The group $2^6{{}^{cdot}} G_2(2)$ is a maximal subgroup of the Rudvalis group $Ru$ of index 188500 and has order 774144 = $2^{12}.3^3.7$. In this paper, we construct the character table of the group $2^6{{}^{cdot}} G_2(2)$ by using the technique of Fischer-Clifford matrices.

in this paper, various elementary properties of vague rings are obtained. furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

The full automorphism group of $U_6(2)$ is a group of the form $U_6(2){:}S_3$. The group $U_6(2){:}S_3$ has a maximal subgroup $2^9{:}(L_3(4){:}S_3)$ of order 61931520. In the present paper, we determine the Fischer-Clifford matrices (which are not known yet) and hence compute the character table of the split extension $2^9{:}(L_3(4){:}S_3)$.

We prove the following results: (1) Every group is a maximal subgroup of some free idempotent generated semigroup. (2) Every finitely presented group is a maximal subgroup of some free idempotent generated semigroup arising from a finite semigroup. (3) Every group is a maximal subgroup of some free regular idempotent generated semigroup. (4) Every finite group is a maximal subgroup of some free...

the group $2^6{{}^{cdot}} g_2(2)$ is a maximal subgroup of the rudvalis group $ru$ of index 188500 and has order 774144 = $2^{12}.3^3.7$. in this paper, we construct the character table of the group $2^6{{}^{cdot}} g_2(2)$ by using the technique of fischer-clifford matrices.

In this note we determine (1) the class of LCA groups for which every proper closed subgroup is contained in a maximal subgroup, (2) the class of LCA groups for which every proper dense subgroup is contained in a maximal subgroup, and (3) the class for which every proper subgroup is contained in a maximal one. We also determine when both an LCA group and its dual have these properties.