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Magma
magma: G := TransitiveGroup(47, 2);
Group action invariants
| Degree $n$: | $47$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $2$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $D_{47}$ | ||
| 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));
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| 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), (1,46)(2,45)(3,44)(4,43)(5,42)(6,41)(7,40)(8,39)(9,38)(10,37)(11,36)(12,35)(13,34)(14,33)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ 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 $ | $1$ | $1$ | $()$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1 $ | $47$ | $2$ | $( 2,47)( 3,46)( 4,45)( 5,44)( 6,43)( 7,42)( 8,41)( 9,40)(10,39)(11,38)(12,37) (13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26) (24,25)$ |
| $ 47 $ | $2$ | $47$ | $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25, 26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)$ |
| $ 47 $ | $2$ | $47$ | $( 1, 3, 5, 7, 9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47, 2, 4, 6, 8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46)$ |
| $ 47 $ | $2$ | $47$ | $( 1, 4, 7,10,13,16,19,22,25,28,31,34,37,40,43,46, 2, 5, 8,11,14,17,20,23,26, 29,32,35,38,41,44,47, 3, 6, 9,12,15,18,21,24,27,30,33,36,39,42,45)$ |
| $ 47 $ | $2$ | $47$ | $( 1, 5, 9,13,17,21,25,29,33,37,41,45, 2, 6,10,14,18,22,26,30,34,38,42,46, 3, 7,11,15,19,23,27,31,35,39,43,47, 4, 8,12,16,20,24,28,32,36,40,44)$ |
| $ 47 $ | $2$ | $47$ | $( 1, 6,11,16,21,26,31,36,41,46, 4, 9,14,19,24,29,34,39,44, 2, 7,12,17,22,27, 32,37,42,47, 5,10,15,20,25,30,35,40,45, 3, 8,13,18,23,28,33,38,43)$ |
| $ 47 $ | $2$ | $47$ | $( 1, 7,13,19,25,31,37,43, 2, 8,14,20,26,32,38,44, 3, 9,15,21,27,33,39,45, 4, 10,16,22,28,34,40,46, 5,11,17,23,29,35,41,47, 6,12,18,24,30,36,42)$ |
| $ 47 $ | $2$ | $47$ | $( 1, 8,15,22,29,36,43, 3,10,17,24,31,38,45, 5,12,19,26,33,40,47, 7,14,21,28, 35,42, 2, 9,16,23,30,37,44, 4,11,18,25,32,39,46, 6,13,20,27,34,41)$ |
| $ 47 $ | $2$ | $47$ | $( 1, 9,17,25,33,41, 2,10,18,26,34,42, 3,11,19,27,35,43, 4,12,20,28,36,44, 5, 13,21,29,37,45, 6,14,22,30,38,46, 7,15,23,31,39,47, 8,16,24,32,40)$ |
| $ 47 $ | $2$ | $47$ | $( 1,10,19,28,37,46, 8,17,26,35,44, 6,15,24,33,42, 4,13,22,31,40, 2,11,20,29, 38,47, 9,18,27,36,45, 7,16,25,34,43, 5,14,23,32,41, 3,12,21,30,39)$ |
| $ 47 $ | $2$ | $47$ | $( 1,11,21,31,41, 4,14,24,34,44, 7,17,27,37,47,10,20,30,40, 3,13,23,33,43, 6, 16,26,36,46, 9,19,29,39, 2,12,22,32,42, 5,15,25,35,45, 8,18,28,38)$ |
| $ 47 $ | $2$ | $47$ | $( 1,12,23,34,45, 9,20,31,42, 6,17,28,39, 3,14,25,36,47,11,22,33,44, 8,19,30, 41, 5,16,27,38, 2,13,24,35,46,10,21,32,43, 7,18,29,40, 4,15,26,37)$ |
| $ 47 $ | $2$ | $47$ | $( 1,13,25,37, 2,14,26,38, 3,15,27,39, 4,16,28,40, 5,17,29,41, 6,18,30,42, 7, 19,31,43, 8,20,32,44, 9,21,33,45,10,22,34,46,11,23,35,47,12,24,36)$ |
| $ 47 $ | $2$ | $47$ | $( 1,14,27,40, 6,19,32,45,11,24,37, 3,16,29,42, 8,21,34,47,13,26,39, 5,18,31, 44,10,23,36, 2,15,28,41, 7,20,33,46,12,25,38, 4,17,30,43, 9,22,35)$ |
| $ 47 $ | $2$ | $47$ | $( 1,15,29,43,10,24,38, 5,19,33,47,14,28,42, 9,23,37, 4,18,32,46,13,27,41, 8, 22,36, 3,17,31,45,12,26,40, 7,21,35, 2,16,30,44,11,25,39, 6,20,34)$ |
| $ 47 $ | $2$ | $47$ | $( 1,16,31,46,14,29,44,12,27,42,10,25,40, 8,23,38, 6,21,36, 4,19,34, 2,17,32, 47,15,30,45,13,28,43,11,26,41, 9,24,39, 7,22,37, 5,20,35, 3,18,33)$ |
| $ 47 $ | $2$ | $47$ | $( 1,17,33, 2,18,34, 3,19,35, 4,20,36, 5,21,37, 6,22,38, 7,23,39, 8,24,40, 9, 25,41,10,26,42,11,27,43,12,28,44,13,29,45,14,30,46,15,31,47,16,32)$ |
| $ 47 $ | $2$ | $47$ | $( 1,18,35, 5,22,39, 9,26,43,13,30,47,17,34, 4,21,38, 8,25,42,12,29,46,16,33, 3,20,37, 7,24,41,11,28,45,15,32, 2,19,36, 6,23,40,10,27,44,14,31)$ |
| $ 47 $ | $2$ | $47$ | $( 1,19,37, 8,26,44,15,33, 4,22,40,11,29,47,18,36, 7,25,43,14,32, 3,21,39,10, 28,46,17,35, 6,24,42,13,31, 2,20,38, 9,27,45,16,34, 5,23,41,12,30)$ |
| $ 47 $ | $2$ | $47$ | $( 1,20,39,11,30, 2,21,40,12,31, 3,22,41,13,32, 4,23,42,14,33, 5,24,43,15,34, 6,25,44,16,35, 7,26,45,17,36, 8,27,46,18,37, 9,28,47,19,38,10,29)$ |
| $ 47 $ | $2$ | $47$ | $( 1,21,41,14,34, 7,27,47,20,40,13,33, 6,26,46,19,39,12,32, 5,25,45,18,38,11, 31, 4,24,44,17,37,10,30, 3,23,43,16,36, 9,29, 2,22,42,15,35, 8,28)$ |
| $ 47 $ | $2$ | $47$ | $( 1,22,43,17,38,12,33, 7,28, 2,23,44,18,39,13,34, 8,29, 3,24,45,19,40,14,35, 9,30, 4,25,46,20,41,15,36,10,31, 5,26,47,21,42,16,37,11,32, 6,27)$ |
| $ 47 $ | $2$ | $47$ | $( 1,23,45,20,42,17,39,14,36,11,33, 8,30, 5,27, 2,24,46,21,43,18,40,15,37,12, 34, 9,31, 6,28, 3,25,47,22,44,19,41,16,38,13,35,10,32, 7,29, 4,26)$ |
| $ 47 $ | $2$ | $47$ | $( 1,24,47,23,46,22,45,21,44,20,43,19,42,18,41,17,40,16,39,15,38,14,37,13,36, 12,35,11,34,10,33, 9,32, 8,31, 7,30, 6,29, 5,28, 4,27, 3,26, 2,25)$ |
magma: ConjugacyClasses(G);
Group invariants
| Order: | $94=2 \cdot 47$ | 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: | 94.1 | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);