Two sporadic subgroups of the Baby Monster

Statement

The Baby Monster $\mathbb B$ has maximal subgroups isomorphic to the Fischer group $\mathrm{Fi}_{23}$ and the Thompson sporadic group $\mathrm{Th}$ . Consequently there are injective group homomorphisms

\mathrm{Fi}_{23}\hookrightarrow\mathbb B, \qquad\mathrm{Th}\hookrightarrow\mathbb B.

The corresponding subgroup indices are

\begin{aligned} [\mathbb B:\mathrm{Fi}_{23}]&=1015970529280000,\\ [\mathbb B:\mathrm{Th}]&=45784762417152000. \end{aligned}

Interpretation

The assertion is that subgroups of these isomorphism types exist. It does not specify images of the matrix generators chosen in the individual catalogue models and does not classify all homomorphisms. The indices agree with exact division of the respective group orders.

References

ATLAS, Baby Monster, Maximal subgroups of B, Fi23 and Th rows.