a and
b as
133 × 133 matrices over GF(19) - phi9 in the modular atlas.
a and
b as
133 × 133 matrices over GF(19) - phi10 in the modular atlas.
a and
b as
209 × 209 matrices over GF(19) - phi11 in the modular atlas.
Source: Janko's original 7 × 7 matrices over GF(11), from which most
of the given representations can be derived with the Meat-axe.
Some of this work has been done by Peter Walsh in his Ph.D. thesis
(Birmingham, 1996), with details given in his M.Phil. thesis (Birmingham, 1994).
The matrix representations were mostly made by uncondensing them
out of condensed permutation representations.