Galois group: 21T33

• Label: 21T33
• Degree: $21$
• Order: $2520$
• Cyclic: no
• Abelian: no
• Solvable: no
• Primitive: yes
• $p$-group: no
• Group: $A_7$

Group action invariants

Degree $n$:		$21$
Transitive number $t$:		$33$
Group:		$A_7$
Parity:		$1$
Primitive:		yes
$\card{\Aut(F/K)}$:		$1$
Generators:		(1,7,12,16,19,21,6)(2,8,13,17,20,5,11)(3,9,14,18,4,10,15), (4,6,5)(9,11,10)(13,15,14)(16,18,17)(19,20,21)

Low degree resolvents

none

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 7: None

Low degree siblings

7T6, 15T47 x 2, 35T28, 42T294, 42T299

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	Representative
	$1^{21}$	$1$	$1$	$()$
	$7^{3}$	$360$	$7$	$( 1,15,19, 8, 2,21,16)( 3, 6,20, 9, 7,14,17)( 4,11,13,10,12, 5,18)$
	$7^{3}$	$360$	$7$	$( 1,16,21, 2, 8,19,15)( 3,17,14, 7, 9,20, 6)( 4,18, 5,12,10,13,11)$
	$2^{8},1^{5}$	$105$	$2$	$( 1, 8)( 2,16)( 4,12)( 5,17)( 6,18)( 7, 9)(14,19)(15,20)$
	$3^{5},1^{6}$	$70$	$3$	$( 1, 5, 6)( 7,14,15)( 8,17,18)( 9,19,20)(10,21,11)$
	$6^{2},3,2^{2},1^{2}$	$210$	$6$	$( 1,18, 5, 8, 6,17)( 2,16)( 4,12)( 7,20,14, 9,15,19)(10,11,21)$
	$4^{4},2^{2},1$	$630$	$4$	$( 1,14, 8,19)( 2,12,16, 4)( 3,13)( 5, 7,17, 9)( 6,15,18,20)(11,21)$
	$3^{7}$	$280$	$3$	$( 1, 7,10)( 2,14, 5)( 3,13,21)( 4,15,17)( 6,12,19)( 8, 9,11)(16,20,18)$
	$5^{4},1$	$504$	$5$	$( 1,12, 9, 2,16)( 3, 8, 7,13, 4)( 5,17,10,14,19)( 6,18,11,15,20)$

Group invariants

Order:		$2520=2^{3} \cdot 3^{2} \cdot 5 \cdot 7$
Cyclic:		no
Abelian:		no
Solvable:		no
Nilpotency class:		not nilpotent
Label:		2520.a
Character table:

	Size
	2 P
	3 P
	5 P
	7 P
	Type