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Magma
magma: G := TransitiveGroup(46, 17);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $17$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $D_{23}^2:D_{11}$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,39,17,45,10,28,3,34,19,40,12,46,5,29,21,35,14,41,7,24,23,30,16,36,9,42,2,25,18,31,11,37,4,43,20,26,13,32,6,38,22,44,15,27,8,33), (1,26,3,29)(2,39)(4,42,23,36)(5,32,22,46)(6,45,21,33)(7,35,20,43)(8,25,19,30)(9,38,18,40)(10,28,17,27)(11,41,16,37)(12,31,15,24)(13,44,14,34) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $8$: $D_{4}$ $22$: $D_{11}$ $44$: $D_{22}$ $88$: 44T6 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 23: 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, 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 $ | $1$ | $1$ | $()$ | |
| $ 23, 23 $ | $44$ | $23$ | $( 1,17,10, 3,19,12, 5,21,14, 7,23,16, 9, 2,18,11, 4,20,13, 6,22,15, 8) (24,30,36,42,25,31,37,43,26,32,38,44,27,33,39,45,28,34,40,46,29,35,41)$ | |
| $ 23, 23 $ | $44$ | $23$ | $( 1,12,23,11,22,10,21, 9,20, 8,19, 7,18, 6,17, 5,16, 4,15, 3,14, 2,13) (24,31,38,45,29,36,43,27,34,41,25,32,39,46,30,37,44,28,35,42,26,33,40)$ | |
| $ 23, 23 $ | $44$ | $23$ | $( 1,10,19, 5,14,23, 9,18, 4,13,22, 8,17, 3,12,21, 7,16, 2,11,20, 6,15) (24,36,25,37,26,38,27,39,28,40,29,41,30,42,31,43,32,44,33,45,34,46,35)$ | |
| $ 23, 23 $ | $44$ | $23$ | $( 1,23,22,21,20,19,18,17,16,15,14,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2) (24,38,29,43,34,25,39,30,44,35,26,40,31,45,36,27,41,32,46,37,28,42,33)$ | |
| $ 23, 23 $ | $44$ | $23$ | $( 1,19,14, 9, 4,22,17,12, 7, 2,20,15,10, 5,23,18,13, 8, 3,21,16,11, 6) (24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46)$ | |
| $ 23, 23 $ | $44$ | $23$ | $( 1,22,20,18,16,14,12,10, 8, 6, 4, 2,23,21,19,17,15,13,11, 9, 7, 5, 3) (24,29,34,39,44,26,31,36,41,46,28,33,38,43,25,30,35,40,45,27,32,37,42)$ | |
| $ 23, 23 $ | $44$ | $23$ | $( 1,14, 4,17, 7,20,10,23,13, 3,16, 6,19, 9,22,12, 2,15, 5,18, 8,21,11) (24,26,28,30,32,34,36,38,40,42,44,46,25,27,29,31,33,35,37,39,41,43,45)$ | |
| $ 23, 23 $ | $44$ | $23$ | $( 1,20,16,12, 8, 4,23,19,15,11, 7, 3,22,18,14,10, 6, 2,21,17,13, 9, 5) (24,34,44,31,41,28,38,25,35,45,32,42,29,39,26,36,46,33,43,30,40,27,37)$ | |
| $ 23, 23 $ | $44$ | $23$ | $( 1, 4, 7,10,13,16,19,22, 2, 5, 8,11,14,17,20,23, 3, 6, 9,12,15,18,21) (24,28,32,36,40,44,25,29,33,37,41,45,26,30,34,38,42,46,27,31,35,39,43)$ | |
| $ 23, 23 $ | $44$ | $23$ | $( 1,16, 8,23,15, 7,22,14, 6,21,13, 5,20,12, 4,19,11, 3,18,10, 2,17, 9) (24,44,41,38,35,32,29,26,46,43,40,37,34,31,28,25,45,42,39,36,33,30,27)$ | |
| $ 23, 23 $ | $44$ | $23$ | $( 1, 7,13,19, 2, 8,14,20, 3, 9,15,21, 4,10,16,22, 5,11,17,23, 6,12,18) (24,32,40,25,33,41,26,34,42,27,35,43,28,36,44,29,37,45,30,38,46,31,39)$ | |
| $ 23, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $44$ | $23$ | $(24,38,29,43,34,25,39,30,44,35,26,40,31,45,36,27,41,32,46,37,28,42,33)$ | |
| $ 11, 11, 11, 11, 1, 1 $ | $1058$ | $11$ | $( 2, 4,10, 5,13,14,17, 3, 7,19, 9)( 6,16,23,21,15,20,12,11, 8,22,18) (25,32,42,30,26,40,37,36,28,33,27)(29,41,45,31,34,35,43,38,44,46,39)$ | |
| $ 11, 11, 11, 11, 1, 1 $ | $1058$ | $11$ | $( 2,10,13,17, 7, 9, 4, 5,14, 3,19)( 6,23,15,12, 8,18,16,21,20,11,22) (25,42,26,37,28,27,32,30,40,36,33)(29,45,34,43,44,39,41,31,35,38,46)$ | |
| $ 11, 11, 11, 11, 1, 1 $ | $1058$ | $11$ | $( 2,13, 7, 4,14,19,10,17, 9, 5, 3)( 6,15, 8,16,20,22,23,12,18,21,11) (25,26,28,32,40,33,42,37,27,30,36)(29,34,44,41,35,46,45,43,39,31,38)$ | |
| $ 11, 11, 11, 11, 1, 1 $ | $1058$ | $11$ | $( 2, 7,14,10, 9, 3,13, 4,19,17, 5)( 6, 8,20,23,18,11,15,16,22,12,21) (25,28,40,42,27,36,26,32,33,37,30)(29,44,35,45,39,38,34,41,46,43,31)$ | |
| $ 11, 11, 11, 11, 1, 1 $ | $1058$ | $11$ | $( 2,14, 9,13,19, 5, 7,10, 3, 4,17)( 6,20,18,15,22,21, 8,23,11,16,12) (25,40,27,26,33,30,28,42,36,32,37)(29,35,39,34,46,31,44,45,38,41,43)$ | |
| $ 46 $ | $1012$ | $46$ | $( 1,39,17,45,10,28, 3,34,19,40,12,46, 5,29,21,35,14,41, 7,24,23,30,16,36, 9, 42, 2,25,18,31,11,37, 4,43,20,26,13,32, 6,38,22,44,15,27, 8,33)$ | |
| $ 46 $ | $1012$ | $46$ | $( 1,45, 3,40, 5,35, 7,30, 9,25,11,43,13,38,15,33,17,28,19,46,21,41,23,36, 2, 31, 4,26, 6,44, 8,39,10,34,12,29,14,24,16,42,18,37,20,32,22,27)$ | |
| $ 46 $ | $1012$ | $46$ | $( 1,46,16,43, 8,40,23,37,15,34, 7,31,22,28,14,25, 6,45,21,42,13,39, 5,36,20, 33,12,30, 4,27,19,24,11,44, 3,41,18,38,10,35, 2,32,17,29, 9,26)$ | |
| $ 46 $ | $1012$ | $46$ | $( 1,28,12,35,23,42,11,26,22,33,10,40,21,24, 9,31,20,38, 8,45,19,29, 7,36,18, 43, 6,27,17,34, 5,41,16,25, 4,32,15,39, 3,46,14,30, 2,37,13,44)$ | |
| $ 46 $ | $1012$ | $46$ | $( 1,30,15,41, 6,29,20,40,11,28, 2,39,16,27, 7,38,21,26,12,37, 3,25,17,36, 8, 24,22,35,13,46, 4,34,18,45, 9,33,23,44,14,32, 5,43,19,31,10,42)$ | |
| $ 46 $ | $1012$ | $46$ | $( 1,40, 7,25,13,33,19,41, 2,26, 8,34,14,42,20,27, 3,35, 9,43,15,28,21,36, 4, 44,10,29,16,37,22,45, 5,30,11,38,17,46,23,31, 6,39,12,24,18,32)$ | |
| $ 46 $ | $1012$ | $46$ | $( 1,41,20,28,16,38,12,25, 8,35, 4,45,23,32,19,42,15,29,11,39, 7,26, 3,36,22, 46,18,33,14,43,10,30, 6,40, 2,27,21,37,17,24,13,34, 9,44, 5,31)$ | |
| $ 46 $ | $1012$ | $46$ | $( 1,43,23,34,22,25,21,39,20,30,19,44,18,35,17,26,16,40,15,31,14,45,13,36,12, 27,11,41,10,32, 9,46, 8,37, 7,28, 6,42, 5,33, 4,24, 3,38, 2,29)$ | |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ | $506$ | $2$ | $( 1,36)( 2,45)( 3,31)( 4,40)( 5,26)( 6,35)( 7,44)( 8,30)( 9,39)(10,25)(11,34) (12,43)(13,29)(14,38)(15,24)(16,33)(17,42)(18,28)(19,37)(20,46)(21,32)(22,41) (23,27)$ | |
| $ 46 $ | $1012$ | $46$ | $( 1,24, 6,46,11,45,16,44,21,43, 3,42, 8,41,13,40,18,39,23,38, 5,37,10,36,15, 35,20,34, 2,33, 7,32,12,31,17,30,22,29, 4,28, 9,27,14,26,19,25)$ | |
| $ 46 $ | $1012$ | $46$ | $( 1,38, 4,42, 7,46,10,27,13,31,16,35,19,39,22,43, 2,24, 5,28, 8,32,11,36,14, 40,17,44,20,25,23,29, 3,33, 6,37, 9,41,12,45,15,26,18,30,21,34)$ | |
| $ 46 $ | $1012$ | $46$ | $( 1,37,14,39, 4,41,17,43, 7,45,20,24,10,26,23,28,13,30, 3,32,16,34, 6,36,19, 38, 9,40,22,42,12,44, 2,46,15,25, 5,27,18,29, 8,31,21,33,11,35)$ | |
| $ 22, 22, 1, 1 $ | $1058$ | $22$ | $( 2, 8, 4,22,10,18, 5, 6,13,16,14,23,17,21, 3,15, 7,20,19,12, 9,11) (25,34,32,35,42,43,30,38,26,44,40,46,37,39,36,29,28,41,33,45,27,31)$ | |
| $ 22, 22, 1, 1 $ | $1058$ | $22$ | $( 2,22, 5,16,17,15,19,11, 4,18,13,23, 3,20, 9, 8,10, 6,14,21, 7,12) (25,35,30,44,37,29,33,31,32,43,26,46,36,41,27,34,42,38,40,39,28,45)$ | |
| $ 22, 22, 1, 1 $ | $1058$ | $22$ | $( 2,18,14,15, 9,22,13,21,19, 8, 5,23, 7,11,10,16, 3,12, 4, 6,17,20) (25,43,40,29,27,35,26,39,33,34,30,46,28,31,42,44,36,45,32,38,37,41)$ | |
| $ 22, 22, 1, 1 $ | $1058$ | $22$ | $( 2,16,19,18, 3, 8,14,12, 5,15, 4,23, 9, 6, 7,22,17,11,13,20,10,21) (25,44,33,43,36,34,40,45,30,29,32,46,27,38,28,35,37,31,26,41,42,39)$ | |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ | $529$ | $2$ | $( 2,23)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(12,13) (25,46)(26,45)(27,44)(28,43)(29,42)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)$ | |
| $ 22, 22, 1, 1 $ | $1058$ | $22$ | $( 2,15,13, 8, 7,16, 4,20,14,22,19,23,10,12,17,18, 9,21, 5,11, 3, 6) (25,29,26,34,28,44,32,41,40,35,33,46,42,45,37,43,27,39,30,31,36,38)$ | |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $46$ | $2$ | $(25,46)(26,45)(27,44)(28,43)(29,42)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)$ | |
| $ 23, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1 $ | $1012$ | $46$ | $( 1,17,10, 3,19,12, 5,21,14, 7,23,16, 9, 2,18,11, 4,20,13, 6,22,15, 8)(24,30) (25,29)(26,28)(31,46)(32,45)(33,44)(34,43)(35,42)(36,41)(37,40)(38,39)$ | |
| $ 22, 11, 11, 1, 1 $ | $1058$ | $22$ | $( 2, 4,10, 5,13,14,17, 3, 7,19, 9)( 6,16,23,21,15,20,12,11, 8,22,18) (25,39,42,41,26,31,37,35,28,38,27,46,32,29,30,45,40,34,36,43,33,44)$ | |
| $ 22, 11, 11, 1, 1 $ | $1058$ | $22$ | $( 2,10,13,17, 7, 9, 4, 5,14, 3,19)( 6,23,15,12, 8,18,16,21,20,11,22) (25,29,26,34,28,44,32,41,40,35,33,46,42,45,37,43,27,39,30,31,36,38)$ | |
| $ 22, 11, 11, 1, 1 $ | $1058$ | $22$ | $( 2,13, 7, 4,14,19,10,17, 9, 5, 3)( 6,15, 8,16,20,22,23,12,18,21,11) (25,45,28,39,40,38,42,34,27,41,36,46,26,43,32,31,33,29,37,44,30,35)$ | |
| $ 22, 11, 11, 1, 1 $ | $1058$ | $22$ | $( 2, 7,14,10, 9, 3,13, 4,19,17, 5)( 6, 8,20,23,18,11,15,16,22,12,21) (25,43,40,29,27,35,26,39,33,34,30,46,28,31,42,44,36,45,32,38,37,41)$ | |
| $ 22, 11, 11, 1, 1 $ | $1058$ | $22$ | $( 2,14, 9,13,19, 5, 7,10, 3, 4,17)( 6,20,18,15,22,21, 8,23,11,16,12) (25,31,27,45,33,41,28,29,36,39,37,46,40,44,26,38,30,43,42,35,32,34)$ | |
| $ 22, 11, 11, 1, 1 $ | $1058$ | $22$ | $( 2, 9,19, 7, 3,17,14,13, 5,10, 4)( 6,18,22, 8,11,12,20,15,21,23,16) (25,44,33,43,36,34,40,45,30,29,32,46,27,38,28,35,37,31,26,41,42,39)$ | |
| $ 22, 11, 11, 1, 1 $ | $1058$ | $22$ | $( 2,19, 3,14, 5, 4, 9, 7,17,13,10)( 6,22,11,20,21,16,18, 8,12,15,23) (25,38,36,31,30,39,27,43,37,45,42,46,33,35,40,41,32,44,28,34,26,29)$ | |
| $ 22, 11, 11, 1, 1 $ | $1058$ | $22$ | $( 2, 3, 5, 9,17,10,19,14, 4, 7,13)( 6,11,21,18,12,23,22,20,16, 8,15) (25,35,30,44,37,29,33,31,32,43,26,46,36,41,27,34,42,38,40,39,28,45)$ | |
| $ 22, 11, 11, 1, 1 $ | $1058$ | $22$ | $( 2, 5,17,19, 4,13, 3, 9,10,14, 7)( 6,21,12,22,16,15,11,18,23,20, 8) (25,41,37,38,32,45,36,44,42,31,28,46,30,34,33,39,26,35,27,29,40,43)$ | |
| $ 22, 11, 11, 1, 1 $ | $1058$ | $22$ | $( 2,17, 4, 3,10, 7, 5,19,13, 9,14)( 6,12,16,11,23, 8,21,22,15,18,20) (25,34,32,35,42,43,30,38,26,44,40,46,37,39,36,29,28,41,33,45,27,31)$ | |
| $ 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2 $ | $11638$ | $4$ | $( 1,39, 6,38)( 2,25, 5,29)( 3,34, 4,43)( 7,24,23,30)( 8,33,22,44)( 9,42,21,35) (10,28,20,26)(11,37,19,40)(12,46,18,31)(13,32,17,45)(14,41,16,36)(15,27)$ |
magma: ConjugacyClasses(G);
Group invariants
| Order: | $46552=2^{3} \cdot 11 \cdot 23^{2}$ | 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: | 46552.a | magma: IdentifyGroup(G);
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| Character table: | 49 x 49 character table |
magma: CharacterTable(G);