(a) |SL_2(4)| = 60; element orders: {1: 1, 2: 15, 3: 20, 5: 24}
(b) elements of order 3 and 5 fixed-point-free: True; elements with a fixed vector have order 1 or 2: True
(c) lines of F_4^2: 5; invariant under SL_2(4): 0
(d) nonzero proper F_2-subspaces of F_2^4: 65; invariant: 0; commutant of <A, B> in M_4(F_2): 4 elements
(e) <(a,A),(b,B)>: 60 elements, 60 distinct even first and 60 distinct second coordinates: True; types (5), (3,1,1) fixed-point-free: True; control with A replaced by the identity: 180 elements (not a graph: True)
(f) Brauer character of the 4-dimensional module: at a 5-element -1.000000000000, at a 3-element -2.000000000000; dim V^g = 0.0, dim V^h = 0.0
TOTAL PASS
