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LSpice
LSpice
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I don't think the cohomology is known. As an indication of this I would refer to the 2007 paper "On the Stiefel–Whitney classes of the representations associated with Spin(15)"On the Stiefel–Whitney classes of the representations associated with Spin(15)" by Mamoru Mimura and Tetsu Nishimoto (see https://msp.org/gtm/2007/11/p007.xhtml). There they state that "calculating $H^\ast(BSs(16);Z/2Z)$ seems to be as difficult as calculating $H^\ast(BE_8;Z/2Z)$" (which is also still unknown).

I don't think the cohomology is known. As an indication of this I would refer to the 2007 paper "On the Stiefel–Whitney classes of the representations associated with Spin(15)" by Mamoru Mimura and Tetsu Nishimoto (see https://msp.org/gtm/2007/11/p007.xhtml). There they state that "calculating $H^\ast(BSs(16);Z/2Z)$ seems to be as difficult as calculating $H^\ast(BE_8;Z/2Z)$" (which is also still unknown).

I don't think the cohomology is known. As an indication of this I would refer to the 2007 paper "On the Stiefel–Whitney classes of the representations associated with Spin(15)" by Mamoru Mimura and Tetsu Nishimoto (see https://msp.org/gtm/2007/11/p007.xhtml). There they state that "calculating $H^\ast(BSs(16);Z/2Z)$ seems to be as difficult as calculating $H^\ast(BE_8;Z/2Z)$" (which is also still unknown).

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Martin Sleziak
Martin Sleziak
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I don't think the cohomology is known. As an indication of this I would refer to the 2007 paper "On the Stiefel–Whitney classes of the representations associated with Spin(15)" by Mamoru Mimura and Tetsu Nishimoto (see http://www.msp.warwick.ac.uk/gtm/2007/11/p007.xhtmlhttps://msp.org/gtm/2007/11/p007.xhtml). There they state that "calculating $H^\ast(BSs(16);Z/2Z)$ seems to be as difficult as calculating $H^\ast(BE_8;Z/2Z)$" (which is also still unknown).

I don't think the cohomology is known. As an indication of this I would refer to the 2007 paper "On the Stiefel–Whitney classes of the representations associated with Spin(15)" by Mamoru Mimura and Tetsu Nishimoto (see http://www.msp.warwick.ac.uk/gtm/2007/11/p007.xhtml). There they state that "calculating $H^\ast(BSs(16);Z/2Z)$ seems to be as difficult as calculating $H^\ast(BE_8;Z/2Z)$" (which is also still unknown).

I don't think the cohomology is known. As an indication of this I would refer to the 2007 paper "On the Stiefel–Whitney classes of the representations associated with Spin(15)" by Mamoru Mimura and Tetsu Nishimoto (see https://msp.org/gtm/2007/11/p007.xhtml). There they state that "calculating $H^\ast(BSs(16);Z/2Z)$ seems to be as difficult as calculating $H^\ast(BE_8;Z/2Z)$" (which is also still unknown).

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Christian Nassau
Christian Nassau
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I don't think the cohomology is known. As an indication of this I would refer to the 2007 paper "On the Stiefel–Whitney classes of the representations associated with Spin(15)" by Mamoru Mimura and Tetsu Nishimoto (see http://www.msp.warwick.ac.uk/gtm/2007/11/p007.xhtml). There they state that "calculating $H^\ast(BSs(16);Z/2Z)$ seems to be as difficult as calculating $H^\ast(BE_8;Z/2Z)$" (which is also still unknown).