↑

Properties

Label 35T13
35T13 1 14 1->14 29 1->29 2 15 2->15 27 2->27 3 13 3->13 30 3->30 4 12 4->12 28 4->28 5 11 5->11 26 5->26 6 16 6->16 33 6->33 7 18 7->18 34 7->34 8 19 8->19 31 8->31 9 20 9->20 32 9->32 10 17 10->17 35 10->35 11->3 24 11->24 12->5 21 12->21 13->1 25 13->25 14->2 23 14->23 15->4 22 15->22 16->9 16->28 17->7 17->26 18->8 18->29 19->6 19->30 20->10 20->27 21->15 21->35 22->11 22->33 23->13 23->32 24->14 24->31 25->12 25->34 26->1 26->16 27->5 27->18 28->2 28->19 29->3 29->17 30->4 30->20 31->9 31->25 32->7 32->22 33->8 33->21 34->10 34->23 35->6 35->24
Degree $35$
Order $420$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $C_7\times A_5$

Related objects

Downloads

Learn more

Show commands: Magma

Copy content magma:G := TransitiveGroup(35, 13);
 

Group invariants

Abstract group:  $C_7\times A_5$
Copy content magma:IdentifyGroup(G);
 
Order:  $420=2^{2} \cdot 3 \cdot 5 \cdot 7$
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  no
Copy content magma:IsSolvable(G);
 
Nilpotency class:   not nilpotent
Copy content magma:NilpotencyClass(G);
 

Group action invariants

Degree $n$:  $35$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $13$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $7$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,14,23,32,7,18,29,3,13,25,34,10,17,26)(2,15,22,33,8,19,30,4,12,21,35,6,16,28)(5,11,24,31,9,20,27)$, $(1,29,17,7,34,23,13)(2,27,18,8,31,25,12,5,26,16,9,32,22,11,3,30,20,10,35,24,14)(4,28,19,6,33,21,15)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$7$:  $C_7$
$60$:  $A_5$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 5: $A_5$

Degree 7: $C_7$

Low degree siblings

42T86

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

LabelCycle TypeSizeOrderIndexRepresentative
1A $1^{35}$ $1$ $1$ $0$ $()$
2A $2^{14},1^{7}$ $15$ $2$ $14$ $( 1, 3)( 4, 5)( 6, 9)( 7,10)(11,15)(13,14)(17,18)(19,20)(21,24)(23,25)(26,29)(27,28)(31,33)(32,34)$
3A $3^{7},1^{14}$ $20$ $3$ $14$ $( 2, 4, 5)( 6, 9, 8)(11,12,15)(16,19,20)(21,24,22)(27,30,28)(31,35,33)$
5A1 $5^{7}$ $12$ $5$ $28$ $( 1, 4, 5, 2, 3)( 6, 9, 8,10, 7)(11,12,14,13,15)(16,18,17,19,20)(21,24,22,25,23)(26,29,28,27,30)(31,35,32,34,33)$
5A2 $5^{7}$ $12$ $5$ $28$ $( 1, 5, 3, 4, 2)( 6, 8, 7, 9,10)(11,14,15,12,13)(16,17,20,18,19)(21,22,23,24,25)(26,28,30,29,27)(31,32,33,35,34)$
7A1 $7^{5}$ $1$ $7$ $30$ $( 1, 7,13,17,23,29,34)( 2, 8,12,16,22,30,35)( 3,10,14,18,25,26,32)( 4, 6,15,19,21,28,33)( 5, 9,11,20,24,27,31)$
7A-1 $7^{5}$ $1$ $7$ $30$ $( 1,34,29,23,17,13, 7)( 2,35,30,22,16,12, 8)( 3,32,26,25,18,14,10)( 4,33,28,21,19,15, 6)( 5,31,27,24,20,11, 9)$
7A2 $7^{5}$ $1$ $7$ $30$ $( 1,13,23,34, 7,17,29)( 2,12,22,35, 8,16,30)( 3,14,25,32,10,18,26)( 4,15,21,33, 6,19,28)( 5,11,24,31, 9,20,27)$
7A-2 $7^{5}$ $1$ $7$ $30$ $( 1,29,17, 7,34,23,13)( 2,30,16, 8,35,22,12)( 3,26,18,10,32,25,14)( 4,28,19, 6,33,21,15)( 5,27,20, 9,31,24,11)$
7A3 $7^{5}$ $1$ $7$ $30$ $( 1,17,34,13,29, 7,23)( 2,16,35,12,30, 8,22)( 3,18,32,14,26,10,25)( 4,19,33,15,28, 6,21)( 5,20,31,11,27, 9,24)$
7A-3 $7^{5}$ $1$ $7$ $30$ $( 1,23, 7,29,13,34,17)( 2,22, 8,30,12,35,16)( 3,25,10,26,14,32,18)( 4,21, 6,28,15,33,19)( 5,24, 9,27,11,31,20)$
14A1 $14^{2},7$ $15$ $14$ $32$ $( 1,25, 7,26,13,32,17, 3,23,10,29,14,34,18)( 2,22, 8,30,12,35,16)( 4,24, 6,27,15,31,19, 5,21, 9,28,11,33,20)$
14A-1 $14^{2},7$ $15$ $14$ $32$ $( 1,19,34,15,29, 6,23, 4,17,33,13,28, 7,21)( 2,20,35,11,30, 9,22, 5,16,31,12,27, 8,24)( 3,18,32,14,26,10,25)$
14A3 $14^{2},7$ $15$ $14$ $32$ $( 1,29,17, 7,34,23,13)( 2,27,16, 9,35,24,12, 5,30,20, 8,31,22,11)( 3,28,18, 6,32,21,14, 4,26,19,10,33,25,15)$
14A-3 $14^{2},7$ $15$ $14$ $32$ $( 1,15,23,33, 7,19,29, 4,13,21,34, 6,17,28)( 2,12,22,35, 8,16,30)( 3,11,25,31,10,20,26, 5,14,24,32, 9,18,27)$
14A5 $14^{2},7$ $15$ $14$ $32$ $( 1,35,29,22,17,12, 7, 2,34,30,23,16,13, 8)( 3,33,26,21,18,15,10, 4,32,28,25,19,14, 6)( 5,31,27,24,20,11, 9)$
14A-5 $14^{2},7$ $15$ $14$ $32$ $( 1, 7,13,17,23,29,34)( 2,10,12,18,22,26,35, 3, 8,14,16,25,30,32)( 4, 9,15,20,21,27,33, 5, 6,11,19,24,28,31)$
21A1 $21,7^{2}$ $20$ $21$ $32$ $( 1,17,34,13,29, 7,23)( 2,19,31,12,28, 9,22, 4,20,35,15,27, 8,21, 5,16,33,11,30, 6,24)( 3,18,32,14,26,10,25)$
21A-1 $21,7^{2}$ $20$ $21$ $32$ $( 1,23, 7,29,13,34,17)( 2,21, 9,30,15,31,16, 4,24, 8,28,11,35,19, 5,22, 6,27,12,33,20)( 3,25,10,26,14,32,18)$
21A2 $21,7^{2}$ $20$ $21$ $32$ $( 1,34,29,23,17,13, 7)( 2,33,27,22,19,11, 8, 4,31,30,21,20,12, 6, 5,35,28,24,16,15, 9)( 3,32,26,25,18,14,10)$
21A-2 $21,7^{2}$ $20$ $21$ $32$ $( 1, 7,13,17,23,29,34)( 2, 6,11,16,21,27,35, 4, 9,12,19,24,30,33, 5, 8,15,20,22,28,31)( 3,10,14,18,25,26,32)$
21A4 $21,7^{2}$ $20$ $21$ $32$ $( 1,29,17, 7,34,23,13)( 2,28,20, 8,33,24,12, 4,27,16, 6,31,22,15, 5,30,19, 9,35,21,11)( 3,26,18,10,32,25,14)$
21A-4 $21,7^{2}$ $20$ $21$ $32$ $( 1,13,23,34, 7,17,29)( 2,15,24,35, 6,20,30, 4,11,22,33, 9,16,28, 5,12,21,31, 8,19,27)( 3,14,25,32,10,18,26)$
35A1 $35$ $12$ $35$ $34$ $( 1,12,21,32, 9,17,30, 4,14,24,34, 8,19,26, 5,13,22,33,10,20,29, 2,15,25,31, 7,16,28, 3,11,23,35, 6,18,27)$
35A-1 $35$ $12$ $35$ $34$ $( 1,30,20, 6,32,23,12, 5,28,18, 7,35,24,15, 3,29,16, 9,33,25,13, 2,27,19,10,34,22,11, 4,26,17, 8,31,21,14)$
35A2 $35$ $12$ $35$ $34$ $( 1,25, 6,30,11,34,18, 4,22, 9,29,14,33,16, 5,23,10,28,12,31,17, 3,21, 8,27,13,32,19, 2,24, 7,26,15,35,20)$
35A-2 $35$ $12$ $35$ $34$ $( 1,16,33,11,26, 7,22, 4,20,32,13,30, 6,24, 3,17,35,15,27,10,23, 2,19,31,14,29, 8,21, 5,18,34,12,28, 9,25)$
35A3 $35$ $12$ $35$ $34$ $( 1,32,27,21,16,13,10, 5,33,30,23,18,11, 6, 2,34,26,24,19,12, 7, 3,31,28,22,17,14, 9, 4,35,29,25,20,15, 8)$
35A-3 $35$ $12$ $35$ $34$ $( 1,10,12,20,21,29,32, 2, 9,15,17,25,30,31, 4, 7,14,16,24,28,34, 3, 8,11,19,23,26,35, 5, 6,13,18,22,27,33)$
35A4 $35$ $12$ $35$ $34$ $( 1, 9,14,19,22,29,31, 3, 6,12,17,24,26,33, 2, 7,11,18,21,30,34, 5,10,15,16,23,27,32, 4, 8,13,20,25,28,35)$
35A-4 $35$ $12$ $35$ $34$ $( 1,32,28,24,16,13,10, 4,31,30,23,18,15, 9, 2,34,26,21,20,12, 7, 3,33,27,22,17,14, 6, 5,35,29,25,19,11, 8)$
35A8 $35$ $12$ $35$ $34$ $( 1,12,21,31,10,17,30, 4,11,25,34, 8,19,27, 3,13,22,33, 9,18,29, 2,15,24,32, 7,16,28, 5,14,23,35, 6,20,26)$
35A-8 $35$ $12$ $35$ $34$ $( 1,28,18, 9,35,23,15, 3,27,16, 7,33,25,11, 2,29,19,10,31,22,13, 4,26,20, 8,34,21,14, 5,30,17, 6,32,24,12)$
35A9 $35$ $12$ $35$ $34$ $( 1,24, 6,30,14,34,20, 4,22,10,29,11,33,16, 3,23, 9,28,12,32,17, 5,21, 8,26,13,31,19, 2,25, 7,27,15,35,18)$
35A-9 $35$ $12$ $35$ $34$ $( 1,20,35,14,28, 7,24, 2,18,33,13,27, 8,25, 4,17,31,12,26, 6,23, 5,16,32,15,29, 9,22, 3,19,34,11,30,10,21)$

Malle's constant $a(G)$:     $1/14$

Copy content magma:ConjugacyClasses(G);
 

Character table

35 x 35 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed