The data in each file is presented as a table where
-
\(n\): is the degree of the transitive group
-
\(k\): is the number in the library of transitive groups in
Sagemath -
Description: the structure description of the group
-
Density: the intersection density of \(\operatorname{TransitiveGroup}(n,k)\)
-
Information: this entry either is either Abelian (in which case the intersection density is \(1\) and the group is regular) or a link to a file containing further information on the derangement graph of \(\operatorname{TransitiveGroup}(n,k)\).
| n | k | Description | Density | Information |
|---|---|---|---|---|
| 15 | 1 | C15 | 1 | Abelian |
| 15 | 2 | D15 | 1 | details |
| 15 | 3 | C3 x D5 | 1 | details |
| 15 | 4 | C5 x S3 | 1 | details |
| 15 | 5 | A5 | 1 | details |
| 15 | 6 | C15 : C4 | 1 | details |
| 15 | 7 | S3 x D5 | 1 | details |
| 15 | 8 | C3 x (C5 : C4) | 1 | details |
| 15 | 9 | (C5 x C5) : C3 | 1 | details |
| 15 | 10 | S5 | 1 | details |
| 15 | 11 | (C5 : C4) x S3 | 1 | details |
| 15 | 12 | (C5 x C5) : C6 | 1 | details |
| 15 | 13 | (C5 x C5) : S3 | 1 | details |
| 15 | 14 | (C5 x C5) : S3 | 1 | details |
| 15 | 15 | GL(2,4) | 1 | details |
| 15 | 16 | GL(2,4) | 1 | details |
| 15 | 17 | (C5 x C5) : (C3 : C4) | 1 | details |
| 15 | 18 | (C5 x C5) : D6 | 1 | details |
| 15 | 19 | (C5 x C5) : C12 | 1 | details |
| 15 | 20 | A6 | 1.0 | details |
| 15 | 21 | A5 : S3 | 1 | details |
| 15 | 22 | C3 : S5 | 1 | details |
| 15 | 23 | A5 x S3 | 1 | details |
| 15 | 24 | C3 x S5 | 1 | details |
| 15 | 25 | C5 x ((C5 x C5) : C3) | 1 | details |
| 15 | 26 | (C3 x C3 x C3 x C3) : C5 | 1 | details |
| 15 | 27 | (C5 x C5) : (C4 x S3) | 1 | details |
| 15 | 28 | S6 | 1.0 | details |
| 15 | 29 | S5 x S3 | 1 | details |
| 15 | 30 | (C5 x C5 x C5) : C6 | 1 | details |
| 15 | 31 | (C5 x C5 x C5) : S3 | 1 | details |
| 15 | 32 | C5 x ((C5 x C5) : S3) | 1 | details |
| 15 | 33 | (C3 x C3 x C3 x C3) : C10 | 1 | details |
| 15 | 34 | (C3 x C3 x C3 x C3) : D5 | 1 | details |
| 15 | 35 | (C3 x C3 x C3 x C3) : D5 | 1 | details |
| 15 | 36 | C3 x ((C3 x C3 x C3 x C3) : C5) | 1.0 | details |
| 15 | 37 | (C5 x C5 x C5) : (C3 : C4) | 1.0 | details |
| 15 | 38 | (C5 x C5 x C5) : C12 | 1.0 | details |
| 15 | 39 | (C5 x C5 x C5) : A4 | 1.0 | details |
| 15 | 40 | (C5 x C5 x C5) : D6 | 1.0 | details |
| 15 | 41 | (C3 x C3 x C3 x C3) : (C5 : C4) | 1.0 | details |
| 15 | 42 | (C3 x C3 x C3 x C3) : (C5 : C4) | 1.0 | details |
| 15 | 43 | (C3 x C3 x C3 x C3) : D10 | 1.0 | details |
| 15 | 44 | (C3 x C3 x C3 x C3 x C3) : C10 | 1.0 | details |
| 15 | 45 | (C3 x C3 x C3 x C3 x C3) : D5 | 1.0 | details |
| 15 | 46 | C3 x ((C3 x C3 x C3 x C3) : D5) | 1.0 | details |
| 15 | 47 | A7 | 1 | details |
| 15 | 48 | (C5 x C5 x C5) : S4 | 1.0 | details |
| 15 | 49 | (C5 x C5 x C5) : (C4 x S3) | 1.0 | details |
| 15 | 50 | (C5 x C5 x C5) : (C2 x A4) | 1.0 | details |
| 15 | 51 | (C5 x C5 x C5) : S4 | 1.0 | details |
| 15 | 52 | (C3 x C3 x C3 x C3) : (C2 x (C5 : C4)) | 1.0 | details |
| 15 | 53 | (C3 x C3 x C3 x C3) : A5 | 1.0 | details |
| 15 | 54 | (C3 x C3 x C3 x C3 x C3) : (C5 : C4) | 1.0 | details |
| 15 | 55 | (C3 x C3 x C3 x C3 x C3) : D10 | 1.0 | details |
| 15 | 56 | C3 x ((C3 x C3 x C3 x C3) : (C5 : C4)) | 1.0 | details |
| 15 | 57 | (C5 x C5 x C5) : ((C4 x C4) : C3) | 1.0 | details |
| 15 | 58 | (C5 x C5 x C5) : (A4 : C4) | 1.0 | details |
| 15 | 59 | (C5 x C5 x C5) : (C4 x A4) | 1.0 | details |
| 15 | 60 | (C5 x C5 x C5) : (C2 x S4) | 1.0 | details |
| 15 | 61 | (C3 x C3 x C3 x C3) : (C2 x A5) | 1.0 | details |
| 15 | 62 | (C3 x C3 x C3 x C3) : S5 | 1.0 | details |
| 15 | 63 | (C3 x C3 x C3 x C3) : S5 | 1.0 | details |
| 15 | 64 | (C3 x C3 x C3 x C3 x C3) : (C2 x (C5 : C4)) | 1.0 | details |
| 15 | 65 | (C5 x C5 x C5) : (((C4 x C4) : C3) : C2) | 1.0 | details |
| 15 | 66 | (C5 x C5 x C5) : (((C4 x C4) : C3) : C2) | 1.0 | details |
| 15 | 67 | (C5 x C5 x C5) : (C2 x ((C4 x C4) : C3)) | 1.0 | details |
| 15 | 68 | (C5 x C5 x C5) : (C4 x S4) | 1.0 | details |
| 15 | 69 | C3 x ((C3 x C3 x C3 x C3) : A5) | 1.0 | details |
| 15 | 70 | (C3 x C3 x C3 x C3) : (C2 x S5) | 1.0 | details |
| 15 | 71 | (C3 x C3 x C3 x C3 x C3) : ((C2 x C2 x C2 x C2) : C5) | 1.0 | details |
| 15 | 72 | A8 | 1 | details |
| 15 | 73 | (C5 x C5 x C5) : (((C4 x C4) : C3) : C4) | 1.0 | details |
| 15 | 74 | (C5 x C5 x C5) : (C2 x (((C4 x C4) : C3) : C2)) | 1.0 | details |
| 15 | 75 | (C5 x C5 x C5) : (C4 x ((C4 x C4) : C3)) | 1.0 | details |
| 15 | 76 | (C3 x C3 x C3 x C3) : (A5 x S3) | 1.0 | details |
| 15 | 77 | (C3 x C3 x C3 x C3) : (A5 : S3) | 1.0 | details |
| 15 | 78 | C3 x ((C3 x C3 x C3 x C3) : S5) | 1.0 | details |
| 15 | 79 | (C3 x C3 x C3 x C3 x C3) : (((C2 x C2 x C2 x C2) : C5) : C2) | 1.0 | details |
| 15 | 80 | (C3 x C3 x C3 x C3 x C3) : (((C2 x C2 x C2 x C2) : C5) : C2) | 1.0 | details |
| 15 | 81 | (C3 x C3 x C3 x C3 x C3) : (C2 x ((C2 x C2 x C2 x C2) : C5)) | 1.0 | details |
| 15 | 82 | (C5 x C5 x C5) : (C4 x (((C4 x C4) : C3) : C2)) | 1.0 | details |
| 15 | 83 | C3 : ((C3 x C3 x C3 x C3) : (C2 x S5)) | 1.0 | details |
| 15 | 84 | (C3 x C3 x C3 x C3 x C3) : (((C2 x C2 x C2 x C2) : C5) : C4) | 1.0 | details |
| 15 | 85 | (C3 x C3 x C3 x C3 x C3) : (((C2 x C2 x C2 x C2) : C5) : C4) | 1.0 | details |
| 15 | 86 | (C3 x C3 x C3 x C3 x C3) : (C2 x (((C2 x C2 x C2 x C2) : C5) : C2)) | 1.0 | details |
| 15 | 87 | (C3 x C3 x C3 x C3 x C3) : (C2 x (((C2 x C2 x C2 x C2) : C5) : C4)) | 1.0 | details |
| 15 | 88 | (C3 x C3 x C3 x C3 x C3) : ((C2 x C2 x C2 x C2) : A5) | 1.0 | details |
| 15 | 89 | (C3 x C3 x C3 x C3 x C3) : ((C2 x C2 x C2 x C2) : S5) | 1.0 | details |
| 15 | 90 | (C3 x C3 x C3 x C3 x C3) : (C2 x ((C2 x C2 x C2 x C2) : A5)) | 1.0 | details |
| 15 | 91 | (C3 x C3 x C3 x C3 x C3) : ((C2 x C2 x C2 x C2) : S5) | 1.0 | details |
| 15 | 92 | (A5 x A5 x A5) : C3 | 1.0 | details |
| 15 | 93 | (C3 x C3 x C3 x C3 x C3) : (C2 x ((C2 x C2 x C2 x C2) : S5)) | 1.0 | details |
| 15 | 94 | (A5 x A5 x A5) : S3 | 1.0 | details |
| 15 | 95 | (A5 x A5 x A5) : C6 | 1 | details |
| 15 | 96 | (A5 x A5 x A5) : S3 | 1 | details |
| 15 | 97 | (A5 x A5 x A5) : D6 | 1 | details |
| 15 | 98 | (A5 x A5 x A5) : A4 | 1 | details |
| 15 | 99 | (A5 x A5 x A5) : S4 | 1 | details |
| 15 | 100 | (A5 x A5 x A5) : S4 | 1 | details |
| 15 | 101 | (A5 x A5 x A5) : (C2 x A4) | 1 | details |
| 15 | 102 | (A5 x A5 x A5) : (C2 x S4) | 1 | details |
| 15 | 103 | A15 | 1 | details |
| 15 | 104 | S15 | 1 | details |