Properties

 Label 47T4 Degree $47$ Order $2162$ Cyclic no Abelian no Solvable yes Primitive yes $p$-group no Group: $F_{47}$

Related objects

Show commands: Magma

magma: G := TransitiveGroup(47, 4);

Group action invariants

 Degree $n$: $47$ magma: t, n := TransitiveGroupIdentification(G); n; Transitive number $t$: $4$ magma: t, n := TransitiveGroupIdentification(G); t; Group: $F_{47}$ Parity: $-1$ magma: IsEven(G); Primitive: yes magma: IsPrimitive(G); magma: NilpotencyClass(G); $\card{\Aut(F/K)}$: $1$ magma: Order(Centralizer(SymmetricGroup(n), G)); Generators: (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47), (1,5,25,31,14,23,21,11,8,40,12,13,18,43,27,41,17,38,2,10,3,15,28,46,42,22,16,33,24,26,36,39,7,35,34,29,4,20,6,30,9,45,37,44,32,19) magma: Generators(G);

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$23$:  $C_{23}$
$46$:  $C_{46}$

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - 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

 Label Cycle Type Size Order Representative $1^{47}$ $1$ $1$ $()$ $47$ $46$ $47$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25, 26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)$ $23^{2},1$ $47$ $23$ $( 2,26,15,22, 9,13,19,28,18, 3, 4,29,43,17,25,37, 8,35, 5, 7,10,38,33) ( 6,32,24,12,41,14,44,42,39,11,16,47,23,34,27,40,36,30,21,31,46,45,20)$ $23^{2},1$ $47$ $23$ $( 2,13, 4,37,10,15,28,43,35,33, 9, 3,25, 7,26,19,29, 8,38,22,18,17, 5) ( 6,14,16,40,46,24,42,23,30,20,41,11,27,31,32,44,47,36,45,12,39,34,21)$ $23^{2},1$ $47$ $23$ $( 2,15, 9,19,18, 4,43,25, 8, 5,10,33,26,22,13,28, 3,29,17,37,35, 7,38) ( 6,24,41,44,39,16,23,27,36,21,46,20,32,12,14,42,11,47,34,40,30,31,45)$ $23^{2},1$ $47$ $23$ $( 2, 4,10,28,35, 9,25,26,29,38,18, 5,13,37,15,43,33, 3, 7,19, 8,22,17) ( 6,16,46,42,30,41,27,32,47,45,39,21,14,40,24,23,20,11,31,44,36,12,34)$ $23^{2},1$ $47$ $23$ $( 2, 9,18,43, 8,10,26,13, 3,17,35,38,15,19, 4,25, 5,33,22,28,29,37, 7) ( 6,41,39,23,36,46,32,14,11,34,30,45,24,44,16,27,21,20,12,42,47,40,31)$ $23^{2},1$ $47$ $23$ $( 2,10,35,25,29,18,13,15,33, 7, 8,17, 4,28, 9,26,38, 5,37,43, 3,19,22) ( 6,46,30,27,47,39,14,24,20,31,36,34,16,42,41,32,45,21,40,23,11,44,12)$ $23^{2},1$ $47$ $23$ $( 2,18, 8,26, 3,35,15, 4, 5,22,29, 7, 9,43,10,13,17,38,19,25,33,28,37) ( 6,39,36,32,11,30,24,16,21,12,47,31,41,23,46,14,34,45,44,27,20,42,40)$ $23^{2},1$ $47$ $23$ $( 2,35,29,13,33, 8, 4, 9,38,37, 3,22,10,25,18,15, 7,17,28,26, 5,43,19) ( 6,30,47,14,20,36,16,41,45,40,11,12,46,27,39,24,31,34,42,32,21,23,44)$ $23^{2},1$ $47$ $23$ $( 2, 8, 3,15, 5,29, 9,10,17,19,33,37,18,26,35, 4,22, 7,43,13,38,25,28) ( 6,36,11,24,21,47,41,46,34,44,20,40,39,32,30,16,12,31,23,14,45,27,42)$ $23^{2},1$ $47$ $23$ $( 2,29,33, 4,38, 3,10,18, 7,28, 5,19,35,13, 8, 9,37,22,25,15,17,26,43) ( 6,47,20,16,45,11,46,39,31,42,21,44,30,14,36,41,40,12,27,24,34,32,23)$ $23^{2},1$ $47$ $23$ $( 2, 3, 5, 9,17,33,18,35,22,43,38,28, 8,15,29,10,19,37,26, 4, 7,13,25) ( 6,11,21,41,34,20,39,30,12,23,45,42,36,24,47,46,44,40,32,16,31,14,27)$ $23^{2},1$ $47$ $23$ $( 2,33,38,10, 7, 5,35, 8,37,25,17,43,29, 4, 3,18,28,19,13, 9,22,15,26) ( 6,20,45,46,31,21,30,36,40,27,34,23,47,16,11,39,42,44,14,41,12,24,32)$ $23^{2},1$ $47$ $23$ $( 2, 5,17,18,22,38, 8,29,19,26, 7,25, 3, 9,33,35,43,28,15,10,37, 4,13) ( 6,21,34,39,12,45,36,47,44,32,31,27,11,41,20,30,23,42,24,46,40,16,14)$ $23^{2},1$ $47$ $23$ $( 2,38, 7,35,37,17,29, 3,28,13,22,26,33,10, 5, 8,25,43, 4,18,19, 9,15) ( 6,45,31,30,40,34,47,11,42,14,12,32,20,46,21,36,27,23,16,39,44,41,24)$ $23^{2},1$ $47$ $23$ $( 2,17,22, 8,19, 7, 3,33,43,15,37,13, 5,18,38,29,26,25, 9,35,28,10, 4) ( 6,34,12,36,44,31,11,20,23,24,40,14,21,39,45,47,32,27,41,30,42,46,16)$ $23^{2},1$ $47$ $23$ $( 2, 7,37,29,28,22,33, 5,25, 4,19,15,38,35,17, 3,13,26,10, 8,43,18, 9) ( 6,31,40,47,42,12,20,21,27,16,44,24,45,30,34,11,14,32,46,36,23,39,41)$ $23^{2},1$ $47$ $23$ $( 2,22,19, 3,43,37, 5,38,26, 9,28, 4,17, 8, 7,33,15,13,18,29,25,35,10) ( 6,12,44,11,23,40,21,45,32,41,42,16,34,36,31,20,24,14,39,47,27,30,46)$ $23^{2},1$ $47$ $23$ $( 2,37,28,33,25,19,38,17,13,10,43, 9, 7,29,22, 5, 4,15,35, 3,26, 8,18) ( 6,40,42,20,27,44,45,34,14,46,23,41,31,47,12,21,16,24,30,11,32,36,39)$ $23^{2},1$ $47$ $23$ $( 2,19,43, 5,26,28,17, 7,15,18,25,10,22, 3,37,38, 9, 4, 8,33,13,29,35) ( 6,44,23,21,32,42,34,31,24,39,27,46,12,11,40,45,41,16,36,20,14,47,30)$ $23^{2},1$ $47$ $23$ $( 2,28,25,38,13,43, 7,22, 4,35,26,18,37,33,19,17,10, 9,29, 5,15, 3, 8) ( 6,42,27,45,14,23,31,12,16,30,32,39,40,20,44,34,46,41,47,21,24,11,36)$ $23^{2},1$ $47$ $23$ $( 2,43,26,17,15,25,22,37, 9, 8,13,35,19, 5,28, 7,18,10, 3,38, 4,33,29) ( 6,23,32,34,24,27,12,40,41,36,14,30,44,21,42,31,39,46,11,45,16,20,47)$ $23^{2},1$ $47$ $23$ $( 2,25,13, 7, 4,26,37,19,10,29,15, 8,28,38,43,22,35,18,33,17, 9, 5, 3) ( 6,27,14,31,16,32,40,44,46,47,24,36,42,45,23,12,30,39,20,34,41,21,11)$ $46,1$ $47$ $46$ $( 2, 6,26,32,15,24,22,12, 9,41,13,14,19,44,28,42,18,39, 3,11, 4,16,29,47,43, 23,17,34,25,27,37,40, 8,36,35,30, 5,21, 7,31,10,46,38,45,33,20)$ $46,1$ $47$ $46$ $( 2,32,22,41,19,42, 3,16,43,34,37,36, 5,31,38,20,26,24, 9,14,28,39, 4,47,17, 27, 8,30, 7,46,33, 6,15,12,13,44,18,11,29,23,25,40,35,21,10,45)$ $46,1$ $47$ $46$ $( 2,14,29,36,33,41, 4,40,38,12, 3,27,10,24,18,34, 7,32,28,23, 5, 6,19,47,35, 20,13,16, 8,45, 9,11,37,46,22,39,25,31,15,42,17,21,26,44,43,30)$ $46,1$ $47$ $46$ $( 2,24,13,42, 4,23,37,30,10,20,15,41,28,11,43,27,35,31,33,32, 9,44, 3,47,25, 36, 7,45,26,12,19,39,29,34, 8,21,38, 6,22,14,18,16,17,40, 5,46)$ $46,1$ $47$ $46$ $( 2,16,38,39, 7,44,35,41,37,24,17, 6,29,45, 3,31,28,30,13,40,22,34,26,47,33, 11,10,42, 5,14, 8,12,25,32,43,20, 4,46,18,21,19,36, 9,27,15,23)$ $46,1$ $47$ $46$ $( 2,41, 3,34, 5,20, 9,39,17,30,33,12,18,23,35,45,22,42,43,36,38,24,28,47, 8, 46,15,44,29,40,10,32,19,16,37,31,26,14, 4,27, 7, 6,13,11,25,21)$ $46,1$ $47$ $46$ $( 2,46, 5,40,17,16,18,14,22, 6,38,21, 8,34,29,39,19,12,26,45, 7,36,25,47, 3, 44, 9,32,33,31,35,27,43,11,28,41,15,20,10,30,37,23, 4,42,13,24)$ $46,1$ $47$ $46$ $( 2,39,35,24,29,31,13,34,33,42, 8,32, 4,21, 9,23,38,44,37, 6, 3,30,22,47,10, 14,25,20,18,36,15,16, 7,41,17,45,28,40,26,11, 5,12,43,46,19,27)$ $46,1$ $47$ $46$ $( 2,30,43,44,26,21,17,42,15,31,25,39,22,46,37,11, 9,45, 8,16,13,20,35,47,19, 6, 5,23,28,32, 7,34,18,24,10,27, 3,12,38,40, 4,41,33,36,29,14)$ $46,1$ $47$ $46$ $( 2,36, 4,12,10,34,28, 6,35,16, 9,46,25,42,26,30,29,41,38,27,18,32, 5,47,13, 45,37,39,15,21,43,14,33,40, 3,24, 7,23,19,20, 8,11,22,31,17,44)$ $2^{23},1$ $47$ $2$ $( 2,47)( 3,46)( 4,45)( 5,44)( 6,43)( 7,42)( 8,41)( 9,40)(10,39)(11,38)(12,37) (13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26) (24,25)$ $46,1$ $47$ $46$ $( 2,11, 7,14,37,32,29,46,28,36,22,23,33,39, 5,41,25, 6, 4,31,19,40,15,47,38, 42,35,12,17,20, 3,21,13,27,26,16,10,44, 8,24,43,45,18,30, 9,34)$ $46,1$ $47$ $46$ $( 2,20,33,45,38,46,10,31, 7,21, 5,30,35,36, 8,40,37,27,25,34,17,23,43,47,29, 16, 4,11, 3,39,18,42,28,44,19,14,13,41, 9,12,22,24,15,32,26, 6)$ $46,1$ $47$ $46$ $( 2,21,25,11,13, 6, 7,27, 4,14,26,31,37,16,19,32,10,40,29,44,15,46, 8,47,28, 24,38,36,43,42,22,45,35,23,18,12,33,30,17,39, 9,20, 5,34, 3,41)$ $46,1$ $47$ $46$ $( 2,45,10,21,35,40,25,23,29,11,18,44,13,12,15, 6,33,46, 7,30, 8,27,17,47, 4, 39,28,14, 9,24,26,20,38,31, 5,36,37,34,43,16, 3,42,19,41,22,32)$ $46,1$ $47$ $46$ $( 2,34, 9,30,18,45,43,24, 8,44,10,16,26,27,13,21, 3,20,17,12,35,42,38,47,15, 40,19,31, 4, 6,25,41, 5,39,33,23,22,36,28,46,29,32,37,14, 7,11)$ $46,1$ $47$ $46$ $( 2,31, 8,23, 3,14,15,45, 5,27,29,42, 9, 6,10,36,17,11,19,24,33,21,37,47,18, 41,26,46,35,34, 4,44,22,20, 7,40,43,39,13,32,38,30,25,16,28,12)$ $46,1$ $47$ $46$ $( 2,12,28,16,25,30,38,32,13,39,43,40, 7,20,22,44, 4,34,35,46,26,41,18,47,37, 21,33,24,19,11,17,36,10, 6, 9,42,29,27, 5,45,15,14, 3,23, 8,31)$ $46,1$ $47$ $46$ $( 2,40,18, 6, 8,39,26,36, 3,32,35,11,15,30, 4,24, 5,16,22,21,29,12, 7,47, 9, 31,43,41,10,23,13,46,17,14,38,34,19,45,25,44,33,27,28,20,37,42)$ $46,1$ $47$ $46$ $( 2,44,17,31,22,11, 8,20,19,23, 7,24, 3,40,33,14,43,21,15,39,37,45,13,47, 5, 32,18,27,38,41,29,30,26,42,25,46, 9,16,35, 6,28,34,10,12, 4,36)$ $46,1$ $47$ $46$ $( 2,42,37,20,28,27,33,44,25,45,19,34,38,14,17,46,13,23,10,41,43,31, 9,47, 7, 12,29,21,22,16, 5,24, 4,30,15,11,35,32, 3,36,26,39, 8, 6,18,40)$ $46,1$ $47$ $46$ $( 2,23,15,27, 9,36,19,21,18,46, 4,20,43,32,25,12, 8,14, 5,42,10,11,33,47,26, 34,22,40,13,30,28,31, 3,45,29, 6,17,24,37,41,35,44, 7,39,38,16)$ $46,1$ $47$ $46$ $( 2,27,19,46,43,12, 5,11,26,40,28,45,17,41, 7,16,15,36,18,20,25,14,10,47,22, 30, 3, 6,37,44,38,23, 9,21, 4,32, 8,42,33,34,13,31,29,24,35,39)$

magma: ConjugacyClasses(G);

Group invariants

 Order: $2162=2 \cdot 23 \cdot 47$ magma: Order(G); Cyclic: no magma: IsCyclic(G); Abelian: no magma: IsAbelian(G); Solvable: yes magma: IsSolvable(G); Nilpotency class: not nilpotent Label: 2162.1 magma: IdentifyGroup(G); Character table: 47 x 47 character table

magma: CharacterTable(G);