Properties

 Label 19T1 Order $$19$$ n $$19$$ Cyclic Yes Abelian Yes Solvable Yes Primitive Yes $p$-group Yes Group: $C_{19}$

Related objects

Group action invariants

 Degree $n$ : $19$ Transitive number $t$ : $1$ Group : $C_{19}$ Parity: $1$ Primitive: Yes Nilpotency class: $1$ Generators: (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19) $|\Aut(F/K)|$: $19$

Low degree resolvents

None

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - none

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

 Cycle Type Size Order Representative $1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $1$ $1$ $()$ $19$ $1$ $19$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19)$ $19$ $1$ $19$ $( 1, 3, 5, 7, 9,11,13,15,17,19, 2, 4, 6, 8,10,12,14,16,18)$ $19$ $1$ $19$ $( 1, 4, 7,10,13,16,19, 3, 6, 9,12,15,18, 2, 5, 8,11,14,17)$ $19$ $1$ $19$ $( 1, 5, 9,13,17, 2, 6,10,14,18, 3, 7,11,15,19, 4, 8,12,16)$ $19$ $1$ $19$ $( 1, 6,11,16, 2, 7,12,17, 3, 8,13,18, 4, 9,14,19, 5,10,15)$ $19$ $1$ $19$ $( 1, 7,13,19, 6,12,18, 5,11,17, 4,10,16, 3, 9,15, 2, 8,14)$ $19$ $1$ $19$ $( 1, 8,15, 3,10,17, 5,12,19, 7,14, 2, 9,16, 4,11,18, 6,13)$ $19$ $1$ $19$ $( 1, 9,17, 6,14, 3,11,19, 8,16, 5,13, 2,10,18, 7,15, 4,12)$ $19$ $1$ $19$ $( 1,10,19, 9,18, 8,17, 7,16, 6,15, 5,14, 4,13, 3,12, 2,11)$ $19$ $1$ $19$ $( 1,11, 2,12, 3,13, 4,14, 5,15, 6,16, 7,17, 8,18, 9,19,10)$ $19$ $1$ $19$ $( 1,12, 4,15, 7,18,10, 2,13, 5,16, 8,19,11, 3,14, 6,17, 9)$ $19$ $1$ $19$ $( 1,13, 6,18,11, 4,16, 9, 2,14, 7,19,12, 5,17,10, 3,15, 8)$ $19$ $1$ $19$ $( 1,14, 8, 2,15, 9, 3,16,10, 4,17,11, 5,18,12, 6,19,13, 7)$ $19$ $1$ $19$ $( 1,15,10, 5,19,14, 9, 4,18,13, 8, 3,17,12, 7, 2,16,11, 6)$ $19$ $1$ $19$ $( 1,16,12, 8, 4,19,15,11, 7, 3,18,14,10, 6, 2,17,13, 9, 5)$ $19$ $1$ $19$ $( 1,17,14,11, 8, 5, 2,18,15,12, 9, 6, 3,19,16,13,10, 7, 4)$ $19$ $1$ $19$ $( 1,18,16,14,12,10, 8, 6, 4, 2,19,17,15,13,11, 9, 7, 5, 3)$ $19$ $1$ $19$ $( 1,19,18,17,16,15,14,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)$

Group invariants

 Order: $19$ (is prime) Cyclic: Yes Abelian: Yes Solvable: Yes GAP id: [19, 1]
 Character table:  19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1a 19a 19b 19c 19d 19e 19f 19g 19h 19i 19j 19k 19l 19m 19n 19o 19p 19q X.1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X.2 1 A B C D E F G H I /I /H /G /F /E /D /C /B X.3 1 B D F H /I /G /E /C /A A C E G I /H /F /D X.4 1 C F I /G /D /A B E H /H /E /B A D G /I /F X.5 1 D H /G /C A E I /F /B B F /I /E /A C G /H X.6 1 E /I /D A F /H /C B G /G /B C H /F /A D I X.7 1 F /G /A E /H /B D /I /C C I /D B H /E A G X.8 1 G /E B I /C D /H /A F /F A H /D C /I /B E X.9 1 H /C E /F B /I /A G /D D /G A I /B F /E C X.10 1 I /A H /B G /C F /D E /E D /F C /G B /H A X.11 1 /I A /H B /G C /F D /E E /D F /C G /B H /A X.12 1 /H C /E F /B I A /G D /D G /A /I B /F E /C X.13 1 /G E /B /I C /D H A /F F /A /H D /C I B /E X.14 1 /F G A /E H B /D I C /C /I D /B /H E /A /G X.15 1 /E I D /A /F H C /B /G G B /C /H F A /D /I X.16 1 /D /H G C /A /E /I F B /B /F I E A /C /G H X.17 1 /C /F /I G D A /B /E /H H E B /A /D /G I F X.18 1 /B /D /F /H I G E C A /A /C /E /G /I H F D X.19 1 /A /B /C /D /E /F /G /H /I I H G F E D C B 19 1 19r X.1 1 X.2 /A X.3 /B X.4 /C X.5 /D X.6 /E X.7 /F X.8 /G X.9 /H X.10 /I X.11 I X.12 H X.13 G X.14 F X.15 E X.16 D X.17 C X.18 B X.19 A A = E(19) B = E(19)^2 C = E(19)^3 D = E(19)^4 E = E(19)^5 F = E(19)^6 G = E(19)^7 H = E(19)^8 I = E(19)^9