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Properties

Label 46T3
Degree $46$
Order $92$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $D_{46}$

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Show commands: Magma

magma: G := TransitiveGroup(46, 3);
 

Group action invariants

Degree $n$:  $46$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $3$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $D_{46}$
Parity:  $-1$
magma: IsEven(G);
 
Primitive:  no
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $2$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,21)(10,22)(11,20)(12,19)(13,18)(14,17)(31,45)(32,46)(33,43)(34,44)(35,42)(36,41)(37,40)(38,39), (1,23)(2,24)(3,21)(4,22)(5,20)(6,19)(7,17)(8,18)(9,15)(10,16)(11,14)(12,13)(25,45)(26,46)(27,44)(28,43)(29,41)(30,42)(31,39)(32,40)(33,37)(34,38)(35,36)
magma: Generators(G);
 

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$46$:  $D_{23}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: $D_{23}$

Low degree siblings

46T3

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

Cycle TypeSizeOrderRepresentative
$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1$ $1$ $()$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ $23$ $2$ $( 3,45)( 4,46)( 5,44)( 6,43)( 7,41)( 8,42)( 9,39)(10,40)(11,38)(12,37)(13,36) (14,35)(15,34)(16,33)(17,31)(18,32)(19,29)(20,30)(21,27)(22,28)(23,26)(24,25)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $1$ $2$ $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22) (23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44) (45,46)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $23$ $2$ $( 1, 2)( 3,46)( 4,45)( 5,43)( 6,44)( 7,42)( 8,41)( 9,40)(10,39)(11,37)(12,38) (13,35)(14,36)(15,33)(16,34)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,25) (24,26)$
$ 46 $ $2$ $46$ $( 1, 3, 6, 8, 9,12,13,15,18,19,21,23,25,28,30,31,33,35,38,40,41,44,46, 2, 4, 5, 7,10,11,14,16,17,20,22,24,26,27,29,32,34,36,37,39,42,43,45)$
$ 23, 23 $ $2$ $23$ $( 1, 4, 6, 7, 9,11,13,16,18,20,21,24,25,27,30,32,33,36,38,39,41,43,46) ( 2, 3, 5, 8,10,12,14,15,17,19,22,23,26,28,29,31,34,35,37,40,42,44,45)$
$ 46 $ $2$ $46$ $( 1, 5, 9,14,18,22,25,29,33,37,41,45, 4, 8,11,15,20,23,27,31,36,40,43, 2, 6, 10,13,17,21,26,30,34,38,42,46, 3, 7,12,16,19,24,28,32,35,39,44)$
$ 23, 23 $ $2$ $23$ $( 1, 6, 9,13,18,21,25,30,33,38,41,46, 4, 7,11,16,20,24,27,32,36,39,43) ( 2, 5,10,14,17,22,26,29,34,37,42,45, 3, 8,12,15,19,23,28,31,35,40,44)$
$ 23, 23 $ $2$ $23$ $( 1, 7,13,20,25,32,38,43, 4, 9,16,21,27,33,39,46, 6,11,18,24,30,36,41) ( 2, 8,14,19,26,31,37,44, 3,10,15,22,28,34,40,45, 5,12,17,23,29,35,42)$
$ 46 $ $2$ $46$ $( 1, 8,13,19,25,31,38,44, 4,10,16,22,27,34,39,45, 6,12,18,23,30,35,41, 2, 7, 14,20,26,32,37,43, 3, 9,15,21,28,33,40,46, 5,11,17,24,29,36,42)$
$ 23, 23 $ $2$ $23$ $( 1, 9,18,25,33,41, 4,11,20,27,36,43, 6,13,21,30,38,46, 7,16,24,32,39) ( 2,10,17,26,34,42, 3,12,19,28,35,44, 5,14,22,29,37,45, 8,15,23,31,40)$
$ 46 $ $2$ $46$ $( 1,10,18,26,33,42, 4,12,20,28,36,44, 6,14,21,29,38,45, 7,15,24,31,39, 2, 9, 17,25,34,41, 3,11,19,27,35,43, 5,13,22,30,37,46, 8,16,23,32,40)$
$ 23, 23 $ $2$ $23$ $( 1,11,21,32,41, 6,16,25,36,46, 9,20,30,39, 4,13,24,33,43, 7,18,27,38) ( 2,12,22,31,42, 5,15,26,35,45,10,19,29,40, 3,14,23,34,44, 8,17,28,37)$
$ 46 $ $2$ $46$ $( 1,12,21,31,41, 5,16,26,36,45, 9,19,30,40, 4,14,24,34,43, 8,18,28,38, 2,11, 22,32,42, 6,15,25,35,46,10,20,29,39, 3,13,23,33,44, 7,17,27,37)$
$ 23, 23 $ $2$ $23$ $( 1,13,25,38, 4,16,27,39, 6,18,30,41, 7,20,32,43, 9,21,33,46,11,24,36) ( 2,14,26,37, 3,15,28,40, 5,17,29,42, 8,19,31,44,10,22,34,45,12,23,35)$
$ 46 $ $2$ $46$ $( 1,14,25,37, 4,15,27,40, 6,17,30,42, 7,19,32,44, 9,22,33,45,11,23,36, 2,13, 26,38, 3,16,28,39, 5,18,29,41, 8,20,31,43,10,21,34,46,12,24,35)$
$ 46 $ $2$ $46$ $( 1,15,30,44,11,26,39, 8,21,35, 4,17,32,45,13,28,41,10,24,37, 6,19,33, 2,16, 29,43,12,25,40, 7,22,36, 3,18,31,46,14,27,42, 9,23,38, 5,20,34)$
$ 23, 23 $ $2$ $23$ $( 1,16,30,43,11,25,39, 7,21,36, 4,18,32,46,13,27,41, 9,24,38, 6,20,33) ( 2,15,29,44,12,26,40, 8,22,35, 3,17,31,45,14,28,42,10,23,37, 5,19,34)$
$ 46 $ $2$ $46$ $( 1,17,33, 3,20,35, 6,22,38, 8,24,40, 9,26,41,12,27,44,13,29,46,15,32, 2,18, 34, 4,19,36, 5,21,37, 7,23,39,10,25,42,11,28,43,14,30,45,16,31)$
$ 23, 23 $ $2$ $23$ $( 1,18,33, 4,20,36, 6,21,38, 7,24,39, 9,25,41,11,27,43,13,30,46,16,32) ( 2,17,34, 3,19,35, 5,22,37, 8,23,40,10,26,42,12,28,44,14,29,45,15,31)$
$ 46 $ $2$ $46$ $( 1,19,38,10,27,45,18,35, 7,26,43,15,33, 5,24,42,13,31, 4,22,39,12,30, 2,20, 37, 9,28,46,17,36, 8,25,44,16,34, 6,23,41,14,32, 3,21,40,11,29)$
$ 23, 23 $ $2$ $23$ $( 1,20,38, 9,27,46,18,36, 7,25,43,16,33, 6,24,41,13,32, 4,21,39,11,30) ( 2,19,37,10,28,45,17,35, 8,26,44,15,34, 5,23,42,14,31, 3,22,40,12,29)$
$ 23, 23 $ $2$ $23$ $( 1,21,41,16,36, 9,30, 4,24,43,18,38,11,32, 6,25,46,20,39,13,33, 7,27) ( 2,22,42,15,35,10,29, 3,23,44,17,37,12,31, 5,26,45,19,40,14,34, 8,28)$
$ 46 $ $2$ $46$ $( 1,22,41,15,36,10,30, 3,24,44,18,37,11,31, 6,26,46,19,39,14,33, 8,27, 2,21, 42,16,35, 9,29, 4,23,43,17,38,12,32, 5,25,45,20,40,13,34, 7,28)$
$ 46 $ $2$ $46$ $( 1,23,46,22,43,19,41,17,39,15,38,14,36,12,33,10,32, 8,30, 5,27, 3,25, 2,24, 45,21,44,20,42,18,40,16,37,13,35,11,34, 9,31, 7,29, 6,28, 4,26)$
$ 23, 23 $ $2$ $23$ $( 1,24,46,21,43,20,41,18,39,16,38,13,36,11,33, 9,32, 7,30, 6,27, 4,25) ( 2,23,45,22,44,19,42,17,40,15,37,14,35,12,34,10,31, 8,29, 5,28, 3,26)$

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $92=2^{2} \cdot 23$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  92.3
magma: IdentifyGroup(G);
 
Character table: not available.

magma: CharacterTable(G);