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Magma
magma: G := TransitiveGroup(46, 1);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $1$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{46}$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $46$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,33,19,6,38,23,9,41,27,13,46,31,18,3,36,22,7,40,26,11,43,30,15,2,34,20,5,37,24,10,42,28,14,45,32,17,4,35,21,8,39,25,12,44,29,16) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $23$: $C_{23}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 23: $C_{23}$
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, 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 $ | $1$ | $2$ | $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22) (23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44) (45,46)$ | |
| $ 46 $ | $1$ | $46$ | $( 1, 3, 5, 8, 9,11,14,16,18,20,21,23,26,28,29,31,34,35,38,40,42,44,46, 2, 4, 6, 7,10,12,13,15,17,19,22,24,25,27,30,32,33,36,37,39,41,43,45)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1, 4, 5, 7, 9,12,14,15,18,19,21,24,26,27,29,32,34,36,38,39,42,43,46) ( 2, 3, 6, 8,10,11,13,16,17,20,22,23,25,28,30,31,33,35,37,40,41,44,45)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1, 5, 9,14,18,21,26,29,34,38,42,46, 4, 7,12,15,19,24,27,32,36,39,43) ( 2, 6,10,13,17,22,25,30,33,37,41,45, 3, 8,11,16,20,23,28,31,35,40,44)$ | |
| $ 46 $ | $1$ | $46$ | $( 1, 6, 9,13,18,22,26,30,34,37,42,45, 4, 8,12,16,19,23,27,31,36,40,43, 2, 5, 10,14,17,21,25,29,33,38,41,46, 3, 7,11,15,20,24,28,32,35,39,44)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1, 7,14,19,26,32,38,43, 4, 9,15,21,27,34,39,46, 5,12,18,24,29,36,42) ( 2, 8,13,20,25,31,37,44, 3,10,16,22,28,33,40,45, 6,11,17,23,30,35,41)$ | |
| $ 46 $ | $1$ | $46$ | $( 1, 8,14,20,26,31,38,44, 4,10,15,22,27,33,39,45, 5,11,18,23,29,35,42, 2, 7, 13,19,25,32,37,43, 3, 9,16,21,28,34,40,46, 6,12,17,24,30,36,41)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1, 9,18,26,34,42, 4,12,19,27,36,43, 5,14,21,29,38,46, 7,15,24,32,39) ( 2,10,17,25,33,41, 3,11,20,28,35,44, 6,13,22,30,37,45, 8,16,23,31,40)$ | |
| $ 46 $ | $1$ | $46$ | $( 1,10,18,25,34,41, 4,11,19,28,36,44, 5,13,21,30,38,45, 7,16,24,31,39, 2, 9, 17,26,33,42, 3,12,20,27,35,43, 6,14,22,29,37,46, 8,15,23,32,40)$ | |
| $ 46 $ | $1$ | $46$ | $( 1,11,21,31,42, 6,15,25,36,45, 9,20,29,40, 4,13,24,33,43, 8,18,28,38, 2,12, 22,32,41, 5,16,26,35,46,10,19,30,39, 3,14,23,34,44, 7,17,27,37)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1,12,21,32,42, 5,15,26,36,46, 9,19,29,39, 4,14,24,34,43, 7,18,27,38) ( 2,11,22,31,41, 6,16,25,35,45,10,20,30,40, 3,13,23,33,44, 8,17,28,37)$ | |
| $ 46 $ | $1$ | $46$ | $( 1,13,26,37, 4,16,27,40, 5,17,29,41, 7,20,32,44, 9,22,34,45,12,23,36, 2,14, 25,38, 3,15,28,39, 6,18,30,42, 8,19,31,43,10,21,33,46,11,24,35)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1,14,26,38, 4,15,27,39, 5,18,29,42, 7,19,32,43, 9,21,34,46,12,24,36) ( 2,13,25,37, 3,16,28,40, 6,17,30,41, 8,20,31,44,10,22,33,45,11,23,35)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1,15,29,43,12,26,39, 7,21,36, 4,18,32,46,14,27,42, 9,24,38, 5,19,34) ( 2,16,30,44,11,25,40, 8,22,35, 3,17,31,45,13,28,41,10,23,37, 6,20,33)$ | |
| $ 46 $ | $1$ | $46$ | $( 1,16,29,44,12,25,39, 8,21,35, 4,17,32,45,14,28,42,10,24,37, 5,20,34, 2,15, 30,43,11,26,40, 7,22,36, 3,18,31,46,13,27,41, 9,23,38, 6,19,33)$ | |
| $ 46 $ | $1$ | $46$ | $( 1,17,34, 3,19,35, 5,22,38, 8,24,40, 9,25,42,11,27,44,14,30,46,16,32, 2,18, 33, 4,20,36, 6,21,37, 7,23,39,10,26,41,12,28,43,13,29,45,15,31)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1,18,34, 4,19,36, 5,21,38, 7,24,39, 9,26,42,12,27,43,14,29,46,15,32) ( 2,17,33, 3,20,35, 6,22,37, 8,23,40,10,25,41,11,28,44,13,30,45,16,31)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1,19,38, 9,27,46,18,36, 7,26,43,15,34, 5,24,42,14,32, 4,21,39,12,29) ( 2,20,37,10,28,45,17,35, 8,25,44,16,33, 6,23,41,13,31, 3,22,40,11,30)$ | |
| $ 46 $ | $1$ | $46$ | $( 1,20,38,10,27,45,18,35, 7,25,43,16,34, 6,24,41,14,31, 4,22,39,11,29, 2,19, 37, 9,28,46,17,36, 8,26,44,15,33, 5,23,42,13,32, 3,21,40,12,30)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1,21,42,15,36, 9,29, 4,24,43,18,38,12,32, 5,26,46,19,39,14,34, 7,27) ( 2,22,41,16,35,10,30, 3,23,44,17,37,11,31, 6,25,45,20,40,13,33, 8,28)$ | |
| $ 46 $ | $1$ | $46$ | $( 1,22,42,16,36,10,29, 3,24,44,18,37,12,31, 5,25,46,20,39,13,34, 8,27, 2,21, 41,15,35, 9,30, 4,23,43,17,38,11,32, 6,26,45,19,40,14,33, 7,28)$ | |
| $ 46 $ | $1$ | $46$ | $( 1,23,46,22,43,20,42,17,39,16,38,13,36,11,34,10,32, 8,29, 6,27, 3,26, 2,24, 45,21,44,19,41,18,40,15,37,14,35,12,33, 9,31, 7,30, 5,28, 4,25)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1,24,46,21,43,19,42,18,39,15,38,14,36,12,34, 9,32, 7,29, 5,27, 4,26) ( 2,23,45,22,44,20,41,17,40,16,37,13,35,11,33,10,31, 8,30, 6,28, 3,25)$ | |
| $ 46 $ | $1$ | $46$ | $( 1,25, 4,28, 5,30, 7,31, 9,33,12,35,14,37,15,40,18,41,19,44,21,45,24, 2,26, 3,27, 6,29, 8,32,10,34,11,36,13,38,16,39,17,42,20,43,22,46,23)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1,26, 4,27, 5,29, 7,32, 9,34,12,36,14,38,15,39,18,42,19,43,21,46,24) ( 2,25, 3,28, 6,30, 8,31,10,33,11,35,13,37,16,40,17,41,20,44,22,45,23)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1,27, 7,34,14,39,19,46,26, 5,32,12,38,18,43,24, 4,29, 9,36,15,42,21) ( 2,28, 8,33,13,40,20,45,25, 6,31,11,37,17,44,23, 3,30,10,35,16,41,22)$ | |
| $ 46 $ | $1$ | $46$ | $( 1,28, 7,33,14,40,19,45,26, 6,32,11,38,17,43,23, 4,30, 9,35,15,41,21, 2,27, 8,34,13,39,20,46,25, 5,31,12,37,18,44,24, 3,29,10,36,16,42,22)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1,29,12,39,21, 4,32,14,42,24, 5,34,15,43,26, 7,36,18,46,27, 9,38,19) ( 2,30,11,40,22, 3,31,13,41,23, 6,33,16,44,25, 8,35,17,45,28,10,37,20)$ | |
| $ 46 $ | $1$ | $46$ | $( 1,30,12,40,21, 3,32,13,42,23, 5,33,15,44,26, 8,36,17,46,28, 9,37,19, 2,29, 11,39,22, 4,31,14,41,24, 6,34,16,43,25, 7,35,18,45,27,10,38,20)$ | |
| $ 46 $ | $1$ | $46$ | $( 1,31,15,45,29,13,43,28,12,41,26,10,39,23, 7,37,21, 6,36,20, 4,33,18, 2,32, 16,46,30,14,44,27,11,42,25, 9,40,24, 8,38,22, 5,35,19, 3,34,17)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1,32,15,46,29,14,43,27,12,42,26, 9,39,24, 7,38,21, 5,36,19, 4,34,18) ( 2,31,16,45,30,13,44,28,11,41,25,10,40,23, 8,37,22, 6,35,20, 3,33,17)$ | |
| $ 46 $ | $1$ | $46$ | $( 1,33,19, 6,38,23, 9,41,27,13,46,31,18, 3,36,22, 7,40,26,11,43,30,15, 2,34, 20, 5,37,24,10,42,28,14,45,32,17, 4,35,21, 8,39,25,12,44,29,16)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1,34,19, 5,38,24, 9,42,27,14,46,32,18, 4,36,21, 7,39,26,12,43,29,15) ( 2,33,20, 6,37,23,10,41,28,13,45,31,17, 3,35,22, 8,40,25,11,44,30,16)$ | |
| $ 46 $ | $1$ | $46$ | $( 1,35,24,11,46,33,21,10,43,31,19, 8,42,30,18, 6,39,28,15, 3,38,25,14, 2,36, 23,12,45,34,22, 9,44,32,20, 7,41,29,17, 5,40,27,16, 4,37,26,13)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1,36,24,12,46,34,21, 9,43,32,19, 7,42,29,18, 5,39,27,15, 4,38,26,14) ( 2,35,23,11,45,33,22,10,44,31,20, 8,41,30,17, 6,40,28,16, 3,37,25,13)$ | |
| $ 46 $ | $1$ | $46$ | $( 1,37,27,17, 7,44,34,23,14, 3,39,30,19,10,46,35,26,16, 5,41,32,22,12, 2,38, 28,18, 8,43,33,24,13, 4,40,29,20, 9,45,36,25,15, 6,42,31,21,11)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1,38,27,18, 7,43,34,24,14, 4,39,29,19, 9,46,36,26,15, 5,42,32,21,12) ( 2,37,28,17, 8,44,33,23,13, 3,40,30,20,10,45,35,25,16, 6,41,31,22,11)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1,39,32,24,15, 7,46,38,29,21,14, 5,43,36,27,19,12, 4,42,34,26,18, 9) ( 2,40,31,23,16, 8,45,37,30,22,13, 6,44,35,28,20,11, 3,41,33,25,17,10)$ | |
| $ 46 $ | $1$ | $46$ | $( 1,40,32,23,15, 8,46,37,29,22,14, 6,43,35,27,20,12, 3,42,33,26,17, 9, 2,39, 31,24,16, 7,45,38,30,21,13, 5,44,36,28,19,11, 4,41,34,25,18,10)$ | |
| $ 46 $ | $1$ | $46$ | $( 1,41,36,30,24,17,12, 6,46,40,34,28,21,16, 9, 3,43,37,32,25,19,13, 7, 2,42, 35,29,23,18,11, 5,45,39,33,27,22,15,10, 4,44,38,31,26,20,14, 8)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1,42,36,29,24,18,12, 5,46,39,34,27,21,15, 9, 4,43,38,32,26,19,14, 7) ( 2,41,35,30,23,17,11, 6,45,40,33,28,22,16,10, 3,44,37,31,25,20,13, 8)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1,43,39,36,32,27,24,19,15,12, 7, 4,46,42,38,34,29,26,21,18,14, 9, 5) ( 2,44,40,35,31,28,23,20,16,11, 8, 3,45,41,37,33,30,25,22,17,13,10, 6)$ | |
| $ 46 $ | $1$ | $46$ | $( 1,44,39,35,32,28,24,20,15,11, 7, 3,46,41,38,33,29,25,21,17,14,10, 5, 2,43, 40,36,31,27,23,19,16,12, 8, 4,45,42,37,34,30,26,22,18,13, 9, 6)$ | |
| $ 46 $ | $1$ | $46$ | $( 1,45,43,41,39,37,36,33,32,30,27,25,24,22,19,17,15,13,12,10, 7, 6, 4, 2,46, 44,42,40,38,35,34,31,29,28,26,23,21,20,18,16,14,11, 9, 8, 5, 3)$ | |
| $ 23, 23 $ | $1$ | $23$ | $( 1,46,43,42,39,38,36,34,32,29,27,26,24,21,19,18,15,14,12, 9, 7, 5, 4) ( 2,45,44,41,40,37,35,33,31,30,28,25,23,22,20,17,16,13,11,10, 8, 6, 3)$ |
magma: ConjugacyClasses(G);
Group invariants
| Order: | $46=2 \cdot 23$ | magma: Order(G);
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| Cyclic: | yes | magma: IsCyclic(G);
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| Abelian: | yes | magma: IsAbelian(G);
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| Solvable: | yes | magma: IsSolvable(G);
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| Nilpotency class: | $1$ | ||
| Label: | 46.2 | magma: IdentifyGroup(G);
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| Character table: | 46 x 46 character table |
magma: CharacterTable(G);