# Properties

 Label 11T5 Degree $11$ Order $660$ Cyclic no Abelian no Solvable no Primitive yes $p$-group no Group: $\PSL(2,11)$

# Related objects

## Group action invariants

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

## Low degree resolvents

none

Resolvents shown for degrees $\leq 47$

## Subfields

Prime degree - none

## Low degree siblings

11T5, 12T179

Siblings are shown with degree $\leq 47$

A number field with this Galois group has exactly one arithmetically equivalent field.

## Conjugacy classes

 Cycle Type Size Order Representative $1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $1$ $1$ $()$ $2, 2, 2, 2, 1, 1, 1$ $55$ $2$ $( 3, 4)( 5, 7)( 6, 9)( 8,11)$ $3, 3, 3, 1, 1$ $110$ $3$ $( 3, 5, 8)( 4,11, 7)( 6, 9,10)$ $5, 5, 1$ $132$ $5$ $( 2, 3, 6, 9, 4)( 5,10, 7, 8,11)$ $5, 5, 1$ $132$ $5$ $( 2, 3,10, 9, 7)( 4, 5,11, 8, 6)$ $6, 3, 2$ $110$ $6$ $( 1, 2)( 3, 4, 8, 7, 5,11)( 6, 9,10)$ $11$ $60$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)$ $11$ $60$ $11$ $( 1, 2, 3, 6,10, 7, 5, 9,11, 8, 4)$

## Group invariants

 Order: $660=2^{2} \cdot 3 \cdot 5 \cdot 11$ Cyclic: no Abelian: no Solvable: no Label: 660.13
 Character table:  2 2 2 1 . . 1 . . 3 1 1 1 . . 1 . . 5 1 . . 1 1 . . . 11 1 . . . . . 1 1 1a 2a 3a 5a 5b 6a 11a 11b 2P 1a 1a 3a 5b 5a 3a 11b 11a 3P 1a 2a 1a 5b 5a 2a 11a 11b 5P 1a 2a 3a 1a 1a 6a 11a 11b 7P 1a 2a 3a 5b 5a 6a 11b 11a 11P 1a 2a 3a 5a 5b 6a 1a 1a X.1 1 1 1 1 1 1 1 1 X.2 5 1 -1 . . 1 B /B X.3 5 1 -1 . . 1 /B B X.4 10 -2 1 . . 1 -1 -1 X.5 10 2 1 . . -1 -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