↑

Properties

Label 38T31
38T31 1 18 1->18 36 1->36 2 15 2->15 26 2->26 3 12 3->12 35 3->35 4 9 4->9 25 4->25 5 6 5->6 34 5->34 6->3 24 6->24 7 19 7->19 33 7->33 8 16 8->16 23 8->23 13 9->13 32 9->32 10 22 10->22 11 11->7 31 11->31 12->4 21 12->21 13->1 30 13->30 14 17 14->17 20 14->20 15->14 29 15->29 16->11 38 16->38 17->8 28 17->28 18->5 37 18->37 19->2 27 19->27 20->13 20->21 21->18 21->25 22->4 22->29 23->9 23->33 24->14 24->37 25->19 25->22 26->5 27->10 27->30 28->15 28->34 29->1 29->38 30->6 30->23 31->27 32->16 32->31 33->2 33->35 34->7 34->20 35->12 35->24 36->17 36->28 37->3 37->32 38->8 38->36
Degree $38$
Order $19494$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{19}^2:(C_3\times D_9)$

Related objects

Downloads

Learn more

Show commands: Magma

Copy content magma:G := TransitiveGroup(38, 31);
 

Group invariants

Abstract group:  $C_{19}^2:(C_3\times D_9)$
Copy content magma:IdentifyGroup(G);
 
Order:  $19494=2 \cdot 3^{3} \cdot 19^{2}$
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 $n$:  $38$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $31$
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:  $(1,36,17,28,15,29)(2,26,5,34,7,33)(3,35,12,21,18,37)(4,25,19,27,10,22)(6,24,14,20,13,30)(8,23,9,32,16,38)(11,31)$, $(1,18,5,6,3,12,4,9,13)(2,15,14,17,8,16,11,7,19)(20,21,25,22,29,38,36,28,34)(23,33,35,24,37,32,31,27,30)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$6$:  $S_3$, $C_6$
$18$:  $S_3\times C_3$, $D_{9}$
$54$:  18T19

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 19: 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 $1^{38}$ $1$ $1$ $0$ $()$
2A $2^{19}$ $171$ $2$ $19$ $( 1,21)( 2,25)( 3,29)( 4,33)( 5,37)( 6,22)( 7,26)( 8,30)( 9,34)(10,38)(11,23)(12,27)(13,31)(14,35)(15,20)(16,24)(17,28)(18,32)(19,36)$
3A1 $3^{6},1^{20}$ $38$ $3$ $12$ $(20,35,29)(21,27,36)(22,38,24)(23,30,31)(25,33,26)(32,34,37)$
3A-1 $3^{6},1^{20}$ $38$ $3$ $12$ $(20,29,35)(21,36,27)(22,24,38)(23,31,30)(25,26,33)(32,37,34)$
3B1 $3^{12},1^{2}$ $361$ $3$ $24$ $( 1,19, 8)( 2,11,15)( 4,14,10)( 5, 6,17)( 7, 9,12)(13,18,16)(20,26,35)(21,37,23)(22,29,30)(24,32,25)(28,38,34)(31,33,36)$
3B-1 $3^{12},1^{2}$ $361$ $3$ $24$ $( 1, 8,19)( 2,15,11)( 4,10,14)( 5,17, 6)( 7,12, 9)(13,16,18)(20,35,26)(21,23,37)(22,30,29)(24,25,32)(28,34,38)(31,36,33)$
3C $3^{12},1^{2}$ $722$ $3$ $24$ $( 1, 5,11)( 2,16,18)( 3, 8, 6)( 4,19,13)( 7,14,15)( 9,17,10)(20,26,30)(21,33,22)(23,28,25)(24,35,36)(27,37,31)(29,32,34)$
6A1 $6^{6},2$ $3249$ $6$ $31$ $( 1,33,19,36, 8,31)( 2,30,11,22,15,29)( 3,27)( 4,24,14,32,10,25)( 5,21, 6,37,17,23)( 7,34, 9,28,12,38)(13,35,18,20,16,26)$
6A-1 $6^{6},2$ $3249$ $6$ $31$ $( 1,31, 8,36,19,33)( 2,29,15,22,11,30)( 3,27)( 4,25,10,32,14,24)( 5,23,17,37, 6,21)( 7,38,12,28, 9,34)(13,26,16,20,18,35)$
9A1 $9^{4},1^{2}$ $722$ $9$ $32$ $( 1,14, 3, 5,15, 8,11, 7, 6)( 2,19, 9,16,13,17,18, 4,10)(20,23,35,26,28,36,30,25,24)(21,27,32,33,37,34,22,31,29)$
9A2 $9^{4},1^{2}$ $722$ $9$ $32$ $( 1, 3,15,11, 6,14, 5, 8, 7)( 2, 9,13,18,10,19,16,17, 4)(20,35,28,30,24,23,26,36,25)(21,32,37,22,29,27,33,34,31)$
9A4 $9^{4},1^{2}$ $722$ $9$ $32$ $( 1,15, 6, 5, 7, 3,11,14, 8)( 2,13,10,16, 4, 9,18,19,17)(20,28,24,26,25,35,30,23,36)(21,37,29,33,31,32,22,27,34)$
9B1 $9^{4},1^{2}$ $722$ $9$ $32$ $( 1, 7,14,19, 9,10, 8,12, 4)( 2, 5,18,11, 6,16,15,17,13)(20,28,22,36,35,31,34,27,37)(21,32,38,24,25,29,26,33,23)$
9B-1 $9^{4},1^{2}$ $722$ $9$ $32$ $( 1, 4,12, 8,10, 9,19,14, 7)( 2,13,17,15,16, 6,11,18, 5)(20,37,27,34,31,35,36,22,28)(21,23,33,26,29,25,24,38,32)$
9B2 $9^{4},1^{2}$ $722$ $9$ $32$ $( 1,14, 9, 8, 4, 7,19,10,12)( 2,18, 6,15,13, 5,11,16,17)(20,22,35,34,37,28,36,31,27)(21,38,25,26,23,32,24,29,33)$
9B-2 $9^{4},1^{2}$ $722$ $9$ $32$ $( 1,12,10,19, 7, 4, 8, 9,14)( 2,17,16,11, 5,13,15, 6,18)(20,27,31,36,28,37,34,35,22)(21,33,29,24,32,23,26,25,38)$
9B4 $9^{4},1^{2}$ $722$ $9$ $32$ $( 1, 9, 4,19,12,14, 8, 7,10)( 2, 6,13,11,17,18,15, 5,16)(20,35,37,36,27,22,34,28,31)(21,25,23,24,33,38,26,32,29)$
9B-4 $9^{4},1^{2}$ $722$ $9$ $32$ $( 1,10, 7, 8,14,12,19, 4, 9)( 2,16, 5,15,18,17,11,13, 6)(20,31,28,34,22,27,36,37,35)(21,29,32,26,38,33,24,23,25)$
19A1 $19,1^{19}$ $18$ $19$ $18$ $( 1,15,10, 5,19,14, 9, 4,18,13, 8, 3,17,12, 7, 2,16,11, 6)$
19A-1 $19,1^{19}$ $18$ $19$ $18$ $( 1, 6,11,16, 2, 7,12,17, 3, 8,13,18, 4, 9,14,19, 5,10,15)$
19B1 $19^{2}$ $27$ $19$ $36$ $( 1, 8,15, 3,10,17, 5,12,19, 7,14, 2, 9,16, 4,11,18, 6,13)(20,29,38,28,37,27,36,26,35,25,34,24,33,23,32,22,31,21,30)$
19B-1 $19^{2}$ $27$ $19$ $36$ $( 1,13, 6,18,11, 4,16, 9, 2,14, 7,19,12, 5,17,10, 3,15, 8)(20,30,21,31,22,32,23,33,24,34,25,35,26,36,27,37,28,38,29)$
19B2 $19^{2}$ $27$ $19$ $36$ $( 1,15,10, 5,19,14, 9, 4,18,13, 8, 3,17,12, 7, 2,16,11, 6)(20,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21)$
19B-2 $19^{2}$ $27$ $19$ $36$ $( 1, 6,11,16, 2, 7,12,17, 3, 8,13,18, 4, 9,14,19, 5,10,15)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38)$
19B4 $19^{2}$ $27$ $19$ $36$ $( 1,10,19, 9,18, 8,17, 7,16, 6,15, 5,14, 4,13, 3,12, 2,11)(20,37,35,33,31,29,27,25,23,21,38,36,34,32,30,28,26,24,22)$
19B-4 $19^{2}$ $27$ $19$ $36$ $( 1,11, 2,12, 3,13, 4,14, 5,15, 6,16, 7,17, 8,18, 9,19,10)(20,22,24,26,28,30,32,34,36,38,21,23,25,27,29,31,33,35,37)$
19C1 $19^{2}$ $54$ $19$ $36$ $( 1, 6,11,16, 2, 7,12,17, 3, 8,13,18, 4, 9,14,19, 5,10,15)(20,30,21,31,22,32,23,33,24,34,25,35,26,36,27,37,28,38,29)$
19C2 $19^{2}$ $54$ $19$ $36$ $( 1,11, 2,12, 3,13, 4,14, 5,15, 6,16, 7,17, 8,18, 9,19,10)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38)$
19C4 $19^{2}$ $54$ $19$ $36$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19)(20,22,24,26,28,30,32,34,36,38,21,23,25,27,29,31,33,35,37)$
38A1 $38$ $513$ $38$ $37$ $( 1,35, 8,25,15,34, 3,24,10,33,17,23, 5,32,12,22,19,31, 7,21,14,30, 2,20, 9,29,16,38, 4,28,11,37,18,27, 6,36,13,26)$
38A-1 $38$ $513$ $38$ $37$ $( 1,26,13,36, 6,27,18,37,11,28, 4,38,16,29, 9,20, 2,30,14,21, 7,31,19,22,12,32, 5,23,17,33,10,24, 3,34,15,25, 8,35)$
38A3 $38$ $513$ $38$ $37$ $( 1,25, 3,33, 5,22, 7,30, 9,38,11,27,13,35,15,24,17,32,19,21, 2,29, 4,37, 6,26, 8,34,10,23,12,31,14,20,16,28,18,36)$
38A-3 $38$ $513$ $38$ $37$ $( 1,36,18,28,16,20,14,31,12,23,10,34, 8,26, 6,37, 4,29, 2,21,19,32,17,24,15,35,13,27,11,38, 9,30, 7,22, 5,33, 3,25)$
38A9 $38$ $513$ $38$ $37$ $( 1,33, 7,38,13,24,19,29, 6,34,12,20,18,25, 5,30,11,35,17,21, 4,26,10,31,16,36, 3,22, 9,27,15,32, 2,37, 8,23,14,28)$
38A-9 $38$ $513$ $38$ $37$ $( 1,28,14,23, 8,37, 2,32,15,27, 9,22, 3,36,16,31,10,26, 4,21,17,35,11,30, 5,25,18,20,12,34, 6,29,19,24,13,38, 7,33)$
57A1 $19,3^{6},1$ $342$ $57$ $30$ $( 1,12, 4,15, 7,18,10, 2,13, 5,16, 8,19,11, 3,14, 6,17, 9)(20,35,29)(21,27,36)(22,38,24)(23,30,31)(25,33,26)(32,34,37)$
57A-1 $19,3^{6},1$ $342$ $57$ $30$ $( 1, 9,17, 6,14, 3,11,19, 8,16, 5,13, 2,10,18, 7,15, 4,12)(20,29,35)(21,36,27)(22,24,38)(23,31,30)(25,26,33)(32,37,34)$
57A5 $19,3^{6},1$ $342$ $57$ $30$ $( 1,18,16,14,12,10, 8, 6, 4, 2,19,17,15,13,11, 9, 7, 5, 3)(20,29,35)(21,36,27)(22,24,38)(23,31,30)(25,26,33)(32,37,34)$
57A-5 $19,3^{6},1$ $342$ $57$ $30$ $( 1, 3, 5, 7, 9,11,13,15,17,19, 2, 4, 6, 8,10,12,14,16,18)(20,35,29)(21,27,36)(22,38,24)(23,30,31)(25,33,26)(32,34,37)$

Malle's constant $a(G)$:     $1/12$

Copy content magma:ConjugacyClasses(G);
 

Character table

39 x 39 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed