Properties

 Label 17T1 Order $$17$$ n $$17$$ Cyclic Yes Abelian Yes Solvable Yes Primitive Yes $p$-group Yes Group: $C_{17}$

Related objects

Group action invariants

 Degree $n$ : $17$ Transitive number $t$ : $1$ Group : $C_{17}$ 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) $|\Aut(F/K)|$: $17$

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 $1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $1$ $1$ $()$ $17$ $1$ $17$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16,17)$ $17$ $1$ $17$ $( 1, 3, 5, 7, 9,11,13,15,17, 2, 4, 6, 8,10,12,14,16)$ $17$ $1$ $17$ $( 1, 4, 7,10,13,16, 2, 5, 8,11,14,17, 3, 6, 9,12,15)$ $17$ $1$ $17$ $( 1, 5, 9,13,17, 4, 8,12,16, 3, 7,11,15, 2, 6,10,14)$ $17$ $1$ $17$ $( 1, 6,11,16, 4, 9,14, 2, 7,12,17, 5,10,15, 3, 8,13)$ $17$ $1$ $17$ $( 1, 7,13, 2, 8,14, 3, 9,15, 4,10,16, 5,11,17, 6,12)$ $17$ $1$ $17$ $( 1, 8,15, 5,12, 2, 9,16, 6,13, 3,10,17, 7,14, 4,11)$ $17$ $1$ $17$ $( 1, 9,17, 8,16, 7,15, 6,14, 5,13, 4,12, 3,11, 2,10)$ $17$ $1$ $17$ $( 1,10, 2,11, 3,12, 4,13, 5,14, 6,15, 7,16, 8,17, 9)$ $17$ $1$ $17$ $( 1,11, 4,14, 7,17,10, 3,13, 6,16, 9, 2,12, 5,15, 8)$ $17$ $1$ $17$ $( 1,12, 6,17,11, 5,16,10, 4,15, 9, 3,14, 8, 2,13, 7)$ $17$ $1$ $17$ $( 1,13, 8, 3,15,10, 5,17,12, 7, 2,14, 9, 4,16,11, 6)$ $17$ $1$ $17$ $( 1,14,10, 6, 2,15,11, 7, 3,16,12, 8, 4,17,13, 9, 5)$ $17$ $1$ $17$ $( 1,15,12, 9, 6, 3,17,14,11, 8, 5, 2,16,13,10, 7, 4)$ $17$ $1$ $17$ $( 1,16,14,12,10, 8, 6, 4, 2,17,15,13,11, 9, 7, 5, 3)$ $17$ $1$ $17$ $( 1,17,16,15,14,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)$

Group invariants

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