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Properties

Label 22T21
22T21 1 16 1->16 2 10 2->10 21 2->21 3 8 3->8 15 3->15 4 6 4->6 20 4->20 5 5->4 14 5->14 6->2 19 6->19 7 11 7->11 13 7->13 9 8->9 18 8->18 9->7 12 9->12 10->5 17 10->17 11->3 22 11->22 12->1 13->6 13->17 14->11 14->22 15->5 15->16 16->10 16->21 17->4 17->15 18->9 18->20 19->3 19->14 20->8 20->19 21->13 22->7 22->18
Degree $22$
Order $6050$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{11}^2:(C_5\times D_5)$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(22, 21);
 

Group invariants

Abstract group:  $C_{11}^2:(C_5\times D_5)$
Copy content magma:IdentifyGroup(G);
 
Order:  $6050=2 \cdot 5^{2} \cdot 11^{2}$
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  yes
Copy content magma:IsSolvable(G);
 
Nilpotency class:   not nilpotent
Copy content magma:NilpotencyClass(G);
 

Group action invariants

Degree $n$:  $22$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $21$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $-1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $1$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,16,10,17,4,20,8,18,9,12)(2,21)(3,15,5,14,11,22,7,13,6,19)$, $(2,10,5,4,6)(3,8,9,7,11)(13,17,15,16,21)(14,22,18,20,19)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$5$:  $C_5$
$10$:  $D_{5}$, $C_{10}$
$50$:  $D_5\times C_5$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: None

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

LabelCycle TypeSizeOrderIndexRepresentative
1A $1^{22}$ $1$ $1$ $0$ $()$
2A $2^{11}$ $55$ $2$ $11$ $( 1,18)( 2,16)( 3,14)( 4,12)( 5,21)( 6,19)( 7,17)( 8,15)( 9,13)(10,22)(11,20)$
5A1 $5^{2},1^{12}$ $22$ $5$ $8$ $( 1, 9,11, 6, 2)( 3, 4, 7, 5,10)$
5A-1 $5^{2},1^{12}$ $22$ $5$ $8$ $( 1, 2, 6,11, 9)( 3,10, 5, 7, 4)$
5A2 $5^{2},1^{12}$ $22$ $5$ $8$ $( 1,11, 2, 9, 6)( 3, 7,10, 4, 5)$
5A-2 $5^{2},1^{12}$ $22$ $5$ $8$ $( 1, 6, 9, 2,11)( 3, 5, 4,10, 7)$
5B1 $5^{4},1^{2}$ $121$ $5$ $16$ $( 1,11, 8,10, 5)( 2, 3, 6, 4, 9)(12,14,20,16,15)(13,17,18,21,19)$
5B-1 $5^{4},1^{2}$ $121$ $5$ $16$ $( 1, 5,10, 8,11)( 2, 9, 4, 6, 3)(12,15,16,20,14)(13,19,21,18,17)$
5B2 $5^{4},1^{2}$ $121$ $5$ $16$ $( 1, 8, 5,11,10)( 2, 6, 9, 3, 4)(12,20,15,14,16)(13,18,19,17,21)$
5B-2 $5^{4},1^{2}$ $121$ $5$ $16$ $( 1,10,11, 5, 8)( 2, 4, 3, 9, 6)(12,16,14,15,20)(13,21,17,19,18)$
5C1 $5^{4},1^{2}$ $242$ $5$ $16$ $( 1, 8, 3, 5, 2)( 4, 9, 7,10,11)(12,20,22,17,13)(14,15,18,16,21)$
5C2 $5^{4},1^{2}$ $242$ $5$ $16$ $( 1, 3, 2, 8, 5)( 4, 7,11, 9,10)(12,22,13,20,17)(14,18,21,15,16)$
5D1 $5^{4},1^{2}$ $242$ $5$ $16$ $( 2, 5, 6,10, 4)( 3, 9,11, 8, 7)(12,14,13,19,16)(15,18,22,20,21)$
5D-1 $5^{4},1^{2}$ $242$ $5$ $16$ $( 2, 4,10, 6, 5)( 3, 7, 8,11, 9)(12,16,19,13,14)(15,21,20,22,18)$
5D2 $5^{4},1^{2}$ $242$ $5$ $16$ $( 2, 6, 4, 5,10)( 3,11, 7, 9, 8)(12,13,16,14,19)(15,22,21,18,20)$
5D-2 $5^{4},1^{2}$ $242$ $5$ $16$ $( 2,10, 5, 4, 6)( 3, 8, 9, 7,11)(12,19,14,16,13)(15,20,18,21,22)$
10A1 $10^{2},2$ $605$ $10$ $19$ $( 1,14,11,20, 8,16,10,15, 5,12)( 2,19, 3,13, 6,17, 4,18, 9,21)( 7,22)$
10A-1 $10^{2},2$ $605$ $10$ $19$ $( 1,12, 5,15,10,16, 8,20,11,14)( 2,21, 9,18, 4,17, 6,13, 3,19)( 7,22)$
10A3 $10^{2},2$ $605$ $10$ $19$ $( 1,20,10,12,11,16, 5,14, 8,15)( 2,13, 4,21, 3,17, 9,19, 6,18)( 7,22)$
10A-3 $10^{2},2$ $605$ $10$ $19$ $( 1,15, 8,14, 5,16,11,12,10,20)( 2,18, 6,19, 9,17, 3,21, 4,13)( 7,22)$
11A1 $11,1^{11}$ $10$ $11$ $10$ $(12,21,19,17,15,13,22,20,18,16,14)$
11A-1 $11,1^{11}$ $10$ $11$ $10$ $(12,14,16,18,20,22,13,15,17,19,21)$
11B1 $11^{2}$ $25$ $11$ $20$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,16,20,13,17,21,14,18,22,15,19)$
11B-1 $11^{2}$ $25$ $11$ $20$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,19,15,22,18,14,21,17,13,20,16)$
11C $11^{2}$ $50$ $11$ $20$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,15,18,21,13,16,19,22,14,17,20)$
22A1 $22$ $275$ $22$ $21$ $( 1,20,10,13, 8,17, 6,21, 4,14, 2,18,11,22, 9,15, 7,19, 5,12, 3,16)$
22A-1 $22$ $275$ $22$ $21$ $( 1,16, 3,12, 5,19, 7,15, 9,22,11,18, 2,14, 4,21, 6,17, 8,13,10,20)$
55A1 $11,5^{2},1$ $110$ $55$ $18$ $( 1, 9,11, 6, 2)( 3, 4, 7, 5,10)(12,16,20,13,17,21,14,18,22,15,19)$
55A-1 $11,5^{2},1$ $110$ $55$ $18$ $( 1, 2, 6,11, 9)( 3,10, 5, 7, 4)(12,19,15,22,18,14,21,17,13,20,16)$
55A2 $11,5^{2},1$ $110$ $55$ $18$ $( 1,11, 2, 9, 6)( 3, 7,10, 4, 5)(12,20,17,14,22,19,16,13,21,18,15)$
55A-2 $11,5^{2},1$ $110$ $55$ $18$ $( 1, 6, 9, 2,11)( 3, 5, 4,10, 7)(12,15,18,21,13,16,19,22,14,17,20)$
55A4 $11,5^{2},1$ $110$ $55$ $18$ $( 1, 2, 6,11, 9)( 3,10, 5, 7, 4)(12,17,22,16,21,15,20,14,19,13,18)$
55A-4 $11,5^{2},1$ $110$ $55$ $18$ $( 1, 9,11, 6, 2)( 3, 4, 7, 5,10)(12,18,13,19,14,20,15,21,16,22,17)$
55A8 $11,5^{2},1$ $110$ $55$ $18$ $( 1, 6, 9, 2,11)( 3, 5, 4,10, 7)(12,22,21,20,19,18,17,16,15,14,13)$
55A-8 $11,5^{2},1$ $110$ $55$ $18$ $( 1,11, 2, 9, 6)( 3, 7,10, 4, 5)(12,13,14,15,16,17,18,19,20,21,22)$

Malle's constant $a(G)$:     $1/8$

Copy content magma:ConjugacyClasses(G);
 

Character table

35 x 35 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed