Equation 677 Database

This is a Latin 677 magma with a 5-by-7 congruence decomposition, its 7-element fibres use magma#7981e2df rather than magma#baf8b55c. There is a congruence theta with five 7-element classes. In the following coordinate lists, the class index i is in F_5 and the listed entries have fibre coordinate u=0,1,...,6 in F_7: C0: 33,0,10,21,7,25,16 C1: 30,1,12,22,6,27,17 C2: 31,4,11,20,5,26,15 C3: 34,3,14,24,9,29,19 C4: 32,2,13,23,8,28,18 The quotient M/theta is magma#e549b5f8, the F_5 affine law i ◇ j = 2i + 4j. In these coordinates the operation is: (i,u) ◇ (j,v) = (2i+4j, 4u+v) if i=j, (i,u) ◇ (j,v) = (2i+4j, r^{-1}(4r(u)+r(v))) if i≠j, where r=(6,0,2,5,1,3,4), i.e. r(0)=6, r(1)=0, ..., r(6)=4. Thus each theta-class is a copy of magma#7981e2df, the F_7 affine law u◇v=4u+v. The off-diagonal products also use this same affine law, but through the common non-linear-looking fibre relabeling r. Proper submagmas are exactly the five theta-classes above and the five idempotent singletons {30},{31},{32},{33},{34}. Any pair from distinct theta-classes generates the whole 35-element magma, so there is no size-5 complement submagma. The automorphism group has order 20. It induces the full affine automorphism group of the F_5 quotient, with seven 5-point orbits on M: {0..4}, {5..9}, ..., {30..34}.