A065501 -id:A065501 - cp's OEIS frontend

A364847 Number of conjugacy classes in the group SL(2, Z_n), up to conjugacy in GL(2, Z_n).

1, 3, 5, 8, 7, 15, 9, 20, 17, 21, 13, 40, 15, 27, 35, 44, 19, 51, 21, 56, 45, 39, 25, 100, 37, 45, 53, 72, 31, 105, 33, 92, 65, 57, 63, 136, 39, 63, 75, 140, 43, 135, 45, 104, 119, 75, 49, 220, 65, 111, 95, 120, 55, 159, 91, 180, 105, 93, 61, 280, 63, 99, 153, 188, 105, 195, 69

Offset: 1

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Robin Visser, Aug 10 2023

nonn
mult

Here two matrices A, B in SL(2, Z_n) are in the same conjugacy class if P^-1*A*P = B for some matrix P in GL(2, Z_n).

Cf. A062354, A065501.

[#[c[3] : c in Classes(GL(2,ResidueClassRing(n))) | Determinant(c[3]) eq 1] : n in [2..50]];

For an odd prime p : a(p) = p + 2.

cp's OEIS Frontend

A364847 Number of conjugacy classes in the group SL(2, Z_n), up to conjugacy in GL(2, Z_n).

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