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Magma
magma: G := TransitiveGroup(46, 14);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $14$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{23}^2:C_{11}:C_4$ | ||
| 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: | (1,45,15,26)(2,42,14,29)(3,39,13,32)(4,36,12,35)(5,33,11,38)(6,30,10,41)(7,27,9,44)(8,24)(16,46,23,25)(17,43,22,28)(18,40,21,31)(19,37,20,34), (1,38,23,39)(2,37,22,40)(3,36,21,41)(4,35,20,42)(5,34,19,43)(6,33,18,44)(7,32,17,45)(8,31,16,46)(9,30,15,24)(10,29,14,25)(11,28,13,26)(12,27) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $4$: $C_4$ $22$: $D_{11}$ $44$: 44T3 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
| 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 $ | $44$ | $23$ | $( 1,20,16,12, 8, 4,23,19,15,11, 7, 3,22,18,14,10, 6, 2,21,17,13, 9, 5) (24,42,37,32,27,45,40,35,30,25,43,38,33,28,46,41,36,31,26,44,39,34,29)$ |
| $ 23, 23 $ | $44$ | $23$ | $( 1, 4, 7,10,13,16,19,22, 2, 5, 8,11,14,17,20,23, 3, 6, 9,12,15,18,21) (24,45,43,41,39,37,35,33,31,29,27,25,46,44,42,40,38,36,34,32,30,28,26)$ |
| $ 23, 23 $ | $44$ | $23$ | $( 1,16, 8,23,15, 7,22,14, 6,21,13, 5,20,12, 4,19,11, 3,18,10, 2,17, 9) (24,37,27,40,30,43,33,46,36,26,39,29,42,32,45,35,25,38,28,41,31,44,34)$ |
| $ 23, 23 $ | $44$ | $23$ | $( 1, 7,13,19, 2, 8,14,20, 3, 9,15,21, 4,10,16,22, 5,11,17,23, 6,12,18) (24,43,39,35,31,27,46,42,38,34,30,26,45,41,37,33,29,25,44,40,36,32,28)$ |
| $ 23, 23 $ | $44$ | $23$ | $( 1, 8,15,22, 6,13,20, 4,11,18, 2, 9,16,23, 7,14,21, 5,12,19, 3,10,17) (24,27,30,33,36,39,42,45,25,28,31,34,37,40,43,46,26,29,32,35,38,41,44)$ |
| $ 23, 23 $ | $44$ | $23$ | $( 1,13, 2,14, 3,15, 4,16, 5,17, 6,18, 7,19, 8,20, 9,21,10,22,11,23,12) (24,39,31,46,38,30,45,37,29,44,36,28,43,35,27,42,34,26,41,33,25,40,32)$ |
| $ 23, 23 $ | $44$ | $23$ | $( 1,15, 6,20,11, 2,16, 7,21,12, 3,17, 8,22,13, 4,18, 9,23,14, 5,19,10) (24,30,36,42,25,31,37,43,26,32,38,44,27,33,39,45,28,34,40,46,29,35,41)$ |
| $ 23, 23 $ | $44$ | $23$ | $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,22,23) (24,31,38,45,29,36,43,27,34,41,25,32,39,46,30,37,44,28,35,42,26,33,40)$ |
| $ 23, 23 $ | $44$ | $23$ | $( 1, 6,11,16,21, 3, 8,13,18,23, 5,10,15,20, 2, 7,12,17,22, 4, 9,14,19) (24,36,25,37,26,38,27,39,28,40,29,41,30,42,31,43,32,44,33,45,34,46,35)$ |
| $ 23, 23 $ | $44$ | $23$ | $( 1, 3, 5, 7, 9,11,13,15,17,19,21,23, 2, 4, 6, 8,10,12,14,16,18,20,22) (24,38,29,43,34,25,39,30,44,35,26,40,31,45,36,27,41,32,46,37,28,42,33)$ |
| $ 23, 23 $ | $44$ | $23$ | $( 1,11,21, 8,18, 5,15, 2,12,22, 9,19, 6,16, 3,13,23,10,20, 7,17, 4,14) (24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46)$ |
| $ 23, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $44$ | $23$ | $(24,40,33,26,42,35,28,44,37,30,46,39,32,25,41,34,27,43,36,29,45,38,31)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ | $529$ | $2$ | $( 2,23)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(12,13) (25,46)(26,45)(27,44)(28,43)(29,42)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)$ |
| $ 11, 11, 11, 11, 1, 1 $ | $1058$ | $11$ | $( 2, 3, 5, 9,17,10,19,14, 4, 7,13)( 6,11,21,18,12,23,22,20,16, 8,15) (25,36,30,27,37,42,33,40,32,28,26)(29,38,31,39,43,45,46,35,41,44,34)$ |
| $ 22, 22, 1, 1 $ | $1058$ | $22$ | $( 2,22, 5,16,17,15,19,11, 4,18,13,23, 3,20, 9, 8,10, 6,14,21, 7,12) (25,35,30,44,37,29,33,31,32,43,26,46,36,41,27,34,42,38,40,39,28,45)$ |
| $ 11, 11, 11, 11, 1, 1 $ | $1058$ | $11$ | $( 2, 5,17,19, 4,13, 3, 9,10,14, 7)( 6,21,12,22,16,15,11,18,23,20, 8) (25,30,37,33,32,26,36,27,42,40,28)(29,31,43,46,41,34,38,39,45,35,44)$ |
| $ 22, 22, 1, 1 $ | $1058$ | $22$ | $( 2,20,17, 6, 4,12, 3,16,10,11, 7,23, 5, 8,19,21,13,22, 9,15,14,18) (25,41,37,38,32,45,36,44,42,31,28,46,30,34,33,39,26,35,27,29,40,43)$ |
| $ 11, 11, 11, 11, 1, 1 $ | $1058$ | $11$ | $( 2,17, 4, 3,10, 7, 5,19,13, 9,14)( 6,12,16,11,23, 8,21,22,15,18,20) (25,37,32,36,42,28,30,33,26,27,40)(29,43,41,38,45,44,31,46,34,39,35)$ |
| $ 22, 22, 1, 1 $ | $1058$ | $22$ | $( 2, 8, 4,22,10,18, 5, 6,13,16,14,23,17,21, 3,15, 7,20,19,12, 9,11) (25,34,32,35,42,43,30,38,26,44,40,46,37,39,36,29,28,41,33,45,27,31)$ |
| $ 11, 11, 11, 11, 1, 1 $ | $1058$ | $11$ | $( 2, 4,10, 5,13,14,17, 3, 7,19, 9)( 6,16,23,21,15,20,12,11, 8,22,18) (25,32,42,30,26,40,37,36,28,33,27)(29,41,45,31,34,35,43,38,44,46,39)$ |
| $ 22, 22, 1, 1 $ | $1058$ | $22$ | $( 2,21,10,20,13,11,17,22, 7, 6, 9,23, 4,15, 5,12,14, 8, 3,18,19,16) (25,39,42,41,26,31,37,35,28,38,27,46,32,29,30,45,40,34,36,43,33,44)$ |
| $ 11, 11, 11, 11, 1, 1 $ | $1058$ | $11$ | $( 2,10,13,17, 7, 9, 4, 5,14, 3,19)( 6,23,15,12, 8,18,16,21,20,11,22) (25,42,26,37,28,27,32,30,40,36,33)(29,45,34,43,44,39,41,31,35,38,46)$ |
| $ 22, 22, 1, 1 $ | $1058$ | $22$ | $( 2,15,13, 8, 7,16, 4,20,14,22,19,23,10,12,17,18, 9,21, 5,11, 3, 6) (25,29,26,34,28,44,32,41,40,35,33,46,42,45,37,43,27,39,30,31,36,38)$ |
| $ 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2 $ | $5819$ | $4$ | $( 1,45,15,26)( 2,42,14,29)( 3,39,13,32)( 4,36,12,35)( 5,33,11,38)( 6,30,10,41) ( 7,27, 9,44)( 8,24)(16,46,23,25)(17,43,22,28)(18,40,21,31)(19,37,20,34)$ |
| $ 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2 $ | $5819$ | $4$ | $( 1,26)( 2,29,23,46)( 3,32,22,43)( 4,35,21,40)( 5,38,20,37)( 6,41,19,34) ( 7,44,18,31)( 8,24,17,28)( 9,27,16,25)(10,30,15,45)(11,33,14,42)(12,36,13,39)$ |
magma: ConjugacyClasses(G);
Group invariants
| Order: | $23276=2^{2} \cdot 11 \cdot 23^{2}$ | 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: | 23276.b | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);