Galois group: 14T30

• Label: 14T30
• Degree: $14$
• Order: $1092$
• Cyclic: no
• Abelian: no
• Solvable: no
• Primitive: yes
• $p$-group: no
• Group: $\PSL(2,13)$

Group action invariants

Degree $n$:		$14$
Transitive number $t$:		$30$
Group:		$\PSL(2,13)$
CHM label:		$L(14)=PSL(2,13)$
Parity:		$1$
Primitive:		yes
$\card{\Aut(F/K)}$:		$1$
Generators:		(1,12)(2,6)(3,4)(7,11)(9,10)(13,14), (1,4,3,12,9,10)(2,8,6,11,5,7), (1,2,3,4,5,6,7,8,9,10,11,12,14)

Low degree resolvents

none

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 7: None

Low degree siblings

28T120, 42T176

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

Label	Cycle Type	Size	Order	Index	Representative
1A	$1^{14}$	$1$	$1$	$0$	$()$
2A	$2^{6},1^{2}$	$91$	$2$	$6$	$( 1, 3)( 2, 8)( 5,11)( 6, 7)(10,12)(13,14)$
3A	$3^{4},1^{2}$	$182$	$3$	$8$	$( 1, 4, 2)( 5,14, 8)( 6, 7,13)( 9,12,11)$
6A	$6^{2},1^{2}$	$182$	$6$	$10$	$( 1, 6,10, 3, 7,12)( 2, 5,14, 8,11,13)$
7A1	$7^{2}$	$156$	$7$	$12$	$( 1,12, 3, 5,14, 8,10)( 2, 7, 6,11, 4,13, 9)$
7A2	$7^{2}$	$156$	$7$	$12$	$( 1, 3,14,10,12, 5, 8)( 2, 6, 4, 9, 7,11,13)$
7A3	$7^{2}$	$156$	$7$	$12$	$( 1, 5,10, 3, 8,12,14)( 2,11, 9, 6,13, 7, 4)$
13A1	$13,1$	$84$	$13$	$12$	$( 1, 9, 4,12, 7, 2,10, 5,14, 8, 3,11, 6)$
13A2	$13,1$	$84$	$13$	$12$	$( 1, 4, 7,10,14, 3, 6, 9,12, 2, 5, 8,11)$

Malle's constant $a(G)$:     $1/6$

Group invariants

Order:		$1092=2^{2} \cdot 3 \cdot 7 \cdot 13$
Cyclic:		no
Abelian:		no
Solvable:		no
Nilpotency class:		not nilpotent
Label:		1092.25
Character table:

		1A	2A	3A	6A	7A1	7A2	7A3	13A1	13A2
	Size	1	91	182	182	156	156	156	84	84
	2 P	1A	1A	3A	3A	7A2	7A3	7A1	13A2	13A1
	3 P	1A	2A	1A	2A	7A3	7A1	7A2	13A1	13A2
	7 P	1A	2A	3A	6A	1A	1A	1A	13A2	13A1
	13 P	1A	2A	3A	6A	7A1	7A2	7A3	1A	1A
	Type
1092.25.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
1092.25.7a1	R	$7$	$-1$	$1$	$-1$	$0$	$0$	$0$	${\zeta }_{13}^{-6}+{\zeta }_{13}^{-5}+{\zeta }_{13}^{-2}+1+{\zeta }_{13}^2+{\zeta }_{13}^5+{\zeta }_{13}^6$	$-{\zeta }_{13}^{-6}-{\zeta }_{13}^{-5}-{\zeta }_{13}^{-2}-{\zeta }_{13}^2-{\zeta }_{13}^5-{\zeta }_{13}^6$
1092.25.7a2	R	$7$	$-1$	$1$	$-1$	$0$	$0$	$0$	$-{\zeta }_{13}^{-6}-{\zeta }_{13}^{-5}-{\zeta }_{13}^{-2}-{\zeta }_{13}^2-{\zeta }_{13}^5-{\zeta }_{13}^6$	${\zeta }_{13}^{-6}+{\zeta }_{13}^{-5}+{\zeta }_{13}^{-2}+1+{\zeta }_{13}^2+{\zeta }_{13}^5+{\zeta }_{13}^6$
1092.25.12a1	R	$12$	$0$	$0$	$0$	$-{\zeta }_7^{-1}-{\zeta }_7$	$-{\zeta }_7^{-2}-{\zeta }_7^2$	$-{\zeta }_7^{-3}-{\zeta }_7^3$	$-1$	$-1$
1092.25.12a2	R	$12$	$0$	$0$	$0$	$-{\zeta }_7^{-2}-{\zeta }_7^2$	$-{\zeta }_7^{-3}-{\zeta }_7^3$	$-{\zeta }_7^{-1}-{\zeta }_7$	$-1$	$-1$
1092.25.12a3	R	$12$	$0$	$0$	$0$	$-{\zeta }_7^{-3}-{\zeta }_7^3$	$-{\zeta }_7^{-1}-{\zeta }_7$	$-{\zeta }_7^{-2}-{\zeta }_7^2$	$-1$	$-1$
1092.25.13a	R	$13$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$0$	$0$
1092.25.14a	R	$14$	$2$	$-1$	$-1$	$0$	$0$	$0$	$1$	$1$
1092.25.14b	R	$14$	$-2$	$-1$	$1$	$0$	$0$	$0$	$1$	$1$