Galois group search results

Results (47 matches)

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Label	Name	Degree	Order	Parity	Solvable	Nil. class	$\#\Aut(F/K)$	Transitivity	Conj. classes	Subfields	Low Degree Siblings
1T1	Trivial	$1$	$1$	$1$	✓	$0$	$1$	$1$	$1$
2T1	$C_2$	$2$	$2$	$-1$	✓	$1$	$2$	$2$	$2$
3T1	$C_3$	$3$	$3$	$1$	✓	$1$	$3$	$1$	$3$
4T1	$C_4$	$4$	$4$	$-1$	✓	$1$	$4$	$1$	$4$	$C_2$
5T1	$C_5$	$5$	$5$	$1$	✓	$1$	$5$	$1$	$5$
6T1	$C_6$	$6$	$6$	$-1$	✓	$1$	$6$	$1$	$6$	$C_2$, $C_3$
7T1	$C_7$	$7$	$7$	$1$	✓	$1$	$7$	$1$	$7$
8T1	$C_8$	$8$	$8$	$-1$	✓	$1$	$8$	$1$	$8$	$C_2$, $C_4$
9T1	$C_9$	$9$	$9$	$1$	✓	$1$	$9$	$1$	$9$	$C_3$
10T1	$C_{10}$	$10$	$10$	$-1$	✓	$1$	$10$	$1$	$10$	$C_2$, $C_5$
11T1	$C_{11}$	$11$	$11$	$1$	✓	$1$	$11$	$1$	$11$
12T1	$C_{12}$	$12$	$12$	$-1$	✓	$1$	$12$	$1$	$12$	$C_2$, $C_3$, $C_4$, $C_6$
13T1	$C_{13}$	$13$	$13$	$1$	✓	$1$	$13$	$1$	$13$
14T1	$C_{14}$	$14$	$14$	$-1$	✓	$1$	$14$	$1$	$14$	$C_2$, $C_7$
15T1	$C_{15}$	$15$	$15$	$1$	✓	$1$	$15$	$1$	$15$	$C_3$, $C_5$
16T1	$C_{16}$	$16$	$16$	$-1$	✓	$1$	$16$	$1$	$16$	$C_2$, $C_4$, $C_8$
17T1	$C_{17}$	$17$	$17$	$1$	✓	$1$	$17$	$1$	$17$
18T1	$C_{18}$	$18$	$18$	$-1$	✓	$1$	$18$	$1$	$18$	$C_2$, $C_3$, $C_6$, $C_9$
19T1	$C_{19}$	$19$	$19$	$1$	✓	$1$	$19$	$1$	$19$
20T1	$C_{20}$	$20$	$20$	$-1$	✓	$1$	$20$	$1$	$20$	$C_2$, $C_4$, $C_5$, $C_{10}$
21T1	$C_{21}$	$21$	$21$	$1$	✓	$1$	$21$	$1$	$21$	$C_3$, $C_7$
22T1	$C_{22}$	$22$	$22$	$-1$	✓	$1$	$22$	$1$	$22$	$C_2$, $C_{11}$
23T1	$C_{23}$	$23$	$23$	$1$	✓	$1$	$23$	$1$	$23$
24T1	$C_{24}$	$24$	$24$	$-1$	✓	$1$	$24$	$1$	$24$	$C_2$, $C_3$, $C_4$, $C_6$, $C_8$, $C_{12}$
25T1	$C_{25}$	$25$	$25$	$1$	✓	$1$	$25$	$1$	$25$	$C_5$
26T1	$C_{26}$	$26$	$26$	$-1$	✓	$1$	$26$	$1$	$26$	$C_2$, $C_{13}$
27T1	$C_{27}$	$27$	$27$	$1$	✓	$1$	$27$	$1$	$27$	$C_3$, $C_9$
28T1	$C_{28}$	$28$	$28$	$-1$	✓	$1$	$28$	$1$	$28$	$C_2$, $C_4$, $C_7$, $C_{14}$
29T1	$C_{29}$	$29$	$29$	$1$	✓	$1$	$29$	$1$	$29$
30T1	$C_{30}$	$30$	$30$	$-1$	✓	$1$	$30$	$1$	$30$	$C_2$, $C_3$, $C_5$, $C_6$, $C_{10}$, $C_{15}$
31T1	$C_{31}$	$31$	$31$	$1$	✓	$1$	$31$	$1$	$31$
32T33	$C_{32}$	$32$	$32$	$-1$	✓	$1$	$32$	$1$	$32$	$C_2$, $C_4$, $C_8$, $C_{16}$
33T1	$C_{33}$	$33$	$33$	$1$	✓	$1$	$33$	$1$	$33$	$C_3$, $C_{11}$
34T1	$C_{34}$	$34$	$34$	$-1$	✓	$1$	$34$	$1$	$34$	$C_2$, $C_{17}$
35T1	$C_{35}$	$35$	$35$	$1$	✓	$1$	$35$	$1$	$35$	$C_5$, $C_7$
36T1	$C_{36}$	$36$	$36$	$-1$	✓	$1$	$36$	$1$	$36$	$C_2$, $C_3$, $C_4$, $C_6$, $C_9$, $C_{12}$, $C_{18}$
37T1	$C_{37}$	$37$	$37$	$1$	✓	$1$	$37$	$1$	$37$
38T1	$C_{38}$	$38$	$38$	$-1$	✓	$1$	$38$	$1$	$38$	$C_2$, $C_{19}$
39T1	$C_{39}$	$39$	$39$	$1$	✓	$1$	$39$	$1$	$39$	$C_3$, $C_{13}$
40T1	$C_{40}$	$40$	$40$	$-1$	✓	$1$	$40$	$1$	$40$	$C_2$, $C_4$, $C_5$, $C_8$, $C_{10}$, $C_{20}$
41T1	$C_{41}$	$41$	$41$	$1$	✓	$1$	$41$	$1$	$41$
42T1	$C_{42}$	$42$	$42$	$-1$	✓	$1$	$42$	$1$	$42$	$C_2$, $C_3$, $C_6$, $C_7$, $C_{14}$, $C_{21}$
43T1	$C_{43}$	$43$	$43$	$1$	✓	$1$	$43$	$1$	$43$
44T1	$C_{44}$	$44$	$44$	$-1$	✓	$1$	$44$	$1$	$44$	$C_2$, $C_4$, $C_{11}$, $C_{22}$
45T1	$C_{45}$	$45$	$45$	$1$	✓	$1$	$45$	$1$	$45$	$C_3$, $C_5$, $C_9$, $C_{15}$
46T1	$C_{46}$	$46$	$46$	$-1$	✓	$1$	$46$	$1$	$46$	$C_2$, $C_{23}$
47T1	$C_{47}$	$47$	$47$	$1$	✓	$1$	$47$	$1$	$47$

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