Cyclic 6-cycle systems of order 21
Let V = Z21.
There are 378 paiwise nonisomorphic cyclic 6-cycle systems of order 21:
1. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,14,1,10)
2. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,14,1,12)
3. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,14,2,10)
4. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,14,2,13)
5. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,14,4,12)
6. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,14,4,13)
7. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,15,1,10)
8. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,15,1,12)
9. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,15,5,12)
10. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,15,5,14)
11. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,16,2,10)
12. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,16,2,13)
13. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,16,6,13)
14. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,16,6,14)
15. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,18,4,12)
16. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,18,4,13)
17. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,18,5,12)
18. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,18,5,14)
19. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,18,6,13)
20. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,7,18,6,14)
21. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,1,12,4)
22. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,1,12,8)
23. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,1,14,4)
24. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,1,18,8)
25. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,2,13,4)
26. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,2,13,9)
27. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,2,14,4)
28. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,2,19,9)
29. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,6,17,8)
30. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,6,17,9)
31. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,6,18,8)
32. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,6,19,9)
33. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,14,1,12)
34. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,14,2,13)
35. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,14,4,12)
36. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,14,4,13)
37. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,18,1,12)
38. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,18,8,12)
39. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,19,2,13)
40. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,10,19,9,13)
41. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,11,1,5,12)
42. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,11,1,8,12)
43. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,11,15,1,10)
44. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,11,15,1,12)
45. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,11,15,5,12)
46. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,11,18,1,10)
47. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,11,18,1,12)
48. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,11,18,6,10)
49. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,11,18,8,12)
50. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,11,20,6,10)
51. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,12,16,2,10)
52. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,12,19,2,10)
53. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,12,19,6,10)
54. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,12,20,6,10)
55. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,14,5,1,8)
56. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,14,5,12,4)
57. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,14,5,12,8)
58. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,14,5,18,4)
59. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,14,6,2,9)
60. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,14,6,13,4)
61. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,14,6,13,9)
62. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,14,6,18,4)
63. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,14,10,1,8)
64. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,14,10,2,9)
65. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,14,10,17,8)
66. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,14,10,17,9)
67. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,15,1,12,4)
68. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,15,1,12,8)
69. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,15,1,14,4)
70. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,15,1,18,8)
71. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,15,5,1,8)
72. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,15,5,12,4)
73. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,15,5,12,8)
74. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,15,5,18,4)
75. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,15,7,14,4)
76. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,15,7,18,4)
77. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,15,11,1,8)
78. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,15,11,18,8)
79. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,16,2,13,4)
80. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,16,2,14,4)
81. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,16,6,13,4)
82. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,16,6,18,4)
83. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,16,7,14,4)
84. (0,1,7,8,14,15) (0,2,7,9,14,16) (0,3,16,7,18,4)
85. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,14,1,10)
86. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,14,1,12)
87. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,14,4,12)
88. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,14,4,13)
89. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,15,1,10)
90. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,15,1,12)
91. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,15,3,10)
92. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,15,3,14)
93. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,15,5,12)
94. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,15,5,14)
95. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,16,3,10)
96. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,16,3,14)
97. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,16,6,13)
98. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,16,6,14)
99. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,18,4,12)
100. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,18,4,13)
101. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,18,5,12)
102. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,18,5,14)
103. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,18,6,13)
104. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,7,18,6,14)
105. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,9,14,1,10)
106. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,9,14,1,12)
107. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,9,14,4,12)
108. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,9,14,4,13)
109. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,9,17,1,10)
110. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,9,17,1,12)
111. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,9,17,5,10)
112. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,9,17,7,12)
113. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,9,18,5,10)
114. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,9,18,8,13)
115. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,9,20,4,12)
116. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,9,20,4,13)
117. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,9,20,7,12)
118. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,9,20,8,13)
119. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,10,1,12,5)
120. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,10,1,12,7)
121. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,10,1,15,5)
122. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,10,1,17,7)
123. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,10,3,14,5)
124. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,10,3,14,9)
125. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,10,3,15,5)
126. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,10,3,19,9)
127. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,10,5,16,7)
128. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,10,5,16,9)
129. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,10,5,17,7)
130. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,10,5,19,9)
131. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,10,15,1,12)
132. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,10,15,5,12)
133. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,10,17,1,12)
134. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,10,17,7,12)
135. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,11,16,3,10)
136. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,11,18,5,10)
137. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,11,19,3,10)
138. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,11,19,5,10)
139. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,13,4,12,5)
140. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,13,4,12,7)
141. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,13,4,18,5)
142. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,13,4,20,7)
143. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,13,6,1,9)
144. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,13,6,14,5)
145. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,13,6,14,9)
146. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,13,6,18,5)
147. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,13,8,1,9)
148. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,13,8,16,7)
149. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,13,8,16,9)
150. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,13,8,20,7)
151. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,14,1,12,5)
152. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,14,1,12,7)
153. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,14,1,15,5)
154. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,14,1,17,7)
155. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,14,4,12,5)
156. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,14,4,12,7)
157. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,14,4,18,5)
158. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,14,4,20,7)
159. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,14,7,15,5)
160. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,14,7,18,5)
161. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,14,9,17,7)
162. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,14,9,20,7)
163. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,16,3,14,5)
164. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,16,3,15,5)
165. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,16,6,14,5)
166. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,16,6,18,5)
167. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,16,7,15,5)
168. (0,1,7,8,14,15) (0,3,7,10,14,17) (0,2,16,7,18,5)
169. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,12,1,8)
170. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,12,1,14)
171. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,12,4,11)
172. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,12,4,14)
173. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,12,19,8)
174. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,12,19,11)
175. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,14,6,11)
176. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,14,6,16)
177. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,14,19,8)
178. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,14,19,11)
179. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,17,1,8)
180. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,17,1,14)
181. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,17,9,14)
182. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,17,9,16)
183. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,20,4,11)
184. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,20,4,14)
185. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,20,6,11)
186. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,20,6,16)
187. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,20,9,14)
188. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,7,20,9,16)
189. (0,1,7,8,14,15) (0,9,7,16,14,2) (0,3,8,1,12,4)
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376. (0,2,7,9,14,16) (0,8,7,15,14,1) (0,3,13,19,2,9)
377. (0,2,7,9,14,16) (0,8,7,15,14,1) (0,3,13,19,5,9)
378. (0,2,7,9,14,16) (0,8,7,15,14,1) (0,3,13,20,5,9)