb{Z})$ where $O$ is the octahedral group, some error props out. And when I try $x=210$, which corresponds to the same group $O$, it took too long and did not give me any result.

My ultimate goal is to obtain the cohomology group of point group $O$. Can anyone give me the result(by some analytical method or citing from some literature) or simply help me with the GAP program to get the result?

Edit: The octahedral group $O$ (symmetry group of an octahedron with only orientation preserving elements) is isomorphic to $S_4$, therefore it is in fact very easy to deal with.

I'm trying to compute $H^3(point group,\mathbb{Z})$ for all the 32 point groups in 3D which has some applications in physics. Unfortunately, I could not find literature discussing this problem. So I tried to use GAP program to compute it.

I used the following code to do the computation:

gap> GroupCohomology(PointGroup(SpaceGroup(3,x)),3);

which is basically calculating the point group corresponding to the space group No.x. I have to admit it might be a bit inefficient because I'm new to GAP program.

My problem is that when I take $x=207$, because I want to obtain $H^3(O,\mathbb{Z})$ where $O$ is the octahedral group, some error props out. And when I try $x=210$, which corresponds to the same group $O$, it took too long and did not give me any result.

My ultimate goal is to obtain the cohomology group of point group $O$. Can anyone give me the result(by some analytical method or citing from some literature) or simply help me with the GAP program to get the result?

Edit: The octahedral group $O$ (symmetry group of an octahedron with only orientation preserving elements) is isomorphic to $S_4$, therefore it is in fact very easy to deal with.

I'm trying to compute $H^3(point group,\mathbb{Z})$ for all the 32 point groups in 3D which has some applications in physics. Unfortunately, I could not find literature discussing this problem. So I tried to use GAP program to compute it.

I used the following code to do the computation: gap> CroupCohomology(PointGroup(SpaceGroup(3,x)),3);

which is basically calculating the point group corresponding to the space group No.x. I have to admit it might be a bit inefficient because I'm new to GAP program.

My problem is that when I take $x=207$, because I want to obtain $H^3(O,\mathbb{Z})$ where $O$ is the octahedral group, some error props out. And when I try $x=210$, which corresponds to the same group $O$, it took too long and did not give me any result.

My ultimate goal is to obtain the cohomology group of point group $O$. Can anyone give me the result(by some analytical method or citing from some literature) or simply help me with the GAP program to get the result?

Edit: The octahedral group $O$ (symmetry group of an octahedron with only orientation preserving elements) is isomorphic to $S_4$, therefore it is in fact very easy to deal with.

I'm trying to compute $H^3(point group,\mathbb{Z})$ for all the 32 point groups in 3D which has some applications in physics. Unfortunately, I could not find literature discussing this problem. So I tried to use GAP program to compute it.

I used the following code to do the computation:

gap> CroupCohomology(PointGroup(SpaceGroup(3,x)),3);

which is basically calculating the point group corresponding to the space group No.x. I have to admit it might be a bit inefficient because I'm new to GAP program.

My problem is that when I take $x=207$, because I want to obtain $H^3(O,\mathbb{Z})$ where $O$ is the octahedral group, some error props out. And when I try $x=210$, which corresponds to the same group $O$, it took too long and did not give me any result.

My ultimate goal is to obtain the cohomology group of point group $O$. Can anyone give me the result(by some analytical method or citing from some literature) or simply help me with the GAP program to get the result?

Edit: The octahedral group $O$ (symmetry group of an octahedron with only orientation preserving elements) is isomorphic to $S_4$, therefore it is in fact very easy to deal with.

I'm trying to compute $H^3(point group,\mathbb{Z})$ for all the 32 point groups in 3D which has some applications in physics. Unfortunately, I could not find literature discussing this problem. So I tried to use GAP program to compute it.

I used the following code to do the computation: gap> CroupCohomology(PointGroup(SpaceGroup(3,x)),3);

which is basically calculating the point group corresponding to the space group No.x. I have to admit it might be a bit inefficient because I'm new to GAP program.

My problem is that when I take $x=207$, because I want to obtain $H^3(O,\mathbb{Z})$ where $O$ is the octahedron point group, some error props out. And when I try $x=210$, which corresponds to the same group $O$, it took too long and did not give me any result.

My ultimate goal is to obtain the cohomology group of point group $O$. Can anyone give me the result(by some analytical method or citing from some literature) or simply help me with the GAP program to get the result?

I'm trying to compute $H^3(point group,\mathbb{Z})$ for all the 32 point groups in 3D which has some applications in physics. Unfortunately, I could not find literature discussing this problem. So I tried to use GAP program to compute it.

I used the following code to do the computation: gap> CroupCohomology(PointGroup(SpaceGroup(3,x)),3);

which is basically calculating the point group corresponding to the space group No.x. I have to admit it might be a bit inefficient because I'm new to GAP program.

My problem is that when I take $x=207$, because I want to obtain $H^3(O,\mathbb{Z})$ where $O$ is the octahedral group, some error props out. And when I try $x=210$, which corresponds to the same group $O$, it took too long and did not give me any result.

My ultimate goal is to obtain the cohomology group of point group $O$. Can anyone give me the result(by some analytical method or citing from some literature) or simply help me with the GAP program to get the result?

Edit: The octahedral group $O$ (symmetry group of an octahedron with only orientation preserving elements) is isomorphic to $S_4$, therefore it is in fact very easy to deal with.