Properties

Label 44T14
Order \(220\)
n \(44\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_2\times F_{11}$

Learn more about

Group action invariants

Degree $n$ :  $44$
Transitive number $t$ :  $14$
Group :  $C_2\times F_{11}$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,31)(2,32)(3,30)(4,29)(5,25)(6,26)(7,27)(8,28)(9,22)(10,21)(11,23)(12,24)(13,19)(14,20)(15,17)(16,18)(33,44)(34,43)(35,41)(36,42)(37,40)(38,39), (1,2)(3,4)(5,13,38,21,17,6,14,37,22,18)(7,15,40,24,19,8,16,39,23,20)(9,26,29,41,33,10,25,30,42,34)(11,28,31,44,35,12,27,32,43,36)
$|\Aut(F/K)|$:  $4$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
5:  $C_5$
10:  $C_{10}$ x 3
20:  20T3
110:  $F_{11}$

Resolvents shown for degrees $\leq 29$

Subfields

Degree 2: $C_2$ x 3

Degree 4: $C_2^2$

Degree 11: $F_{11}$

Degree 22: 22T4, 22T6 x 2

Low degree siblings

22T6 x 2

Siblings are shown with degree $\leq 29$

Data on whether or not a number field with this Galois group has arithmetically equivalent fields has not been computed.

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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1$ $1$ $()$
$ 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1 $ $11$ $5$ $( 5,14,38,22,17)( 6,13,37,21,18)( 7,16,40,23,19)( 8,15,39,24,20) ( 9,25,29,42,33)(10,26,30,41,34)(11,27,31,43,35)(12,28,32,44,36)$
$ 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1 $ $11$ $5$ $( 5,17,22,38,14)( 6,18,21,37,13)( 7,19,23,40,16)( 8,20,24,39,15) ( 9,33,42,29,25)(10,34,41,30,26)(11,35,43,31,27)(12,36,44,32,28)$
$ 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1 $ $11$ $5$ $( 5,22,14,17,38)( 6,21,13,18,37)( 7,23,16,19,40)( 8,24,15,20,39) ( 9,42,25,33,29)(10,41,26,34,30)(11,43,27,35,31)(12,44,28,36,32)$
$ 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1 $ $11$ $5$ $( 5,38,17,14,22)( 6,37,18,13,21)( 7,40,19,16,23)( 8,39,20,15,24) ( 9,29,33,25,42)(10,30,34,26,41)(11,31,35,27,43)(12,32,36,28,44)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $1$ $2$ $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22) (23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)$
$ 10, 10, 10, 10, 2, 2 $ $11$ $10$ $( 1, 2)( 3, 4)( 5,13,38,21,17, 6,14,37,22,18)( 7,15,40,24,19, 8,16,39,23,20) ( 9,26,29,41,33,10,25,30,42,34)(11,28,31,44,35,12,27,32,43,36)$
$ 10, 10, 10, 10, 2, 2 $ $11$ $10$ $( 1, 2)( 3, 4)( 5,18,22,37,14, 6,17,21,38,13)( 7,20,23,39,16, 8,19,24,40,15) ( 9,34,42,30,25,10,33,41,29,26)(11,36,43,32,27,12,35,44,31,28)$
$ 10, 10, 10, 10, 2, 2 $ $11$ $10$ $( 1, 2)( 3, 4)( 5,21,14,18,38, 6,22,13,17,37)( 7,24,16,20,40, 8,23,15,19,39) ( 9,41,25,34,29,10,42,26,33,30)(11,44,27,36,31,12,43,28,35,32)$
$ 10, 10, 10, 10, 2, 2 $ $11$ $10$ $( 1, 2)( 3, 4)( 5,37,17,13,22, 6,38,18,14,21)( 7,39,19,15,23, 8,40,20,16,24) ( 9,30,33,26,42,10,29,34,25,41)(11,32,35,28,43,12,31,36,27,44)$
$ 10, 10, 10, 10, 2, 2 $ $11$ $10$ $( 1, 3)( 2, 4)( 5, 9,17,33,22,42,38,29,14,25)( 6,10,18,34,21,41,37,30,13,26) ( 7,11,19,35,23,43,40,31,16,27)( 8,12,20,36,24,44,39,32,15,28)$
$ 10, 10, 10, 10, 2, 2 $ $11$ $10$ $( 1, 3)( 2, 4)( 5,25,14,29,38,42,22,33,17, 9)( 6,26,13,30,37,41,21,34,18,10) ( 7,27,16,31,40,43,23,35,19,11)( 8,28,15,32,39,44,24,36,20,12)$
$ 10, 10, 10, 10, 2, 2 $ $11$ $10$ $( 1, 3)( 2, 4)( 5,29,22, 9,14,42,17,25,38,33)( 6,30,21,10,13,41,18,26,37,34) ( 7,31,23,11,16,43,19,27,40,35)( 8,32,24,12,15,44,20,28,39,36)$
$ 10, 10, 10, 10, 2, 2 $ $11$ $10$ $( 1, 3)( 2, 4)( 5,33,38,25,17,42,14, 9,22,29)( 6,34,37,26,18,41,13,10,21,30) ( 7,35,40,27,19,43,16,11,23,31)( 8,36,39,28,20,44,15,12,24,32)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $11$ $2$ $( 1, 3)( 2, 4)( 5,42)( 6,41)( 7,43)( 8,44)( 9,38)(10,37)(11,40)(12,39)(13,34) (14,33)(15,36)(16,35)(17,29)(18,30)(19,31)(20,32)(21,26)(22,25)(23,27)(24,28)$
$ 10, 10, 10, 10, 2, 2 $ $11$ $10$ $( 1, 4)( 2, 3)( 5,10,17,34,22,41,38,30,14,26)( 6, 9,18,33,21,42,37,29,13,25) ( 7,12,19,36,23,44,40,32,16,28)( 8,11,20,35,24,43,39,31,15,27)$
$ 10, 10, 10, 10, 2, 2 $ $11$ $10$ $( 1, 4)( 2, 3)( 5,26,14,30,38,41,22,34,17,10)( 6,25,13,29,37,42,21,33,18, 9) ( 7,28,16,32,40,44,23,36,19,12)( 8,27,15,31,39,43,24,35,20,11)$
$ 10, 10, 10, 10, 2, 2 $ $11$ $10$ $( 1, 4)( 2, 3)( 5,30,22,10,14,41,17,26,38,34)( 6,29,21, 9,13,42,18,25,37,33) ( 7,32,23,12,16,44,19,28,40,36)( 8,31,24,11,15,43,20,27,39,35)$
$ 10, 10, 10, 10, 2, 2 $ $11$ $10$ $( 1, 4)( 2, 3)( 5,34,38,26,17,41,14,10,22,30)( 6,33,37,25,18,42,13, 9,21,29) ( 7,36,40,28,19,44,16,12,23,32)( 8,35,39,27,20,43,15,11,24,31)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $11$ $2$ $( 1, 4)( 2, 3)( 5,41)( 6,42)( 7,44)( 8,43)( 9,37)(10,38)(11,39)(12,40)(13,33) (14,34)(15,35)(16,36)(17,30)(18,29)(19,32)(20,31)(21,25)(22,26)(23,28)(24,27)$
$ 11, 11, 11, 11 $ $10$ $11$ $( 1, 7,10,16,19,23,26,30,34,40,41)( 2, 8, 9,15,20,24,25,29,33,39,42) ( 3, 6,11,13,18,21,27,31,35,37,43)( 4, 5,12,14,17,22,28,32,36,38,44)$
$ 22, 22 $ $10$ $22$ $( 1, 8,10,15,19,24,26,29,34,39,41, 2, 7, 9,16,20,23,25,30,33,40,42) ( 3, 5,11,14,18,22,27,32,35,38,43, 4, 6,12,13,17,21,28,31,36,37,44)$

Group invariants

Order:  $220=2^{2} \cdot 5 \cdot 11$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [220, 7]
Character table: Data not available.