整数模n乘法群
列表

这个表列出了较小 n  (\mathbb {Z} /n\mathbb {Z} )^{\times } 的结构和生成元。生成元不是惟一（mod n）的，比如 (mod 16) 时 {–1, 3} 和{–1, 5} 都可以。生成元以和直积因子相同的顺序列出。
以 n=20 为例。 \varphi (20)=8 意味着  (\mathbb {Z} /20\mathbb {Z} )^{\times } 的阶数是 8（即有 8 个小于 20 的正整数与其互质）； \lambda (20)=4 说明任何和20互质的数的 4 次幂≡ 1(mod 20)；至于生成元，19 的指数为2，3 的指数为 4，而任何 (\mathbb {Z} /20\mathbb {Z} )^{\times } 中元素都是 19a × 3b 的形式，这里 a 为 0 或 1，b 为 0, 1, 2, 或 3。
19 的幂是 {±1}，3 的幂为 {3, 9, 7, 1}。后者和他们的负数 (mod 20)，{17, 11, 13, 19} 是所有小于 20 且与其互质的数。19 的指数为 2 而 3 的指数为 4 意味着任何  \mathbb {Z} _{20}^{\times } 中数的 4 次幂 ≡ 1 (mod 20)。
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
|  n |  (\mathbb {Z} /n\mathbb {Z} )^{\times } |  \varphi (n) |  \lambda (n) | 生成元 |   |  n |  (\mathbb {Z} /n\mathbb {Z} )^{\times } |  \varphi (n) |  \lambda (n) | 生成元 |   |  n |  (\mathbb {Z} /n\mathbb {Z} )^{\times } |  \varphi (n) |  \lambda (n) | 生成元 |
| 1 | C1 | 1 | 1 | 0 |   | 32 | C2×C8 | 16 | 8 | 31, 3 |   | 63 | C6×C6 | 36 | 6 | 2, 5 |
| 2 | C1 | 1 | 1 | 1 |   | 33 | C2×C10 | 20 | 10 | 10, 2 |   | 64 | C2×C16 | 32 | 16 | 3, 63 |
| 3 | C2 | 2 | 2 | 2 |   | 34 | C16 | 16 | 16 | 3 |   | 65 | C4×C12 | 48 | 12 | 2, 12 |
| 4 | C2 | 2 | 2 | 3 |   | 35 | C2×C12 | 24 | 12 | 6, 2 |   | 66 | C2×C10 | 20 | 10 | 5, 7 |
| 5 | C4 | 4 | 4 | 2 |   | 36 | C2×C6 | 12 | 6 | 19, 5 |   | 67 | C66 | 66 | 66 | 2 |
| 6 | C2 | 2 | 2 | 5 |   | 37 | C36 | 36 | 36 | 2 |   | 68 | C2×C16 | 32 | 16 | 3, 67 |
| 7 | C6 | 6 | 6 | 3 |   | 38 | C18 | 18 | 18 | 3 |   | 69 | C2×C22 | 44 | 22 | 2, 68 |
| 8 | C2×C2 | 4 | 2 | 7, 3 |   | 39 | C2×C12 | 24 | 12 | 38, 2 |   | 70 | C2×C12 | 24 | 12 | 3, 11 |
| 9 | C6 | 6 | 6 | 2 |   | 40 | C2×C2×C4 | 16 | 4 | 39, 11, 3 |   | 71 | C70 | 70 | 70 | 7 |
| 10 | C4 | 4 | 4 | 3 |   | 41 | C40 | 40 | 40 | 6 |   | 72 | C2×C2×C6 | 24 | 12 | 5, 7, 11 |
| 11 | C10 | 10 | 10 | 2 |   | 42 | C2×C6 | 12 | 6 | 13, 5 |   | 73 | C72 | 72 | 72 | 5 |
| 12 | C2×C2 | 4 | 2 | 5, 7 |   | 43 | C42 | 42 | 42 | 3 |   | 74 | C36 | 36 | 36 | 5 |
| 13 | C12 | 12 | 12 | 2 |   | 44 | C2×C10 | 20 | 10 | 43, 3 |   | 75 | C2×C20 | 40 | 20 | 2, 74 |
| 14 | C6 | 6 | 6 | 3 |   | 45 | C2×C12 | 24 | 12 | 44, 2 |   | 76 | C2×C18 | 36 | 18 | 3, 75 |
| 15 | C2×C4 | 8 | 4 | 14, 2 |   | 46 | C22 | 22 | 22 | 5 |   | 77 | C2×C30 | 60 | 30 | 2, 76 |
| 16 | C2×C4 | 8 | 4 | 15, 3 |   | 47 | C46 | 46 | 46 | 5 |   | 78 | C2×C12 | 24 | 12 | 5, 7 |
| 17 | C16 | 16 | 16 | 3 |   | 48 | C2×C2×C4 | 16 | 4 | 47, 7, 5 |   | 79 | C78 | 78 | 78 | 3 |
| 18 | C6 | 6 | 6 | 5 |   | 49 | C42 | 42 | 42 | 3 |   | 80 | C2×C4×C4 | 32 | 4 | 3, 7, 11 |
| 19 | C18 | 18 | 18 | 2 |   | 50 | C20 | 20 | 20 | 3 |   | 81 | C54 | 54 | 54 | 2 |
| 20 | C2×C4 | 8 | 4 | 19, 3 |   | 51 | C2×C16 | 32 | 16 | 50, 5 |   | 82 | C40 | 40 | 40 | 7 |
| 21 | C2×C6 | 12 | 6 | 20, 2 |   | 52 | C2×C12 | 24 | 12 | 51, 7 |   | 83 | C82 | 82 | 82 | 2 |
| 22 | C10 | 10 | 10 | 7 |   | 53 | C52 | 52 | 52 | 2 |   | 84 | C2×C2×C6 | 24 | 12 | 5, 11, 13 |
| 23 | C22 | 22 | 22 | 5 |   | 54 | C18 | 18 | 18 | 5 |   | 85 | C4×C16 | 64 | 16 | 2, 3 |
| 24 | C2×C2×C2 | 8 | 2 | 5, 7, 13 |   | 55 | C2×C20 | 40 | 20 | 21, 2 |   | 86 | C42 | 42 | 42 | 3 |
| 25 | C20 | 20 | 20 | 2 |   | 56 | C2×C2×C6 | 24 | 6 | 13, 29, 3 |   | 87 | C2×C28 | 56 | 28 | 2, 86 |
| 26 | C12 | 12 | 12 | 7 |   | 57 | C2×C18 | 36 | 18 | 20, 2 |   | 88 | C2×C2×C10 | 40 | 10 | 3, 5, 7 |
| 27 | C18 | 18 | 18 | 2 |   | 58 | C28 | 28 | 28 | 3 |   | 89 | C88 | 88 | 88 | 3 |
| 28 | C2×C6 | 12 | 6 | 13, 3 |   | 59 | C58 | 58 | 58 | 2 |   | 90 | C2×C12 | 24 | 12 | 7, 11 |
| 29 | C28 | 28 | 28 | 2 |   | 60 | C2×C2×C4 | 16 | 4 | 11, 19, 7 |   | 91 | C6×C12 | 72 | 12 | 2, 3 |
| 30 | C2×C4 | 8 | 4 | 11, 7 |   | 61 | C60 | 60 | 60 | 2 |   | 92 | C2×C22 | 44 | 22 | 3, 91 |
| 31 | C30 | 30 | 30 | 3 |   | 62 | C30 | 30 | 30 | 3 |   | 93 | C2×C30 | 60 | 30 | 5, 11 |