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Properties

Label 35T25
35T25 1 10 1->10 25 1->25 2 9 2->9 21 2->21 3 6 3->6 22 3->22 4 8 4->8 24 4->24 5 7 5->7 23 5->23 11 6->11 34 6->34 12 7->12 31 7->31 15 8->15 32 8->32 14 9->14 35 9->35 13 10->13 33 10->33 11->7 16 11->16 12->9 20 12->20 13->8 18 13->18 14->10 19 14->19 15->6 17 15->17 16->18 16->21 17->20 17->25 18->17 18->24 19->23 20->16 20->22 27 21->27 30 21->30 22->27 28 22->28 23->28 29 23->29 26 24->26 24->29 25->26 25->30 26->4 26->35 27->1 27->31 28->3 28->32 29->5 29->34 30->2 30->33 31->2 31->12 32->1 32->11 33->3 33->13 34->4 34->15 35->5 35->14
Degree $35$
Order $2520$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $C_7:C_3\times S_5$

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Copy content magma:G := TransitiveGroup(35, 25);
 

Group invariants

Abstract group:  $C_7:C_3\times S_5$
Copy content magma:IdentifyGroup(G);
 
Order:  $2520=2^{3} \cdot 3^{2} \cdot 5 \cdot 7$
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 $t$:  $25$
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:  $(1,10,13,18,24,26,35,5,7,12,20,22,28,32)(2,9,14,19,23,29,34,4,8,15,17,25,30,33,3,6,11,16,21,27,31)$, $(1,25,26,4,24,29,5,23,28,3,22,27)(2,21,30)(6,34,15)(7,31,12,9,35,14,10,33,13,8,32,11)(16,18,17,20)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$6$:  $C_6$
$21$:  $C_7:C_3$
$42$:  $(C_7:C_3) \times C_2$
$120$:  $S_5$
$360$:  $S_5 \times C_3$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 5: $S_5$

Degree 7: $C_7:C_3$

Low degree siblings

42T296

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 $2^{7},1^{21}$ $10$ $2$ $7$ $( 2, 5)( 6,10)(12,15)(18,19)(21,22)(26,30)(32,34)$
2B $2^{14},1^{7}$ $15$ $2$ $14$ $( 1, 4)( 2, 5)( 6,10)( 7, 9)(11,13)(12,15)(17,20)(18,19)(21,22)(23,24)(26,30)(27,28)(32,34)(33,35)$
3A1 $3^{10},1^{5}$ $7$ $3$ $20$ $( 1,24,35)( 2,21,34)( 3,25,31)( 4,23,33)( 5,22,32)(11,27,17)(12,26,18)(13,28,20)(14,29,16)(15,30,19)$
3A-1 $3^{10},1^{5}$ $7$ $3$ $20$ $( 1,35,24)( 2,34,21)( 3,31,25)( 4,33,23)( 5,32,22)(11,17,27)(12,18,26)(13,20,28)(14,16,29)(15,19,30)$
3B $3^{7},1^{14}$ $20$ $3$ $14$ $( 1, 3, 4)( 7, 8, 9)(11,13,14)(16,17,20)(23,24,25)(27,28,29)(31,33,35)$
3C1 $3^{11},1^{2}$ $140$ $3$ $22$ $( 1,29, 6)( 2,28, 8)( 3,30, 7)( 4,27, 9)( 5,26,10)(13,14,15)(16,21,35)(17,23,33)(18,22,32)(19,24,31)(20,25,34)$
3C-1 $3^{11},1^{2}$ $140$ $3$ $22$ $( 1, 6,29)( 2, 8,28)( 3, 7,30)( 4, 9,27)( 5,10,26)(13,15,14)(16,35,21)(17,33,23)(18,32,22)(19,31,24)(20,34,25)$
4A $4^{7},1^{7}$ $30$ $4$ $21$ $( 1, 2, 4, 5)( 6, 9,10, 7)(11,12,13,15)(17,18,20,19)(21,23,22,24)(26,28,30,27)(32,35,34,33)$
5A $5^{7}$ $24$ $5$ $28$ $( 1, 3, 4, 5, 2)( 6, 7, 8, 9,10)(11,12,15,13,14)(16,17,18,19,20)(21,24,25,23,22)(26,30,28,29,27)(31,33,32,34,35)$
6A $3^{7},2^{7}$ $20$ $6$ $21$ $( 1, 4, 3)( 2, 5)( 6,10)( 7, 9, 8)(11,14,13)(12,15)(16,20,17)(18,19)(21,22)(23,25,24)(26,30)(27,29,28)(31,35,33)(32,34)$
6B1 $6^{2},3^{6},2,1^{3}$ $70$ $6$ $23$ $( 1,23,35, 4,24,33)( 2,21,34)( 3,25,31)( 5,22,32)( 7, 9)(11,28,17,13,27,20)(12,26,18)(14,29,16)(15,30,19)$
6B-1 $6^{2},3^{6},2,1^{3}$ $70$ $6$ $23$ $( 1,33,24, 4,35,23)( 2,34,21)( 3,31,25)( 5,32,22)( 7, 9)(11,20,27,13,17,28)(12,18,26)(14,16,29)(15,19,30)$
6C1 $6^{4},3^{2},2^{2},1$ $105$ $6$ $26$ $( 1,28,24)( 2,29,21, 3,30,25)( 4,26,23, 5,27,22)( 6,14,34, 8,15,31)( 7,13,35)( 9,12,33,10,11,32)(16,19)(17,18)$
6C-1 $6^{4},3^{2},2^{2},1$ $105$ $6$ $26$ $( 1,24,28)( 2,25,30, 3,21,29)( 4,22,27, 5,23,26)( 6,31,15, 8,34,14)( 7,35,13)( 9,32,11,10,33,12)(16,19)(17,18)$
6D1 $6^{2},3^{7},2$ $140$ $6$ $25$ $( 1, 6,29)( 2, 8,28)( 3, 7,30)( 4,10,27, 5, 9,26)(11,12)(13,15,14)(16,35,21)(17,32,23,18,33,22)(19,31,24)(20,34,25)$
6D-1 $6^{2},3^{7},2$ $140$ $6$ $25$ $( 1,29, 6)( 2,28, 8)( 3,30, 7)( 4,26, 9, 5,27,10)(11,12)(13,14,15)(16,21,35)(17,22,33,18,23,32)(19,24,31)(20,25,34)$
7A1 $7^{5}$ $3$ $7$ $30$ $( 1,20,35,13,28, 7,24)( 2,19,34,15,30, 6,21)( 3,16,31,14,29, 8,25)( 4,17,33,11,27, 9,23)( 5,18,32,12,26,10,22)$
7A-1 $7^{5}$ $3$ $7$ $30$ $( 1,24, 7,28,13,35,20)( 2,21, 6,30,15,34,19)( 3,25, 8,29,14,31,16)( 4,23, 9,27,11,33,17)( 5,22,10,26,12,32,18)$
12A1 $12^{2},4,3^{2},1$ $210$ $12$ $29$ $( 1,24,28)( 2,23,29, 5,21,27, 3,22,30, 4,25,26)( 6,33,14,10,34,11, 8,32,15, 9,31,12)( 7,35,13)(16,18,19,17)$
12A-1 $12^{2},4,3^{2},1$ $210$ $12$ $29$ $( 1,28,24)( 2,26,25, 4,30,22, 3,27,21, 5,29,23)( 6,12,31, 9,15,32, 8,11,34,10,14,33)( 7,13,35)(16,17,19,18)$
14A1 $14,7^{3}$ $30$ $14$ $31$ $( 1,35,28,24,20,13, 7)( 2,32,30,22,19,12, 6, 5,34,26,21,18,15,10)( 3,31,29,25,16,14, 8)( 4,33,27,23,17,11, 9)$
14A-1 $14,7^{3}$ $30$ $14$ $31$ $( 1, 7,13,20,24,28,35)( 2,10,15,18,21,26,34, 5, 6,12,19,22,30,32)( 3, 8,14,16,25,29,31)( 4, 9,11,17,23,27,33)$
14B1 $14^{2},7$ $45$ $14$ $32$ $( 1,27,20, 9,35,23,13, 4,28,17, 7,33,24,11)( 2,26,19,10,34,22,15, 5,30,18, 6,32,21,12)( 3,29,16, 8,31,25,14)$
14B-1 $14^{2},7$ $45$ $14$ $32$ $( 1,11,24,33, 7,17,28, 4,13,23,35, 9,20,27)( 2,12,21,32, 6,18,30, 5,15,22,34,10,19,26)( 3,14,25,31, 8,16,29)$
15A1 $15^{2},5$ $168$ $15$ $32$ $( 1,33,21, 3,32,24, 4,34,25, 5,35,23, 2,31,22)( 6, 8,10, 7, 9)(11,19,29,12,20,27,15,16,26,13,17,30,14,18,28)$
15A-1 $15^{2},5$ $168$ $15$ $32$ $( 1,22,31, 2,23,35, 5,25,34, 4,24,32, 3,21,33)( 6, 9, 7,10, 8)(11,28,18,14,30,17,13,26,16,15,27,20,12,29,19)$
21A1 $21,7^{2}$ $60$ $21$ $32$ $( 1,25, 9,28,14,33,20, 3,23, 7,29,11,35,16, 4,24, 8,27,13,31,17)( 2,21, 6,30,15,34,19)( 5,22,10,26,12,32,18)$
21A-1 $21,7^{2}$ $60$ $21$ $32$ $( 1,17,31,13,27, 8,24, 4,16,35,11,29, 7,23, 3,20,33,14,28, 9,25)( 2,19,34,15,30, 6,21)( 5,18,32,12,26,10,22)$
28A1 $28,7$ $90$ $28$ $33$ $( 1,32,27,21,20,12, 9, 2,35,26,23,19,13,10, 4,34,28,22,17,15, 7, 5,33,30,24,18,11, 6)( 3,31,29,25,16,14, 8)$
28A-1 $28,7$ $90$ $28$ $33$ $( 1, 6,11,18,24,30,33, 5, 7,15,17,22,28,34, 4,10,13,19,23,26,35, 2, 9,12,20,21,27,32)( 3, 8,14,16,25,29,31)$
35A1 $35$ $72$ $35$ $34$ $( 1,10,11,16,21,28,32, 4, 8,15,20,22,27,31, 2, 7,12,17,25,30,35, 5, 9,14,19,24,26,33, 3, 6,13,18,23,29,34)$
35A-1 $35$ $72$ $35$ $34$ $( 1,34,29,23,18,13, 6, 3,33,26,24,19,14, 9, 5,35,30,25,17,12, 7, 2,31,27,22,20,15, 8, 4,32,28,21,16,11,10)$
42A1 $21,14$ $60$ $42$ $33$ $( 1,11,25,35, 9,16,28, 4,14,24,33, 8,20,27, 3,13,23,31, 7,17,29)( 2,12,21,32, 6,18,30, 5,15,22,34,10,19,26)$
42A-1 $21,14$ $60$ $42$ $33$ $( 1,29,17, 7,31,23,13, 3,27,20, 8,33,24,14, 4,28,16, 9,35,25,11)( 2,26,19,10,34,22,15, 5,30,18, 6,32,21,12)$

Malle's constant $a(G)$:     $1/7$

Copy content magma:ConjugacyClasses(G);
 

Character table

35 x 35 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed