p4 No. 10 p4

Generators selected (1); t(1, 0); t(0, 1); (2); (3)

General position

Multiplicity, Wyckoff letter,
Site symmetry		 Coordinates
 
4 d 1
(1) x, y(2) -x, -y(3) -y, x(4) y, -x

I Maximal translationengleiche subgroups

[2] p2 (2)1; 2

II Maximal klassengleiche subgroups

[2] a' = 2a, b' = 2b

c4 (10, p4)<2; 3>a - b, a + b
c4 (10, p4)<2 + (1, 1); 3 + (1, 0)>a - b, a + b1/2, 1/2

[p2] a' = pa, b' = pb

p4 (10)<2 + (2u, 2v); 3 + (u + v, -u + v)>pa, pbu, v
 p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for prime p ≡ 3 (mod 4)

[p = q2 + r2] a' = qa - rb, b' = ra + qb

p4 (10)<2 + (2u, 0); 3 + (u, -u)>qa - rb, ra + qbu, 0
 p > 2; q > 0; r > 0; 0 ≤ u < p
p conjugate subgroups for each pair of q and r

I Minimal translationengleiche supergroups

[2] p4mm (11); [2] p4gm (12)

II Minimal non-isomorphic klassengleiche supergroups

none
none








































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