T | Name(s) | |G| | Parity | |CS15(G)| | Subfields | Other Representations | Resolvents |
---|---|---|---|---|---|---|---|
1 | C(15)=5[x]3 | 15 = 3 · 5 | 1 | 15 | 3T1, 5T1 | 3: 3T1 5: 5T1 | |
2 | D(15) | 30 = 2 · 3 · 5 | -1 | 1 | 3T2, 5T2 | 2: 2T1 6: 3T2 10: 5T2 | |
3 | D(5)[x]3 | 30 = 2 · 3 · 5 | 1 | 3 | 3T1, 5T2 | 2: 2T1 3: 3T1 6: 6T1 10: 5T2 | |
4 | 5[x]S(3) | 30 = 2 · 3 · 5 | -1 | 5 | 3T2, 5T1 | 2: 2T1 5: 5T1 6: 3T2 10: 10T1 | |
5 | A_5(15) | 60 = 22 · 3 · 5 | 1 | 3 | 5T4 | 5T4, 6T12, 10T7, 12T33, 20T15 | |
6 | F(5)[1/2]S(3) | 60 = 22 · 3 · 5 | 1 | 1 | 3T2, 5T3 | 2: 2T1 4: 4T1 6: 3T2 12: 12T5 20: 5T3 | |
7 | D(5)[x]S(3) | 60 = 22 · 3 · 5 | -1 | 1 | 3T2, 5T2 | 2: 2T1, 2T1, 2T1 4: 4T2 6: 3T2 10: 5T2 12: 6T3 20: 10T3 | |
8 | F(5)[x]3 | 60 = 22 · 3 · 5 | -1 | 3 | 3T1, 5T3 | 2: 2T1 3: 3T1 4: 4T1 6: 6T1 12: 12T1 20: 5T3 | |
9 | [5^2]3 | 75 = 3 · 52 | 1 | 5 | 3T1 | 15T9 | 3: 3T1 |
10 | S_5(15) | 120 = 23 · 3 · 5 | 1 | 1 | 5T5 | 5T5, 6T14, 10T12, 10T13, 12T74, 20T30, 20T35, 20T32 | 2: 2T1 |
11 | F(5)[x]S(3) | 120 = 23 · 3 · 5 | -1 | 1 | 3T2, 5T3 | 2: 2T1, 2T1, 2T1 4: 4T1, 4T1, 4T2 6: 3T2 8: 8T2 12: 6T3 20: 5T3 24: 12T11 40: 10T5 | |
12 | [5^2:2]3 | 150 = 2 · 3 · 52 | 1 | 1 | 3T1 | 15T12 | 2: 2T1 3: 3T1 6: 6T1 |
13 | [5^2]S(3) | 150 = 2 · 3 · 52 | -1 | 5 | 3T2 | 15T14 | 2: 2T1 6: 3T2 |
14 | 5^2:2[1/2]S(3) | 150 = 2 · 3 · 52 | -1 | 1 | 3T2 | 15T13 | 2: 2T1 6: 3T2 |
15 | 3A_5(15)=[3]A(5)=GL(2,4) | 180 = 22 · 32 · 5 | 1 | 3 | 5T4 | 15T16, 15T15, 18T90 | 3: 3T1 60: 5T4 |
16 | A(5)[x]3 | 180 = 22 · 32 · 5 | 1 | 3 | 3T1, 5T4 | 15T15, 15T15, 18T90 | 3: 3T1 60: 5T4 |
17 | 1/2[5^2:4]S(3) | 300 = 22 · 3 · 52 | 1 | 1 | 3T2 | 15T17 | 2: 2T1 4: 4T1 6: 3T2 12: 12T5 |
18 | [5^2:2]S(3) | 300 = 22 · 3 · 52 | -1 | 1 | 3T2 | 15T18 | 2: 2T1, 2T1, 2T1 4: 4T2 6: 3T2 12: 6T3 |
19 | [5^2:4]3 | 300 = 22 · 3 · 52 | -1 | 1 | 3T1 | 15T19 | 2: 2T1 3: 3T1 4: 4T1 6: 6T1 12: 12T1 |
20 | A_6(15) | 360 = 23 · 32 · 5 | 1 | 1 | 6T15, 6T15, 10T26, 15T20, 20T89 | ||
21 | 3S_5(15) | 360 = 23 · 32 · 5 | 1 | 1 | 5T5 | 15T21, 15T22, 18T146 | 2: 2T1 6: 3T2 120: 5T5 |
22 | S(5)[1/2]S(3) | 360 = 23 · 32 · 5 | 1 | 1 | 3T2, 5T5 | 15T21, 15T21, 18T146 | 2: 2T1 6: 3T2 120: 5T5 |
23 | A(5)[x]S(3) | 360 = 23 · 32 · 5 | -1 | 1 | 3T2, 5T4 | 18T145 | 2: 2T1 6: 3T2 60: 5T4 120: 10T11 |
24 | S(5)[x]3 | 360 = 23 · 32 · 5 | -1 | 3 | 3T1, 5T5 | 18T144 | 2: 2T1 3: 3T1 6: 6T1 120: 5T5 |
25 | [5^3]3=5wr3 | 375 = 3 · 53 | 1 | 5 | 3T1 | 15T25, 15T25, 15T25, 15T25, 15T25, 15T25, 15T25 | 3: 3T1 5: 5T1 15: 15T1 75: 15T9 |
26 | [3^4]5 | 405 = 34 · 5 | 1 | 3 | 5T1 | 15T26, 15T26, 15T26, 15T26, 15T26, 15T26, 15T26 | 5: 5T1 |
27 | [5^2:4]S(3) | 600 = 23 · 3 · 52 | -1 | 1 | 3T2 | 15T27 | 2: 2T1, 2T1, 2T1 4: 4T1, 4T1, 4T2 6: 3T2 8: 8T2 12: 6T3 24: 12T11 |
28 | S_6(15) | 720 = 24 · 32 · 5 | 1 | 1 | 6T16, 6T16, 10T32, 12T183, 12T183, 15T28, 20T145, 20T149, 20T149 | 2: 2T1 | |
29 | S(5)[x]S(3) | 720 = 24 · 32 · 5 | -1 | 1 | 3T2, 5T5 | 18T227 | 2: 2T1, 2T1, 2T1 4: 4T2 6: 3T2 12: 6T3 120: 5T5 240: 10T22 |
30 | [5^3:2]3 | 750 = 2 · 3 · 53 | 1 | 1 | 3T1 | 15T30, 15T30, 15T30, 15T30, 15T30, 15T30, 15T30 | 2: 2T1 3: 3T1 6: 6T1 10: 5T2 30: 15T3 150: 15T12 |
31 | 1/2[5^3:2]S(3) | 750 = 2 · 3 · 53 | -1 | 1 | 3T2 | 15T31, 15T31, 15T31 | 2: 2T1 6: 3T2 10: 5T2 30: 15T2 150: 15T13 |
32 | [5^3]S(3) | 750 = 2 · 3 · 53 | -1 | 5 | 3T2 | 15T32, 15T32, 15T32 | 2: 2T1 5: 5T1 6: 3T2 10: 10T1 30: 15T4 150: 15T13 |
33 | [3^4:2]5 | 810 = 2 · 34 · 5 | -1 | 1 | 5T1 | 15T33, 15T33, 15T33, 15T33, 15T33, 15T33, 15T33 | 2: 2T1 5: 5T1 10: 10T1 |
34 | [3^4]D(5) | 810 = 2 · 34 · 5 | 1 | 3 | 5T2 | 15T35, 15T35, 15T35, 15T35, 15T34, 15T34, 15T34 | 2: 2T1 10: 5T2 |
35 | 1/2[3^4:2]D(5) | 810 = 2 · 34 · 5 | -1 | 1 | 5T2 | 15T34, 15T34, 15T34, 15T34, 15T35, 15T35, 15T35 | 2: 2T1 10: 5T2 |
36 | [3^5]5=3wr5 | 1215 = 35 · 5 | 1 | 3 | 5T1 | 15T36, 15T36, 15T36, 15T36, 15T36, 15T36, 15T36, 15T36, 15T36, 15T36, 15T36, 15T36, 15T36, 15T36, 15T36 | 3: 3T1 5: 5T1 15: 15T1 405: 15T26 |
37 | 1/2[5^3:4]S(3) | 1500 = 22 · 3 · 53 | 1 | 1 | 3T2 | 15T37, 15T37, 15T37 | 2: 2T1 4: 4T1 6: 3T2 12: 12T5 20: 5T3 60: 15T6 300: 15T17 |
38 | [5^3:4]3 | 1500 = 22 · 3 · 53 | -1 | 1 | 3T1 | 15T38, 15T38, 15T38, 15T38, 15T38, 15T38, 15T38 | 2: 2T1 3: 3T1 4: 4T1 6: 6T1 12: 12T1 20: 5T3 60: 15T8 300: 15T19 |
39 | [1/2.D(5)^3]3 | 1500 = 22 · 3 · 53 | 1 | 1 | 3T1 | 20T209 | 3: 3T1 12: 4T4 |
40 | [5^3:2]S(3) | 1500 = 22 · 3 · 53 | -1 | 1 | 3T2 | 15T40, 15T40, 15T40 | 2: 2T1, 2T1, 2T1 4: 4T2 6: 3T2 10: 5T2 12: 6T3 20: 10T3 60: 15T7 300: 15T18 |
41 | [3^4]F(5) | 1620 = 22 · 34 · 5 | -1 | 3 | 5T3 | 15T42 | 2: 2T1 4: 4T1 20: 5T3 |
42 | 1/2[3^4:2]F(5) | 1620 = 22 · 34 · 5 | 1 | 1 | 5T3 | 15T41 | 2: 2T1 4: 4T1 20: 5T3 |
43 | [3^4:2]D(5) | 1620 = 22 · 34 · 5 | -1 | 1 | 5T2 | 15T43, 15T43, 15T43, 15T43, 15T43, 15T43, 15T43 | 2: 2T1, 2T1, 2T1 4: 4T2 10: 5T2 20: 10T3 |
44 | [3^5:2]5 | 2430 = 2 · 35 · 5 | -1 | 1 | 5T1 | 15T44, 15T44, 15T44, 15T44, 15T44, 15T44, 15T44, 15T44, 15T44, 15T44, 15T44, 15T44, 15T44, 15T44, 15T44 | 2: 2T1 5: 5T1 6: 3T2 10: 10T1 30: 15T4 810: 15T33 |
45 | 1/2[3^5:2]D(5) | 2430 = 2 · 35 · 5 | -1 | 1 | 5T2 | 15T45, 15T45, 15T45, 15T45, 15T45, 15T45, 15T45 | 2: 2T1 6: 3T2 10: 5T2 30: 15T2 810: 15T34 |
46 | [3^5]D(5)=3wrD(5) | 2430 = 2 · 35 · 5 | 1 | 3 | 5T2 | 15T46, 15T46, 15T46, 15T46, 15T46, 15T46, 15T46 | 2: 2T1 3: 3T1 6: 6T1 10: 5T2 30: 15T3 810: 15T34 |
47 | A_7(15) | 2520 = 23 · 32 · 5 · 7 | 1 | 1 | 7T6, 15T47, 21T33 | ||
48 | 1/2[D(5)^3]S(3) | 3000 = 23 · 3 · 53 | -1 | 1 | 3T2 | 20T270 | 2: 2T1 6: 3T2 24: 4T5 |
49 | [5^3:4]S(3) | 3000 = 23 · 3 · 53 | -1 | 1 | 3T2 | 15T49, 15T49, 15T49 | 2: 2T1, 2T1, 2T1 4: 4T1, 4T1, 4T2 6: 3T2 8: 8T2 12: 6T3 20: 5T3 24: 12T11 40: 10T5 120: 15T11 600: 15T27 |
50 | [D(5)^3]3=D(5)wr3 | 3000 = 23 · 3 · 53 | 1 | 1 | 3T1 | 20T269 | 2: 2T1 3: 3T1 6: 6T1 12: 4T4 24: 6T6 |
51 | [1/2.D(5)^3]S(3) | 3000 = 23 · 3 · 53 | -1 | 1 | 3T2 | 20T268 | 2: 2T1 6: 3T2 24: 4T5 |
52 | [3^4:2]F(5) | 3240 = 23 · 34 · 5 | -1 | 1 | 5T3 | 15T52 | 2: 2T1, 2T1, 2T1 4: 4T1, 4T1, 4T2 8: 8T2 20: 5T3 40: 10T5 |
53 | [3^4]A(5) | 4860 = 22 · 35 · 5 | 1 | 3 | 5T4 | 15T53, 15T53 | 60: 5T4 |
54 | 1/2[3^5:2]F(5) | 4860 = 22 · 35 · 5 | 1 | 1 | 5T3 | 15T54 | 2: 2T1 4: 4T1 6: 3T2 12: 12T5 20: 5T3 60: 15T6 1620: 15T41 |
55 | [3^5:2]D(5) | 4860 = 22 · 35 · 5 | -1 | 1 | 5T2 | 15T55, 15T55, 15T55, 15T55, 15T55, 15T55, 15T55 | 2: 2T1, 2T1, 2T1 4: 4T2 6: 3T2 10: 5T2 12: 6T3 20: 10T3 60: 15T7 1620: 15T43 |
56 | [3^5]F(5)=3wrF(5) | 4860 = 22 · 35 · 5 | -1 | 3 | 5T3 | 15T56 | 2: 2T1 3: 3T1 4: 4T1 6: 6T1 12: 12T1 20: 5T3 60: 15T8 1620: 15T41 |
57 | [1/4.F(5)^3]3 | 6000 = 24 · 3 · 53 | 1 | 1 | 3T1 | 3: 3T1 12: 4T4 48: 12T31 | |
58 | 1/2[D(5)^3:2]S(3) | 6000 = 24 · 3 · 53 | 1 | 1 | 3T2 | 20T360 | 2: 2T1 4: 4T1 6: 3T2 12: 12T5 24: 4T5 48: 12T27 |
59 | [D(5)^3:2]3 | 6000 = 24 · 3 · 53 | -1 | 1 | 3T1 | 20T359 | 2: 2T1 3: 3T1 4: 4T1 6: 6T1 12: 4T4, 12T1 24: 6T6 48: 12T29 |
60 | [D(5)^3]S(3)=D(5)wrS(3) | 6000 = 24 · 3 · 53 | -1 | 1 | 3T2 | 20T361 | 2: 2T1, 2T1, 2T1 4: 4T2 6: 3T2 12: 6T3 24: 4T5 48: 6T11 |
61 | [3^4:2]A(5) | 9720 = 23 · 35 · 5 | -1 | 1 | 5T4 | 2: 2T1 60: 5T4 120: 10T11 | |
62 | 1/2[3^4:2]S(5) | 9720 = 23 · 35 · 5 | 1 | 1 | 5T5 | 15T62, 15T62 | 2: 2T1 120: 5T5 |
63 | [3^4]S(5) | 9720 = 23 · 35 · 5 | -1 | 3 | 5T5 | 2: 2T1 120: 5T5 | |
64 | [3^5:2]F(5) | 9720 = 23 · 35 · 5 | -1 | 1 | 5T3 | 15T64 | 2: 2T1, 2T1, 2T1 4: 4T1, 4T1, 4T2 6: 3T2 8: 8T2 12: 6T3 20: 5T3 24: 12T11 40: 10T5 120: 15T11 3240: 15T52 |
65 | 1/2[1/2.F(5)^3]S(3) | 12000 = 25 · 3 · 53 | -1 | 1 | 3T2 | 2: 2T1 6: 3T2 24: 4T5 96: 12T62 | |
66 | [1/4.F(5)^3]S(3) | 12000 = 25 · 3 · 53 | -1 | 1 | 3T2 | 2: 2T1 6: 3T2 24: 4T5 96: 12T62 | |
67 | [1/2.F(5)^3]3 | 12000 = 25 · 3 · 53 | 1 | 1 | 3T1 | 2: 2T1 3: 3T1 6: 6T1 12: 4T4 24: 6T6 48: 12T31 96: 12T55 | |
68 | [D(5)^3:2]S(3) | 12000 = 25 · 3 · 53 | -1 | 1 | 3T2 | 20T454 | 2: 2T1, 2T1, 2T1 4: 4T1, 4T1, 4T2 6: 3T2 8: 8T2 12: 6T3 24: 4T5, 12T11 48: 6T11 96: 12T53 |
69 | [3^5]A(5)=3wrA(5) | 14580 = 22 · 36 · 5 | 1 | 3 | 5T4 | 15T69, 15T69, 15T69, 15T69, 15T69 | 3: 3T1 60: 5T4 180: 15T15 4860: 15T53 |
70 | [3^4:2]S(5) | 19440 = 24 · 35 · 5 | -1 | 1 | 5T5 | 2: 2T1, 2T1, 2T1 4: 4T2 120: 5T5 240: 10T22 | |
71 | [1/2.S(3)^5]5 | 19440 = 24 · 35 · 5 | 1 | 1 | 5T1 | 5: 5T1 80: 10T8 | |
72 | L(15)=A_8(15)=PSL(4,2) | 20160 = 26 · 32 · 5 · 7 | 1 | 1 | 8T49, 15T72 | ||
73 | 1/2[F(5)^3]S(3) | 24000 = 26 · 3 · 53 | 1 | 1 | 3T2 | 2: 2T1 4: 4T1 6: 3T2 12: 12T5 24: 4T5 48: 12T27 96: 12T62 192: 12T98 | |
74 | [1/2.F(5)^3]S(3) | 24000 = 26 · 3 · 53 | -1 | 1 | 3T2 | 2: 2T1, 2T1, 2T1 4: 4T2 6: 3T2 12: 6T3 24: 4T5 48: 6T11 96: 12T62 192: 12T95 | |
75 | [F(5)^3]3=F(5)wr3 | 24000 = 26 · 3 · 53 | -1 | 1 | 3T1 | 2: 2T1 3: 3T1 4: 4T1 6: 6T1 12: 4T4, 12T1 24: 6T6 48: 12T29, 12T31 96: 12T55 192: 12T94 | |
76 | [3^5:2]A(5) | 29160 = 23 · 36 · 5 | -1 | 1 | 5T4 | 15T76 | 2: 2T1 6: 3T2 60: 5T4 120: 10T11 360: 15T23 9720: 15T61 |
77 | 1/2[3^5:2]S(5) | 29160 = 23 · 36 · 5 | 1 | 1 | 5T5 | 15T77, 15T77, 15T77, 15T77, 15T77 | 2: 2T1 6: 3T2 120: 5T5 360: 15T21 9720: 15T62 |
78 | [3^5]S(5)=3wrS(5) | 29160 = 23 · 36 · 5 | -1 | 3 | 5T5 | 15T78 | 2: 2T1 3: 3T1 6: 6T1 120: 5T5 360: 15T24 9720: 15T63 |
79 | 1/2[S(3)^5]D(5) | 38880 = 25 · 35 · 5 | -1 | 1 | 5T2 | 2: 2T1 10: 5T2 160: 10T15 | |
80 | [1/2.S(3)^5]D(5) | 38880 = 25 · 35 · 5 | 1 | 1 | 5T2 | 2: 2T1 10: 5T2 160: 10T15 | |
81 | [S(3)^5]5=S(3)wr5 | 38880 = 25 · 35 · 5 | -1 | 1 | 5T1 | 2: 2T1 5: 5T1 10: 10T1 80: 10T8 160: 10T14 | |
82 | [F(5)^3]S(3)=F(5)wrS(3) | 48000 = 27 · 3 · 53 | -1 | 1 | 3T2 | 2: 2T1, 2T1, 2T1 4: 4T1, 4T1, 4T2 6: 3T2 8: 8T2 12: 6T3 24: 4T5, 12T11 48: 6T11 96: 12T53, 12T62 192: 12T95 384: 12T150 | |
83 | [3^5:2]S(5) | 58320 = 24 · 36 · 5 | -1 | 1 | 5T5 | 15T83 | 2: 2T1, 2T1, 2T1 4: 4T2 6: 3T2 12: 6T3 120: 5T5 240: 10T22 720: 15T29 19440: 15T70 |
84 | 1/2[S(3)^5]F(5) | 77760 = 26 · 35 · 5 | 1 | 1 | 5T3 | 2: 2T1 4: 4T1 20: 5T3 320: 10T24 | |
85 | [1/2.S(3)^5]F(5) | 77760 = 26 · 35 · 5 | -1 | 1 | 5T3 | 2: 2T1 4: 4T1 20: 5T3 320: 10T24 | |
86 | [S(3)^5]D(5)=S(3)wrD(5) | 77760 = 26 · 35 · 5 | -1 | 1 | 5T2 | 2: 2T1, 2T1, 2T1 4: 4T2 10: 5T2 20: 10T3 160: 10T15 320: 10T23 | |
87 | [S(3)^5]F(5)=S(3)wrF(5) | 155520 = 27 · 35 · 5 | -1 | 1 | 5T3 | 2: 2T1, 2T1, 2T1 4: 4T1, 4T1, 4T2 8: 8T2 20: 5T3 40: 10T5 320: 10T24 640: 10T29 | |
88 | [1/2.S(3)^5]A(5) | 233280 = 26 · 36 · 5 | 1 | 1 | 5T4 | 60: 5T4 960: 10T34 | |
89 | 1/2[S(3)^5]S(5) | 466560 = 27 · 36 · 5 | 1 | 1 | 5T5 | 2: 2T1 120: 5T5 1920: 10T37 | |
90 | [S(3)^5]A(5)=S(3)wrA(5) | 466560 = 27 · 36 · 5 | -1 | 1 | 5T4 | 2: 2T1 60: 5T4 120: 10T11 960: 10T34 1920: 10T36 | |
91 | [1/2.S(3)^5]S(5) | 466560 = 27 · 36 · 5 | -1 | 1 | 5T5 | 2: 2T1 120: 5T5 1920: 10T37 | |
92 | [A(5)^3]3=A(5)wr3 | 648000 = 26 · 34 · 53 | 1 | 1 | 3T1 | 18T911 | 3: 3T1 |
93 | [S(3)^5]S(5)=S(3)wrS(5) | 933120 = 28 · 36 · 5 | -1 | 1 | 5T5 | 2: 2T1, 2T1, 2T1 4: 4T2 120: 5T5 240: 10T22 1920: 10T37 3840: 10T39 | |
94 | 1/2[A(5)^3:2]S(3) | 1296000 = 27 · 34 · 53 | 1 | 1 | 3T2 | 18T935 | 2: 2T1 6: 3T2 |
95 | [A(5)^3:2]3 | 1296000 = 27 · 34 · 53 | -1 | 1 | 3T1 | 18T933 | 2: 2T1 3: 3T1 6: 6T1 |
96 | [A(5)^3]S(3)=A(5)wrS(3) | 1296000 = 27 · 34 · 53 | -1 | 1 | 3T2 | 18T934 | 2: 2T1 6: 3T2 |
97 | [A(5)^3:2]S(3) | 2592000 = 28 · 34 · 53 | -1 | 1 | 3T2 | 18T946 | 2: 2T1, 2T1, 2T1 4: 4T2 6: 3T2 12: 6T3 |
98 | [1/2.S(5)^3]3 | 2592000 = 28 · 34 · 53 | 1 | 1 | 3T1 | 18T947 | 3: 3T1 12: 4T4 |
99 | 1/2[S(5)^3]S(3) | 5184000 = 29 · 34 · 53 | 1 | 1 | 3T2 | 18T954 | 2: 2T1 6: 3T2 24: 4T5 |
100 | [1/2.S(5)^3]S(3) | 5184000 = 29 · 34 · 53 | -1 | 1 | 3T2 | 18T955 | 2: 2T1 6: 3T2 24: 4T5 |
101 | [S(5)^3]3=S(5)wr3 | 5184000 = 29 · 34 · 53 | -1 | 1 | 3T1 | 18T953 | 2: 2T1 3: 3T1 6: 6T1 12: 4T4 24: 6T6 |
102 | [S(5)^3]S(3)=S(5)wrS(3) | 10368000 = 210 · 34 · 53 | -1 | 1 | 3T2 | 18T958 | 2: 2T1, 2T1, 2T1 4: 4T2 6: 3T2 12: 6T3 24: 4T5 48: 6T11 |
103 | A15 | 653837184000 = 210 · 36 · 53 · 72 · 11 · 13 | 1 | 1 | |||
104 | S15 | 1307674368000 = 211 · 36 · 53 · 72 · 11 · 13 | -1 | 1 | 2: 2T1 |