  The internal degrees of freedom of fermions are in the spin-charge-family
theory described by the Clifford algebra objects, which are superposition of an
odd number of $\gamma^a$'s. Arranged into irreducible representations of
"eigenvectors" of the Cartan subalgebra of the Lorentz algebra $S^{ab}$ $(=
\frac{i}{2} \gamma^a \gamma^b|_{a \ne b})$ these objects form
$2^{\frac{d}{2}-1}$ families with $2^{\frac{d}{2}-1}$ family members each.
Family members of each family offer the description of all the observed quarks
and leptons and antiquarks and antileptons, appearing in families. Families are
reachable by $\tilde{S}^{ab}$ $=\frac{1}{2} \tilde{\gamma}^a
\tilde{\gamma}^b|_{a \ne b}$. Creation operators, carrying the family member
and family quantum numbers form the basic vectors. The action of the operators
$\gamma^a$'s, $S^{ab}$, $\tilde{\gamma}^a$'s and $\tilde{S}^{ab}$, applying on
the basic vectors, manifests as matrices. In this paper the basic vectors in
$d=(3+1)$ Clifford space are discussed, chosen in a way that the matrix
representations of $\gamma^a$ and of $S^{ab}$ coincide for each family quantum
number, determined by $\tilde{S}^{ab} $, with the Dirac matrices. The
appearance of charges in Clifford space is discussed by embedding $d=(3+1)$
space into $d=(5+1)$-dimensional space.
