Properties

Label 12T179
Order \(660\)
n \(12\)
Cyclic No
Abelian No
Solvable No
Primitive Yes
$p$-group No
Group: $\PSL(2,11)$

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Group action invariants

Degree $n$ :  $12$
Transitive number $t$ :  $179$
Group :  $\PSL(2,11)$
CHM label :  $L(2,11)$
Parity:  $1$
Primitive:  Yes
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,2,3,4,5,6,7,8,9,10,12), (1,10)(2,5)(3,7)(4,8)(6,9)(11,12)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

None

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: None

Degree 4: None

Degree 6: None

Low degree siblings

11T5 x 2

Siblings are shown 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 $ $1$ $1$ $()$
$ 5, 5, 1, 1 $ $132$ $5$ $( 3, 4,10,12, 7)( 5,11, 9, 6, 8)$
$ 5, 5, 1, 1 $ $132$ $5$ $( 3,10, 7, 4,12)( 5, 9, 8,11, 6)$
$ 11, 1 $ $60$ $11$ $( 2, 3,11,10,12, 4, 6, 5, 8, 7, 9)$
$ 11, 1 $ $60$ $11$ $( 2, 5,10, 9, 6,11, 7, 4, 3, 8,12)$
$ 2, 2, 2, 2, 2, 2 $ $55$ $2$ $( 1, 2)( 3, 5)( 4, 8)( 6,10)( 7,11)( 9,12)$
$ 3, 3, 3, 3 $ $110$ $3$ $( 1, 2, 3)( 4, 8,10)( 5, 7,12)( 6,11, 9)$
$ 6, 6 $ $110$ $6$ $( 1, 2, 3, 5,11,10)( 4,12, 8, 6, 9, 7)$

Group invariants

Order:  $660=2^{2} \cdot 3 \cdot 5 \cdot 11$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  [660, 13]
Character table:   
     2  2  .  .   .   .  2  1  1
     3  1  .  .   .   .  1  1  1
     5  1  1  1   .   .  .  .  .
    11  1  .  .   1   1  .  .  .

       1a 5a 5b 11a 11b 2a 3a 6a
    2P 1a 5b 5a 11b 11a 1a 3a 3a
    3P 1a 5b 5a 11a 11b 2a 1a 2a
    5P 1a 1a 1a 11a 11b 2a 3a 6a
    7P 1a 5b 5a 11b 11a 2a 3a 6a
   11P 1a 5a 5b  1a  1a 2a 3a 6a

X.1     1  1  1   1   1  1  1  1
X.2     5  .  .   B  /B  1 -1  1
X.3     5  .  .  /B   B  1 -1  1
X.4    10  .  .  -1  -1 -2  1  1
X.5    10  .  .  -1  -1  2  1 -1
X.6    11  1  1   .   . -1 -1 -1
X.7    12  A *A   1   1  .  .  .
X.8    12 *A  A   1   1  .  .  .

A = E(5)^2+E(5)^3
  = (-1-Sqrt(5))/2 = -1-b5
B = E(11)+E(11)^3+E(11)^4+E(11)^5+E(11)^9
  = (-1+Sqrt(-11))/2 = b11