Properties

Label 22T40
Order \(871200\)
n \(22\)
Cyclic No
Abelian No
Solvable No
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $22$
Transitive number $t$ :  $40$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (2,4,9,6,3)(5,11,8,7,10)(12,13,20)(14,17,18,22,21,19)(15,16), (1,13,3,12,6,18,9,17,7,21,8,14,10,15,4,20,5,19,11,22,2,16)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: None

Low degree siblings

22T40, 24T21362

Siblings are shown with degree $\leq 47$

A number field with this Galois group has exactly one arithmetically equivalent field.

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 $ $1$ $1$ $()$
$ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $3025$ $2$ $( 3, 4)( 5, 7)( 6, 9)( 8,11)(12,18)(13,15)(17,20)(19,21)$
$ 3, 3, 3, 3, 3, 3, 1, 1, 1, 1 $ $12100$ $3$ $( 3, 5, 8)( 4,11, 7)( 6, 9,10)(12,18,14)(13,20,21)(15,19,17)$
$ 5, 5, 5, 5, 1, 1 $ $17424$ $5$ $( 2, 3, 6, 9, 4)( 5,10, 7, 8,11)(12,18,15,22,13)(14,17,21,19,20)$
$ 5, 5, 5, 5, 1, 1 $ $17424$ $5$ $( 2, 3,10, 9, 7)( 4, 5,11, 8, 6)(12,15,20,19,21)(13,14,18,17,22)$
$ 6, 6, 3, 3, 2, 2 $ $12100$ $6$ $( 1, 2)( 3, 4, 8, 7, 5,11)( 6, 9,10)(12,18,14)(13,15,21,17,20,19)(16,22)$
$ 11, 11 $ $3600$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,17,21,18,14,19,16,22,13,15,20)$
$ 11, 11 $ $3600$ $11$ $( 1, 2, 3, 6,10, 7, 5, 9,11, 8, 4)(12,14,17,20,18,19,21,15,16,22,13)$
$ 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $110$ $2$ $(12,18)(13,15)(17,20)(19,21)$
$ 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $220$ $3$ $(12,18,14)(13,20,21)(15,19,17)$
$ 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $264$ $5$ $(12,18,15,22,13)(14,17,21,19,20)$
$ 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $264$ $5$ $(12,15,20,19,21)(13,14,18,17,22)$
$ 6, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $220$ $6$ $(12,18,14)(13,15,21,17,20,19)(16,22)$
$ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $120$ $11$ $(12,17,21,18,14,19,16,22,13,15,20)$
$ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $120$ $11$ $(12,14,17,20,18,19,21,15,16,22,13)$
$ 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1 $ $12100$ $6$ $( 3, 4)( 5, 7)( 6, 9)( 8,11)(12,18,14)(13,20,21)(15,19,17)$
$ 5, 5, 2, 2, 2, 2, 1, 1, 1, 1 $ $14520$ $10$ $( 3, 4)( 5, 7)( 6, 9)( 8,11)(12,18,15,22,13)(14,17,21,19,20)$
$ 5, 5, 2, 2, 2, 2, 1, 1, 1, 1 $ $14520$ $10$ $( 3, 4)( 5, 7)( 6, 9)( 8,11)(12,15,20,19,21)(13,14,18,17,22)$
$ 6, 3, 2, 2, 2, 2, 2, 1, 1, 1 $ $12100$ $6$ $( 3, 4)( 5, 7)( 6, 9)( 8,11)(12,18,14)(13,15,21,17,20,19)(16,22)$
$ 11, 2, 2, 2, 2, 1, 1, 1 $ $6600$ $22$ $( 3, 4)( 5, 7)( 6, 9)( 8,11)(12,17,21,18,14,19,16,22,13,15,20)$
$ 11, 2, 2, 2, 2, 1, 1, 1 $ $6600$ $22$ $( 3, 4)( 5, 7)( 6, 9)( 8,11)(12,14,17,20,18,19,21,15,16,22,13)$
$ 5, 5, 3, 3, 3, 1, 1, 1 $ $29040$ $15$ $( 3, 5, 8)( 4,11, 7)( 6, 9,10)(12,18,15,22,13)(14,17,21,19,20)$
$ 5, 5, 3, 3, 3, 1, 1, 1 $ $29040$ $15$ $( 3, 5, 8)( 4,11, 7)( 6, 9,10)(12,15,20,19,21)(13,14,18,17,22)$
$ 6, 3, 3, 3, 3, 2, 1, 1 $ $24200$ $6$ $( 3, 5, 8)( 4,11, 7)( 6, 9,10)(12,18,14)(13,15,21,17,20,19)(16,22)$
$ 11, 3, 3, 3, 1, 1 $ $13200$ $33$ $( 3, 5, 8)( 4,11, 7)( 6, 9,10)(12,17,21,18,14,19,16,22,13,15,20)$
$ 11, 3, 3, 3, 1, 1 $ $13200$ $33$ $( 3, 5, 8)( 4,11, 7)( 6, 9,10)(12,14,17,20,18,19,21,15,16,22,13)$
$ 5, 5, 5, 5, 1, 1 $ $34848$ $5$ $( 2, 3, 6, 9, 4)( 5,10, 7, 8,11)(12,15,20,19,21)(13,14,18,17,22)$
$ 6, 5, 5, 3, 2, 1 $ $29040$ $30$ $( 2, 3, 6, 9, 4)( 5,10, 7, 8,11)(12,18,14)(13,15,21,17,20,19)(16,22)$
$ 11, 5, 5, 1 $ $15840$ $55$ $( 2, 3, 6, 9, 4)( 5,10, 7, 8,11)(12,17,21,18,14,19,16,22,13,15,20)$
$ 11, 5, 5, 1 $ $15840$ $55$ $( 2, 3, 6, 9, 4)( 5,10, 7, 8,11)(12,14,17,20,18,19,21,15,16,22,13)$
$ 6, 5, 5, 3, 2, 1 $ $29040$ $30$ $( 2, 3,10, 9, 7)( 4, 5,11, 8, 6)(12,18,14)(13,15,21,17,20,19)(16,22)$
$ 11, 5, 5, 1 $ $15840$ $55$ $( 2, 3,10, 9, 7)( 4, 5,11, 8, 6)(12,17,21,18,14,19,16,22,13,15,20)$
$ 11, 5, 5, 1 $ $15840$ $55$ $( 2, 3,10, 9, 7)( 4, 5,11, 8, 6)(12,14,17,20,18,19,21,15,16,22,13)$
$ 11, 6, 3, 2 $ $13200$ $66$ $( 1, 2)( 3, 4, 8, 7, 5,11)( 6, 9,10)(12,17,21,18,14,19,16,22,13,15,20)$
$ 11, 6, 3, 2 $ $13200$ $66$ $( 1, 2)( 3, 4, 8, 7, 5,11)( 6, 9,10)(12,14,17,20,18,19,21,15,16,22,13)$
$ 11, 11 $ $7200$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,14,17,20,18,19,21,15,16,22,13)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $660$ $2$ $( 1,16)( 2,22)( 3,13)( 4,15)( 5,20)( 6,12)( 7,17)( 8,21)( 9,18)(10,14)(11,19)$
$ 4, 4, 4, 4, 2, 2, 2 $ $36300$ $4$ $( 1,16)( 2,22)( 3,15, 4,13)( 5,17, 7,20)( 6,18, 9,12)( 8,19,11,21)(10,14)$
$ 22 $ $39600$ $22$ $( 1,22, 2,13, 3,15, 4,20, 5,12, 6,17, 7,21, 8,18, 9,14,10,19,11,16)$
$ 22 $ $39600$ $22$ $( 1,22, 2,13, 3,12, 6,14,10,17, 7,20, 5,18, 9,19,11,21, 8,15, 4,16)$
$ 6, 6, 6, 2, 2 $ $72600$ $6$ $( 1,16)( 2,22)( 3,20, 5,21, 8,13)( 4,19,11,17, 7,15)( 6,18, 9,14,10,12)$
$ 12, 6, 4 $ $72600$ $12$ $( 1,22, 2,16)( 3,15, 4,21, 8,17, 7,20, 5,19,11,13)( 6,18, 9,14,10,12)$
$ 10, 10, 2 $ $87120$ $10$ $( 1,16)( 2,13, 3,12, 6,18, 9,15, 4,22)( 5,14,10,17, 7,21, 8,19,11,20)$
$ 10, 10, 2 $ $87120$ $10$ $( 1,16)( 2,13, 3,14,10,18, 9,17, 7,22)( 4,20, 5,19,11,21, 8,12, 6,15)$

Group invariants

Order:  $871200=2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2}$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.