# Properties

 Label 47T1 Degree $47$ Order $47$ Cyclic yes Abelian yes Solvable yes Primitive yes $p$-group yes Group: $C_{47}$

# Related objects

Show commands: Magma

magma: G := TransitiveGroup(47, 1);

## Group action invariants

 Degree $n$: $47$ magma: t, n := TransitiveGroupIdentification(G); n; Transitive number $t$: $1$ magma: t, n := TransitiveGroupIdentification(G); t; Group: $C_{47}$ Parity: $1$ magma: IsEven(G); Primitive: yes magma: IsPrimitive(G); magma: NilpotencyClass(G); $\card{\Aut(F/K)}$: $47$ 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) magma: Generators(G);

## Low degree resolvents

none

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

magma: ConjugacyClasses(G);

## Group invariants

 Order: $47$ (is prime) magma: Order(G); Cyclic: yes magma: IsCyclic(G); Abelian: yes magma: IsAbelian(G); Solvable: yes magma: IsSolvable(G); Nilpotency class: $1$ Label: 47.1 magma: IdentifyGroup(G); Character table: 47 x 47 character table

magma: CharacterTable(G);