Properties

Label 27T1
Order \(27\)
n \(27\)
Cyclic Yes
Abelian Yes
Solvable Yes
Primitive No
$p$-group Yes
Group: $C_{27}$

Related objects

Learn more about

Group action invariants

Degree $n$ :  $27$
Transitive number $t$ :  $1$
Group :  $C_{27}$
Parity:  $1$
Primitive:  No
Nilpotency class:  $1$
Generators:  (1,6,9,12,14,16,19,23,27,2,4,7,10,15,17,20,24,25,3,5,8,11,13,18,21,22,26)
$|\Aut(F/K)|$:  $27$

Low degree resolvents

|G/N|Galois groups for stem field(s)
3:  $C_3$
9:  $C_9$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 9: $C_9$

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 TypeSizeOrderRepresentative
$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1$ $1$ $()$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $1$ $3$ $( 1, 2, 3)( 4, 5, 6)( 7, 8, 9)(10,11,12)(13,14,15)(16,17,18)(19,20,21) (22,23,24)(25,26,27)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $1$ $3$ $( 1, 3, 2)( 4, 6, 5)( 7, 9, 8)(10,12,11)(13,15,14)(16,18,17)(19,21,20) (22,24,23)(25,27,26)$
$ 27 $ $1$ $27$ $( 1, 4, 8,12,15,18,19,24,26, 2, 5, 9,10,13,16,20,22,27, 3, 6, 7,11,14,17,21, 23,25)$
$ 27 $ $1$ $27$ $( 1, 5, 7,12,13,17,19,22,25, 2, 6, 8,10,14,18,20,23,26, 3, 4, 9,11,15,16,21, 24,27)$
$ 27 $ $1$ $27$ $( 1, 6, 9,12,14,16,19,23,27, 2, 4, 7,10,15,17,20,24,25, 3, 5, 8,11,13,18,21, 22,26)$
$ 27 $ $1$ $27$ $( 1, 7,13,19,25, 6,10,18,23, 3, 9,15,21,27, 5,12,17,22, 2, 8,14,20,26, 4,11, 16,24)$
$ 27 $ $1$ $27$ $( 1, 8,15,19,26, 5,10,16,22, 3, 7,14,21,25, 4,12,18,24, 2, 9,13,20,27, 6,11, 17,23)$
$ 27 $ $1$ $27$ $( 1, 9,14,19,27, 4,10,17,24, 3, 8,13,21,26, 6,12,16,23, 2, 7,15,20,25, 5,11, 18,22)$
$ 9, 9, 9 $ $1$ $9$ $( 1,10,21, 2,11,19, 3,12,20)( 4,13,23, 5,14,24, 6,15,22)( 7,18,27, 8,16,25, 9, 17,26)$
$ 9, 9, 9 $ $1$ $9$ $( 1,11,20, 2,12,21, 3,10,19)( 4,14,22, 5,15,23, 6,13,24)( 7,16,26, 8,17,27, 9, 18,25)$
$ 9, 9, 9 $ $1$ $9$ $( 1,12,19, 2,10,20, 3,11,21)( 4,15,24, 5,13,22, 6,14,23)( 7,17,25, 8,18,26, 9, 16,27)$
$ 27 $ $1$ $27$ $( 1,13,25,10,23, 9,21, 5,17, 2,14,26,11,24, 7,19, 6,18, 3,15,27,12,22, 8,20, 4,16)$
$ 27 $ $1$ $27$ $( 1,14,27,10,24, 8,21, 6,16, 2,15,25,11,22, 9,19, 4,17, 3,13,26,12,23, 7,20, 5,18)$
$ 27 $ $1$ $27$ $( 1,15,26,10,22, 7,21, 4,18, 2,13,27,11,23, 8,19, 5,16, 3,14,25,12,24, 9,20, 6,17)$
$ 27 $ $1$ $27$ $( 1,16, 4,20, 8,22,12,27,15, 3,18, 6,19, 7,24,11,26,14, 2,17, 5,21, 9,23,10, 25,13)$
$ 27 $ $1$ $27$ $( 1,17, 6,20, 9,24,12,25,14, 3,16, 5,19, 8,23,11,27,13, 2,18, 4,21, 7,22,10, 26,15)$
$ 27 $ $1$ $27$ $( 1,18, 5,20, 7,23,12,26,13, 3,17, 4,19, 9,22,11,25,15, 2,16, 6,21, 8,24,10, 27,14)$
$ 9, 9, 9 $ $1$ $9$ $( 1,19,10, 3,21,12, 2,20,11)( 4,24,13, 6,23,15, 5,22,14)( 7,25,18, 9,27,17, 8, 26,16)$
$ 9, 9, 9 $ $1$ $9$ $( 1,20,12, 3,19,11, 2,21,10)( 4,22,15, 6,24,14, 5,23,13)( 7,26,17, 9,25,16, 8, 27,18)$
$ 9, 9, 9 $ $1$ $9$ $( 1,21,11, 3,20,10, 2,19,12)( 4,23,14, 6,22,13, 5,24,15)( 7,27,16, 9,26,18, 8, 25,17)$
$ 27 $ $1$ $27$ $( 1,22,18,11, 5,25,20,15, 7, 2,23,16,12, 6,26,21,13, 8, 3,24,17,10, 4,27,19, 14, 9)$
$ 27 $ $1$ $27$ $( 1,23,17,11, 6,27,20,13, 9, 2,24,18,12, 4,25,21,14, 7, 3,22,16,10, 5,26,19, 15, 8)$
$ 27 $ $1$ $27$ $( 1,24,16,11, 4,26,20,14, 8, 2,22,17,12, 5,27,21,15, 9, 3,23,18,10, 6,25,19, 13, 7)$
$ 27 $ $1$ $27$ $( 1,25,23,21,17,14,11, 7, 6, 3,27,22,20,16,13,10, 9, 5, 2,26,24,19,18,15,12, 8, 4)$
$ 27 $ $1$ $27$ $( 1,26,22,21,18,13,11, 8, 5, 3,25,24,20,17,15,10, 7, 4, 2,27,23,19,16,14,12, 9, 6)$
$ 27 $ $1$ $27$ $( 1,27,24,21,16,15,11, 9, 4, 3,26,23,20,18,14,10, 8, 6, 2,25,22,19,17,13,12, 7, 5)$

Group invariants

Order:  $27=3^{3}$
Cyclic:  Yes
Abelian:  Yes
Solvable:  Yes
GAP id:  [27, 1]
Character table: Data not available.