The Conway group $Co_{1}$ is one of the $26$ sporadic simple groups. It is the largest of the three Conway groups with order $4157776806543360000=2^{21}.3^9.5^4.7^2.11.13.23$ and has $22$ conjugacy classes of maximal subgroups. In this paper, we discuss a group of the form $\overline{G}=N\colon G$, where $N=2^{11}$ and $G=M_{24}$. This group $\overline{G}=N\colon G=2^{11}\colon M_{24}$ is a split extension of an elementary abelian group $N=2^{11}$ by a Mathieu group $G=M_{24}$. Using the computed Fischer matrices for each class representative $g$ of $G$ and ordinary character tables of the inertia factor groups of $G$, we obtain the full character table of $\overline{G}$. The complete fusion of $\overline{G}$ into its mother group $Co_1$ is also determined using the permutation character of $Co_1$.
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Mugala, V., Chikopela, D., & Ng'ambi, R. (2024). On a group of the form $2^{11}:M_{24}$. AUT Journal of Mathematics and Computing, 5(2), 167-193. doi: 10.22060/ajmc.2023.22289.1151
MLA
Vasco Mugala; Dennis Siwila Chikopela; Richard Ng'ambi. "On a group of the form $2^{11}:M_{24}$". AUT Journal of Mathematics and Computing, 5, 2, 2024, 167-193. doi: 10.22060/ajmc.2023.22289.1151
HARVARD
Mugala, V., Chikopela, D., Ng'ambi, R. (2024). 'On a group of the form $2^{11}:M_{24}$', AUT Journal of Mathematics and Computing, 5(2), pp. 167-193. doi: 10.22060/ajmc.2023.22289.1151
VANCOUVER
Mugala, V., Chikopela, D., Ng'ambi, R. On a group of the form $2^{11}:M_{24}$. AUT Journal of Mathematics and Computing, 2024; 5(2): 167-193. doi: 10.22060/ajmc.2023.22289.1151