On the non-split group extension $2^6{cdot}S_8$
Faryad Ali
Al-Imam Mohammad Ibn Saud Islamic University (IMSIU),
Riyadh 11623,
Kingdom of Saudi Arabia
Abstract
The projective special orthogonal group $PSO^+_8( 3) cong O^+_8(3).2_1$ is a group obtained from the special orthogonal group $SO_8(3)$ on factoring by the group of scalar matrices it contains. The group $PSO^+_8( 3)$ has a maximal subgroup of the form $2^6{cdot}S_8$ with index $3838185$. The group $ar{Q}cong 2^6{cdot}S_8$ is a non-split group extension of an elemenrary abelian $2$-group of order $64$ by the symmetric group $S_8$. In the present article, we construct the non-split extension $ar{Q}$ and compute its character table by using the Fischer-Clifford matrices.
Keywords: Fischer matrices; Non-split extension; Character table
Topic: Applied Mathematics