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Magma
magma: G := TransitiveGroup(47, 3);
Group action invariants
| Degree $n$: | $47$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $3$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{47}:C_{23}$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | yes | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $1$ | 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), (1,25,14,21,8,12,18,27,17,2,3,28,42,16,24,36,7,34,4,6,9,37,32)(5,31,23,11,40,13,43,41,38,10,15,46,22,33,26,39,35,29,20,30,45,44,19) | magma: Generators(G);
|
Low degree resolvents
|G/N| Galois groups for stem field(s) $23$: $C_{23}$ 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
| Cycle Type | Size | Order | Representative |
| $ 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 $ | $1$ | $1$ | $()$ |
| $ 47 $ | $23$ | $47$ | $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25, 26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)$ |
| $ 47 $ | $23$ | $47$ | $( 1, 6,11,16,21,26,31,36,41,46, 4, 9,14,19,24,29,34,39,44, 2, 7,12,17,22,27, 32,37,42,47, 5,10,15,20,25,30,35,40,45, 3, 8,13,18,23,28,33,38,43)$ |
| $ 23, 23, 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, 23, 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, 23, 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, 23, 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, 23, 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, 23, 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, 23, 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, 23, 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, 23, 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, 23, 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, 23, 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, 23, 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, 23, 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, 23, 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, 23, 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, 23, 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, 23, 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, 23, 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, 23, 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, 23, 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, 23, 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, 23, 1 $ | $47$ | $23$ | $( 2,25,13, 7, 4,26,37,19,10,29,15, 8,28,38,43,22,35,18,33,17, 9, 5, 3) ( 6,27,14,31,16,32,40,44,46,47,24,36,42,45,23,12,30,39,20,34,41,21,11)$ |
magma: ConjugacyClasses(G);
Group invariants
| Order: | $1081=23 \cdot 47$ | magma: Order(G);
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| Cyclic: | no | magma: IsCyclic(G);
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| Abelian: | no | magma: IsAbelian(G);
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| Solvable: | yes | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 1081.1 | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);