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Properties

Label 20T281
Order \(3840\)
n \(20\)
Cyclic No
Abelian No
Solvable No
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $20$
Transitive number $t$ :  $281$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,8,15,6,11,2,7,16,5,12)(3,18,14,9,19,4,17,13,10,20), (1,5,2,6)(3,14,8,15)(4,13,7,16)(9,12,20,18,10,11,19,17)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
120:  $S_5$
1920:  16T1329

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: None

Degree 5: None

Degree 10: $S_5$

Low degree siblings

12T257 x 2, 20T281, 20T291 x 2, 24T7238, 24T7255, 32T206828 x 4, 40T2727 x 2, 40T2744, 40T2745, 40T2755 x 2, 40T2837 x 2, 40T2844 x 2

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

Cycle TypeSizeOrderRepresentative
$ 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $15$ $2$ $(13,14)(15,16)(17,18)(19,20)$
$ 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $15$ $2$ $( 3, 4)( 7, 8)( 9,10)(13,14)(15,16)(19,20)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $1$ $2$ $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)$
$ 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $40$ $2$ $( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)$
$ 4, 4, 2, 2, 2, 2, 1, 1, 1, 1 $ $120$ $4$ $( 3, 4)( 7, 8)( 9,11,10,12)(13,15)(14,16)(17,19,18,20)$
$ 4, 4, 2, 2, 2, 2, 1, 1, 1, 1 $ $120$ $4$ $( 5, 6)( 7, 8)( 9,11)(10,12)(13,16,14,15)(17,20,18,19)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $40$ $2$ $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,12)(10,11)(13,15)(14,16)(17,19)(18,20)$
$ 4, 4, 2, 2, 2, 2, 2, 2 $ $60$ $4$ $( 1, 2)( 3,19, 4,20)( 5,15)( 6,16)( 7,12, 8,11)( 9,17)(10,18)(13,14)$
$ 4, 4, 4, 2, 2, 2, 1, 1 $ $240$ $4$ $( 1, 2)( 3,20)( 4,19)( 5,16, 6,15)( 7,12, 8,11)( 9,18,10,17)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $60$ $2$ $( 1, 2)( 3,19)( 4,20)( 5,15)( 6,16)( 7,12)( 8,11)( 9,18)(10,17)(13,14)$
$ 4, 4, 2, 2, 2, 2, 1, 1, 1, 1 $ $60$ $4$ $( 3,19, 4,20)( 5,15)( 6,16)( 7,11, 8,12)( 9,17)(10,18)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1 $ $60$ $2$ $( 3,19)( 4,20)( 5,15)( 6,16)( 7,11)( 8,12)( 9,18)(10,17)$
$ 6, 6, 6, 2 $ $320$ $6$ $( 1, 2)( 3,19, 9, 7,12,18)( 4,20,10, 8,11,17)( 5,15,14, 6,16,13)$
$ 6, 6, 3, 3, 1, 1 $ $320$ $6$ $( 3,20,10, 7,11,18)( 4,19, 9, 8,12,17)( 5,16,13)( 6,15,14)$
$ 3, 3, 3, 3, 3, 3, 1, 1 $ $320$ $3$ $( 3,11,10)( 4,12, 9)( 5,16,13)( 6,15,14)( 7,20,18)( 8,19,17)$
$ 6, 6, 6, 2 $ $320$ $6$ $( 1, 2)( 3,12, 9, 4,11,10)( 5,15,14, 6,16,13)( 7,19,18, 8,20,17)$
$ 10, 10 $ $384$ $10$ $( 1, 8,15, 5,11, 2, 7,16, 6,12)( 3,17,14, 9,20, 4,18,13,10,19)$
$ 5, 5, 5, 5 $ $384$ $5$ $( 1, 8,16, 6,12)( 2, 7,15, 5,11)( 3,18,14, 9,19)( 4,17,13,10,20)$
$ 4, 4, 4, 4, 2, 2 $ $240$ $4$ $( 1, 8,15,10)( 2, 7,16, 9)( 3,17)( 4,18)( 5,11,20,13)( 6,12,19,14)$
$ 8, 4, 4, 4 $ $240$ $8$ $( 1, 8,16, 9, 2, 7,15,10)( 3,18, 4,17)( 5,11,19,13)( 6,12,20,14)$
$ 4, 4, 4, 4, 2, 2 $ $240$ $4$ $( 1, 7,16,10)( 2, 8,15, 9)( 3,18)( 4,17)( 5,11,20,13)( 6,12,19,14)$
$ 8, 4, 4, 4 $ $240$ $8$ $( 1, 7,15, 9, 2, 8,16,10)( 3,17, 4,18)( 5,11,19,13)( 6,12,20,14)$

Group invariants

Order:  $3840=2^{8} \cdot 3 \cdot 5$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.