THE CHARACTER TABLE OF A SPLIT EXTENSION OF THE HEISENBERG GROUP H1(q) BY Sp(2, q), q ODD
نویسندگان
چکیده
In this paper we determine the full character table of a certain split extension H1(q)⋊Sp(2, q) of the Heisenberg group H1 by the odd-characteristic symplectic group Sp(2, q).
منابع مشابه
On the non-split extension group $2^{6}{^{cdot}}Sp(6,2)$
In this paper we first construct the non-split extension $overline{G}= 2^{6} {^{cdot}}Sp(6,2)$ as a permutation group acting on 128 points. We then determine the conjugacy classes using the coset analysis technique, inertia factor groups and Fischer matrices, which are required for the computations of the character table of $overline{G}$ by means of Clifford-Fischer Theory. There are two inerti...
متن کاملTHE RATIONAL CHARACTER TABLE OF SPECIAL LINEAR GROUPS
In this paper we will give the character table of the irreducible rational representations of G=SL (2, q) where q= , p prime, n>O, by using the character table and the Schur indices of SL(2,q).
متن کاملOn the non-split extension $2^{2n}{^{cdot}}Sp(2n,2)$
In this paper we give some general results on the non-splitextension group $overline{G}_{n} = 2^{2n}{^{cdot}}Sp(2n,2), ngeq2.$ We then focus on the group $overline{G}_{4} =2^{8}{^{cdot}}Sp(8,2).$ We construct $overline{G}_{4}$ as apermutation group acting on 512 points. The conjugacy classes aredetermined using the coset analysis technique. Then we determine theinertia factor groups and Fischer...
متن کاملPERMUTATION GROUPS WITH BOUNDED MOVEMENT ATTAINING THE BOUNDS FOR ODD PRIMES
Let G be a transitive permutation group on a set ? and let m be a positive integer. If no element of G moves any subset of ? by more than m points, then |? | [2mp I (p-1)] wherep is the least odd primedividing |G |. When the bound is attained, we show that | ? | = 2 p q ….. q where ? is a non-negative integer with 2 < p, r 1 and q is a prime satisfying p < q < 2p, ? = 0 or 1, I i n....
متن کاملMaximum sum element orders of all proper subgroups of PGL(2, q)
In this paper we show that if q is a power of a prime p , then the projective special linear group PSL(2, q) and the stabilizer of a point of the projective line have maximum sum element orders among all proper subgroups of projective general linear group PGL(2, q) for q odd and even respectively
متن کامل