Group action invariants
| Degree $n$ : | $23$ | |
| Transitive number $t$ : | $5$ | |
| Group : | $M_{23}$ | |
| Parity: | $1$ | |
| Primitive: | Yes | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,7,12,16,19,21,6)(2,8,13,17,20,5,11)(3,9,14,18,4,10,15), (2,14,18,20,8)(3,7,12,13,19)(4,21,17,15,10)(5,11,16,6,9), (3,19)(4,14)(5,20)(6,10)(8,15)(11,18)(17,21)(22,23), (1,22)(2,10)(3,14)(4,17)(8,15)(9,11)(13,20)(19,21) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
NoneResolvents 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 $ | $1$ | $1$ | $()$ |
| $ 7, 7, 7, 1, 1 $ | $728640$ | $7$ | $( 1,18,15,13,12,14, 9)( 2,16, 3,10, 8,17, 5)( 4, 6,23,21,11, 7,22)$ |
| $ 7, 7, 7, 1, 1 $ | $728640$ | $7$ | $( 1, 9,14,12,13,15,18)( 2, 5,17, 8,10, 3,16)( 4,22, 7,11,21,23, 6)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1 $ | $3795$ | $2$ | $( 1,10)( 2,12)( 3, 9)( 5,13)( 8,18)(14,16)(15,17)(19,20)$ |
| $ 14, 7, 2 $ | $728640$ | $14$ | $( 1,16,13, 8, 9, 2,15,10,14, 5,18, 3,12,17)( 4, 7,21, 6,22,11,23)(19,20)$ |
| $ 14, 7, 2 $ | $728640$ | $14$ | $( 1, 8,15, 5,12,16, 9,10,18,17,13, 2,14, 3)( 4, 6,23,21,11, 7,22)(19,20)$ |
| $ 23 $ | $443520$ | $23$ | $( 1,20,11,12, 3, 6,22,13, 4,18,19, 7, 5,14, 8,21,10,16,17,23, 9, 2,15)$ |
| $ 23 $ | $443520$ | $23$ | $( 1,15, 2, 9,23,17,16,10,21, 8,14, 5, 7,19,18, 4,13,22, 6, 3,12,11,20)$ |
| $ 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1 $ | $56672$ | $3$ | $( 1,10,11)( 2,13,22)( 3, 7,18)( 4,16, 5)( 6,19,21)( 8,15,23)$ |
| $ 6, 6, 3, 3, 2, 2, 1 $ | $850080$ | $6$ | $( 1, 7,10,18,11, 3)( 2,23,13, 8,22,15)( 4, 5,16)( 6,21,19)( 9,12)(14,20)$ |
| $ 5, 5, 5, 5, 1, 1, 1 $ | $680064$ | $5$ | $( 1,15, 4, 6, 3)( 2,12,10, 8,11)( 5,21, 7,16,14)( 9,23,17,18,20)$ |
| $ 15, 5, 3 $ | $680064$ | $15$ | $( 1, 5,12,15,21,10, 4, 7, 8, 6,16,11, 3,14, 2)( 9,17,20,23,18)(13,19,22)$ |
| $ 15, 5, 3 $ | $680064$ | $15$ | $( 1,11, 7,15, 2,16, 4,12,14, 6,10, 5, 3, 8,21)( 9,17,20,23,18)(13,22,19)$ |
| $ 11, 11, 1 $ | $927360$ | $11$ | $( 1,19,12,22, 5, 9, 2,18, 7, 3, 6)( 4,14, 8,15,13,20,16,10,23,21,11)$ |
| $ 11, 11, 1 $ | $927360$ | $11$ | $( 1, 6, 3, 7,18, 2, 9, 5,22,12,19)( 4,11,21,23,10,16,20,13,15, 8,14)$ |
| $ 4, 4, 4, 4, 2, 2, 1, 1, 1 $ | $318780$ | $4$ | $( 1,13,14,18)( 2,21)( 3,19, 6,16)( 4, 7, 8,23)( 5,17,22,11)( 9,12)$ |
| $ 8, 8, 4, 2, 1 $ | $1275120$ | $8$ | $( 1, 6,13,16,14, 3,18,19)( 2,12,21, 9)( 4,22, 7,11, 8, 5,23,17)(15,20)$ |
Group invariants
| Order: | $10200960=2^{7} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 23$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |