Show commands:
Magma
magma: G := TransitiveGroup(46, 27);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
| Transitive number $t$: | $27$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
| Group: | $C_2\times M_{23}$ | ||
| Parity: | $-1$ | magma: IsEven(G);
| |
| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
|
| $\card{\Aut(F/K)}$: | $2$ | magma: Order(Centralizer(SymmetricGroup(n), G));
| |
| Generators: | (1,34,26)(2,33,25)(3,15,11,24,7,36)(4,16,12,23,8,35)(5,27,14)(6,28,13)(9,44,42,20,39,37)(10,43,41,19,40,38)(17,31)(18,32)(21,45)(22,46), (1,12,46,13,17,2,11,45,14,18)(3,8,5,10,29,4,7,6,9,30)(15,19,44,21,27,16,20,43,22,28)(23,42,32,36,25,24,41,31,35,26)(33,34)(37,38)(39,40) | magma: Generators(G);
|
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $10200960$: $M_{23}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 23: $M_{23}$
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 $ | $443520$ | $46$ | $( 1,12,14,19,29, 8,39,43,37,23,22,18,34,41,27, 6, 3,32,46,25,15,35, 9, 2,11, 13,20,30, 7,40,44,38,24,21,17,33,42,28, 5, 4,31,45,26,16,36,10)$ | |
| $ 23, 23 $ | $443520$ | $23$ | $( 1,11,14,20,29, 7,39,44,37,24,22,17,34,42,27, 5, 3,31,46,26,15,36, 9) ( 2,12,13,19,30, 8,40,43,38,23,21,18,33,41,28, 6, 4,32,45,25,16,35,10)$ | |
| $ 23, 23 $ | $443520$ | $23$ | $( 1, 9,36,15,26,46,31, 3, 5,27,42,34,17,22,24,37,44,39, 7,29,20,14,11) ( 2,10,35,16,25,45,32, 4, 6,28,41,33,18,21,23,38,43,40, 8,30,19,13,12)$ | |
| $ 46 $ | $443520$ | $46$ | $( 1,10,36,16,26,45,31, 4, 5,28,42,33,17,21,24,38,44,40, 7,30,20,13,11, 2, 9, 35,15,25,46,32, 3, 6,27,41,34,18,22,23,37,43,39, 8,29,19,14,12)$ | |
| $ 10, 10, 10, 10, 2, 2, 2 $ | $680064$ | $10$ | $( 1,25,14,43,36, 2,26,13,44,35)( 3,30, 9,45,24, 4,29,10,46,23)( 5,41,34,32,20, 6,42,33,31,19)( 7,21,37,16,17, 8,22,38,15,18)(11,12)(27,28)(39,40)$ | |
| $ 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1 $ | $680064$ | $5$ | $( 1,26,14,44,36)( 2,25,13,43,35)( 3,29, 9,46,24)( 4,30,10,45,23) ( 5,42,34,31,20)( 6,41,33,32,19)( 7,22,37,15,17)( 8,21,38,16,18)$ | |
| $ 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2 $ | $56672$ | $6$ | $( 1, 6,17, 2, 5,18)( 3, 4)( 7,25,42, 8,26,41)( 9,10)(11,40,27,12,39,28) (13,34,21,14,33,22)(15,35,20,16,36,19)(23,24)(29,30)(31,38,44,32,37,43)(45,46)$ | |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $56672$ | $3$ | $( 1, 5,17)( 2, 6,18)( 7,26,42)( 8,25,41)(11,39,27)(12,40,28)(13,33,21) (14,34,22)(15,36,20)(16,35,19)(31,37,44)(32,38,43)$ | |
| $ 30, 10, 6 $ | $680064$ | $30$ | $( 1,16,31,13, 7, 6,36,38,34,25,17,19,44,21,42, 2,15,32,14, 8, 5,35,37,33,26, 18,20,43,22,41)( 3,23,46,10,29, 4,24,45, 9,30)(11,28,39,12,27,40)$ | |
| $ 15, 15, 5, 5, 3, 3 $ | $680064$ | $15$ | $( 1,15,31,14, 7, 5,36,37,34,26,17,20,44,22,42)( 2,16,32,13, 8, 6,35,38,33,25, 18,19,43,21,41)( 3,24,46, 9,29)( 4,23,45,10,30)(11,27,39)(12,28,40)$ | |
| $ 15, 15, 5, 5, 3, 3 $ | $680064$ | $15$ | $( 1,20,37,14,42,17,36,31,22,26, 5,15,44,34, 7)( 2,19,38,13,41,18,35,32,21,25, 6,16,43,33, 8)( 3,24,46, 9,29)( 4,23,45,10,30)(11,39,27)(12,40,28)$ | |
| $ 30, 10, 6 $ | $680064$ | $30$ | $( 1,19,37,13,42,18,36,32,22,25, 5,16,44,33, 7, 2,20,38,14,41,17,35,31,21,26, 6,15,43,34, 8)( 3,23,46,10,29, 4,24,45, 9,30)(11,40,27,12,39,28)$ | |
| $ 22, 22, 2 $ | $927360$ | $22$ | $( 1,21,20,35,26,38,24,13,27,18, 3, 2,22,19,36,25,37,23,14,28,17, 4) ( 5,16,29, 8,39,45,31,43,34,12,42, 6,15,30, 7,40,46,32,44,33,11,41)( 9,10)$ | |
| $ 11, 11, 11, 11, 1, 1 $ | $927360$ | $11$ | $( 1,22,20,36,26,37,24,14,27,17, 3)( 2,21,19,35,25,38,23,13,28,18, 4) ( 5,15,29, 7,39,46,31,44,34,11,42)( 6,16,30, 8,40,45,32,43,33,12,41)$ | |
| $ 22, 22, 2 $ | $927360$ | $22$ | $( 1, 4,17,28,14,23,37,25,36,19,22, 2, 3,18,27,13,24,38,26,35,20,21) ( 5,41,11,33,44,32,46,40, 7,30,15, 6,42,12,34,43,31,45,39, 8,29,16)( 9,10)$ | |
| $ 11, 11, 11, 11, 1, 1 $ | $927360$ | $11$ | $( 1, 3,17,27,14,24,37,26,36,20,22)( 2, 4,18,28,13,23,38,25,35,19,21) ( 5,42,11,34,44,31,46,39, 7,29,15)( 6,41,12,33,43,32,45,40, 8,30,16)$ | |
| $ 2, 2, 2, 2, 2, 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 $ | $3795$ | $2$ | $( 3,27)( 4,28)( 7,26)( 8,25)(11,17)(12,18)(15,42)(16,41)(19,23)(20,24)(21,43) (22,44)(29,36)(30,35)(33,45)(34,46)$ | |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ | $3795$ | $2$ | $( 1, 2)( 3,28)( 4,27)( 5, 6)( 7,25)( 8,26)( 9,10)(11,18)(12,17)(13,14)(15,41) (16,42)(19,24)(20,23)(21,44)(22,43)(29,35)(30,36)(31,32)(33,46)(34,45)(37,38) (39,40)$ | |
| $ 6, 6, 6, 6, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1 $ | $850080$ | $6$ | $( 1,31, 9)( 2,32,10)( 3,20, 7,27,24,26)( 4,19, 8,28,23,25)(11,17)(12,18) (13,40,38)(14,39,37)(15,29,46,42,36,34)(16,30,45,41,35,33)(21,43)(22,44)$ | |
| $ 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2 $ | $850080$ | $6$ | $( 1,32, 9, 2,31,10)( 3,19, 7,28,24,25)( 4,20, 8,27,23,26)( 5, 6)(11,18)(12,17) (13,39,38,14,40,37)(15,30,46,41,36,33)(16,29,45,42,35,34)(21,44)(22,43)$ | |
| $ 7, 7, 7, 7, 7, 7, 1, 1, 1, 1 $ | $728640$ | $7$ | $( 1, 9, 5,31,14,37,39)( 2,10, 6,32,13,38,40)( 3,20,17,15, 7,22,34) ( 4,19,18,16, 8,21,33)(11,42,26,44,46,27,24)(12,41,25,43,45,28,23)$ | |
| $ 14, 14, 14, 2, 2 $ | $728640$ | $14$ | $( 1,10, 5,32,14,38,39, 2, 9, 6,31,13,37,40)( 3,19,17,16, 7,21,34, 4,20,18,15, 8,22,33)(11,41,26,43,46,28,24,12,42,25,44,45,27,23)(29,30)(35,36)$ | |
| $ 14, 14, 14, 2, 2 $ | $728640$ | $14$ | $( 1,40,37,13,31, 6, 9, 2,39,38,14,32, 5,10)( 3,33,22, 8,15,18,20, 4,34,21, 7, 16,17,19)(11,23,27,45,44,25,42,12,24,28,46,43,26,41)(29,30)(35,36)$ | |
| $ 7, 7, 7, 7, 7, 7, 1, 1, 1, 1 $ | $728640$ | $7$ | $( 1,39,37,14,31, 5, 9)( 2,40,38,13,32, 6,10)( 3,34,22, 7,15,17,20) ( 4,33,21, 8,16,18,19)(11,24,27,46,44,26,42)(12,23,28,45,43,25,41)$ | |
| $ 14, 14, 14, 2, 2 $ | $728640$ | $14$ | $( 1,13, 9,38, 5,40,31, 2,14,10,37, 6,39,32)( 3,25,20,43,17,45,15,28, 7,23,22, 12,34,41)( 4,26,19,44,18,46,16,27, 8,24,21,11,33,42)(29,35)(30,36)$ | |
| $ 14, 14, 7, 7, 2, 2 $ | $728640$ | $14$ | $( 1,14, 9,37, 5,39,31)( 2,13,10,38, 6,40,32)( 3,26,20,44,17,46,15,27, 7,24,22, 11,34,42)( 4,25,19,43,18,45,16,28, 8,23,21,12,33,41)(29,36)(30,35)$ | |
| $ 14, 14, 7, 7, 2, 2 $ | $728640$ | $14$ | $( 1,37,31, 9,39,14, 5)( 2,38,32,10,40,13, 6)( 3,44,15,24,34,26,17,27,22,42,20, 46, 7,11)( 4,43,16,23,33,25,18,28,21,41,19,45, 8,12)(29,36)(30,35)$ | |
| $ 14, 14, 14, 2, 2 $ | $728640$ | $14$ | $( 1,38,31,10,39,13, 5, 2,37,32, 9,40,14, 6)( 3,43,15,23,34,25,17,28,22,41,20, 45, 7,12)( 4,44,16,24,33,26,18,27,21,42,19,46, 8,11)(29,35)(30,36)$ | |
| $ 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2 $ | $318780$ | $4$ | $( 1,40, 9,19)( 2,39,10,20)( 3,33,42, 8)( 4,34,41, 7)( 5,21,46,32)( 6,22,45,31) (11,12)(13,17)(14,18)(15,25,36,38)(16,26,35,37)(23,24)(27,28)(29,43)(30,44)$ | |
| $ 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ | $318780$ | $4$ | $( 1,39, 9,20)( 2,40,10,19)( 3,34,42, 7)( 4,33,41, 8)( 5,22,46,31)( 6,21,45,32) (13,18)(14,17)(15,26,36,37)(16,25,35,38)(29,44)(30,43)$ | |
| $ 8, 8, 8, 8, 4, 4, 2, 2, 1, 1 $ | $1275120$ | $8$ | $( 1,42,39, 7, 9, 3,20,34)( 2,41,40, 8,10, 4,19,33)( 5,37,22,15,46,26,31,36) ( 6,38,21,16,45,25,32,35)(11,24)(12,23)(13,30,18,43)(14,29,17,44)$ | |
| $ 8, 8, 8, 8, 4, 4, 2, 2, 2 $ | $1275120$ | $8$ | $( 1,41,39, 8, 9, 4,20,33)( 2,42,40, 7,10, 3,19,34)( 5,38,22,16,46,25,31,35) ( 6,37,21,15,45,26,32,36)(11,23)(12,24)(13,29,18,44)(14,30,17,43)(27,28)$ |
magma: ConjugacyClasses(G);
Group invariants
| Order: | $20401920=2^{8} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 23$ | magma: Order(G);
| |
| Cyclic: | no | magma: IsCyclic(G);
| |
| Abelian: | no | magma: IsAbelian(G);
| |
| Solvable: | no | magma: IsSolvable(G);
| |
| Nilpotency class: | not nilpotent | ||
| Label: | 20401920.a | magma: IdentifyGroup(G);
| |
| Character table: | 34 x 34 character table |
magma: CharacterTable(G);