The orthogonal groups form a class of finite simple groups of Lie type. In odd dimensions, there is just one type of orthogonal group but, in even dimensions, there are two types of orthogonal groups, distinguished by either $\mathrm{\_mo}\left(''+''\right)$ or $\mathrm{\_mo}\left(''-''\right)$ as indicated in the strings.

The OrthogonalGroup( name ) command returns a permutation group isomorphic to an orthogonal group from among those listed above.

$\mathrm{with}\left(\mathrm{GroupTheory}\right)\:$

$G≔\mathrm{OrthogonalGroup}\left(''O8+(2)''\right)$

$G≔{\Omega }_8^{+}\left(2\right)$

$\mathrm{Degree}\left(G\right)$

$120$

$\mathrm{GroupOrder}\left(\mathrm{OrthogonalGroup}\left(''O10-(2)''\right)\right)$

$25015379558400$

$\mathrm{IsSimple}\left(\mathrm{OrthogonalGroup}\left(''O10+(2)''\right)\right)$

$\mathrm{true}$

$\mathrm{ct}≔\mathrm{CharacterTable}\left(\mathrm{OrthogonalGroup}\left(''O7(3)''\right)\right)\:$

$\mathrm{CharacterDegrees}\left(\mathrm{ct}\right)$

$\left[\left[1\,1\right]\,\left[78\,1\right]\,\left[91\,1\right]\,\left[105\,1\right]\,\left[168\,1\right]\,\left[182\,1\right]\,\left[195\,1\right]\,\left[260\,2\right]\,\left[273\,1\right]\,\left[546\,1\right]\,\left[819\,1\right]\,\left[910\,2\right]\,\left[1092\,1\right]\,\left[1365\,2\right]\,\left[1560\,2\right]\,\left[1638\,1\right]\,\left[1820\,1\right]\,\left[2106\,1\right]\,\left[2184\,1\right]\,\left[2457\,1\right]\,\left[2730\,2\right]\,\left[2835\,1\right]\,\left[4095\,2\right]\,\left[4368\,1\right]\,\left[4536\,1\right]\,\left[5265\,1\right]\,\left[5460\,3\right]\,\left[5824\,2\right]\,\left[6552\,1\right]\,\left[7020\,2\right]\,\left[7280\,3\right]\,\left[7371\,1\right]\,\left[8190\,2\right]\,\left[11648\,1\right]\,\left[14742\,1\right]\,\left[16380\,1\right]\,\left[16640\,2\right]\,\left[17472\,2\right]\,\left[17920\,2\right]\,\left[19683\,1\right]\,\left[21840\,1\right]\,\left[22113\,1\right]\right]$

The GroupTheory[OrthogonalGroup] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.