[GAP Forum] A request for finding a group

[zohreh sayanjali]

Dear  GAP Forum,


I am trying  to figure out  if  there is  any perfect group  G whose normal
minimal subgroup, say  N, is an elementary abelian 2-group of order  2^6,
G/N is isomorphic to L2(8) and cd(G) = {1, 18, 9, 8, 7}, where the number
of irreducible characters whose degrees are 18 is 98.

Unfortunately, I do not know how to construct such a group and figure out
about its character degrees. I would really appreciate it if you help me to
find them, if there exists any.
Regards,
zohreh sayanjali.