Properties

Label 44T28
Order \(484\)
n \(44\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_{11}:D_{11}.C_2$

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
4:  $C_4$

Resolvents shown for degrees $\leq 29$

Subfields

Degree 2: $C_2$

Degree 4: $C_4$

Degree 11: None

Degree 22: 22T8

Low degree siblings

22T8 x 6

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 $ $1$ $1$ $()$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $4$ $11$ $(23,26,27,29,31,34,36,37,39,42,43)(24,25,28,30,32,33,35,38,40,41,44)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $4$ $11$ $(23,27,31,36,39,43,26,29,34,37,42)(24,28,32,35,40,44,25,30,33,38,41)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $4$ $11$ $(23,29,36,42,26,31,37,43,27,34,39)(24,30,35,41,25,32,38,44,28,33,40)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $4$ $11$ $(23,31,39,26,34,42,27,36,43,29,37)(24,32,40,25,33,41,28,35,44,30,38)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $4$ $11$ $(23,34,43,31,42,29,39,27,37,26,36)(24,33,44,32,41,30,40,28,38,25,35)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $121$ $2$ $( 1, 2)( 3,22)( 4,21)( 5,19)( 6,20)( 7,17)( 8,18)( 9,16)(10,15)(11,13)(12,14) (23,24)(25,43)(26,44)(27,41)(28,42)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 4, 6, 7, 9,12,13,15,18,19,22)( 2, 3, 5, 8,10,11,14,16,17,20,21) (23,26,27,29,31,34,36,37,39,42,43)(24,25,28,30,32,33,35,38,40,41,44)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 4, 6, 7, 9,12,13,15,18,19,22)( 2, 3, 5, 8,10,11,14,16,17,20,21) (23,27,31,36,39,43,26,29,34,37,42)(24,28,32,35,40,44,25,30,33,38,41)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 4, 6, 7, 9,12,13,15,18,19,22)( 2, 3, 5, 8,10,11,14,16,17,20,21) (23,29,36,42,26,31,37,43,27,34,39)(24,30,35,41,25,32,38,44,28,33,40)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 4, 6, 7, 9,12,13,15,18,19,22)( 2, 3, 5, 8,10,11,14,16,17,20,21) (23,31,39,26,34,42,27,36,43,29,37)(24,32,40,25,33,41,28,35,44,30,38)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 4, 6, 7, 9,12,13,15,18,19,22)( 2, 3, 5, 8,10,11,14,16,17,20,21) (23,34,43,31,42,29,39,27,37,26,36)(24,33,44,32,41,30,40,28,38,25,35)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 4, 6, 7, 9,12,13,15,18,19,22)( 2, 3, 5, 8,10,11,14,16,17,20,21) (23,37,29,43,36,27,42,34,26,39,31)(24,38,30,44,35,28,41,33,25,40,32)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 4, 6, 7, 9,12,13,15,18,19,22)( 2, 3, 5, 8,10,11,14,16,17,20,21) (23,39,34,27,43,37,31,26,42,36,29)(24,40,33,28,44,38,32,25,41,35,30)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 4, 6, 7, 9,12,13,15,18,19,22)( 2, 3, 5, 8,10,11,14,16,17,20,21) (23,42,37,34,29,26,43,39,36,31,27)(24,41,38,33,30,25,44,40,35,32,28)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 4, 6, 7, 9,12,13,15,18,19,22)( 2, 3, 5, 8,10,11,14,16,17,20,21) (23,43,42,39,37,36,34,31,29,27,26)(24,44,41,40,38,35,33,32,30,28,25)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 6, 9,13,18,22, 4, 7,12,15,19)( 2, 5,10,14,17,21, 3, 8,11,16,20) (23,26,27,29,31,34,36,37,39,42,43)(24,25,28,30,32,33,35,38,40,41,44)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 6, 9,13,18,22, 4, 7,12,15,19)( 2, 5,10,14,17,21, 3, 8,11,16,20) (23,27,31,36,39,43,26,29,34,37,42)(24,28,32,35,40,44,25,30,33,38,41)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 6, 9,13,18,22, 4, 7,12,15,19)( 2, 5,10,14,17,21, 3, 8,11,16,20) (23,29,36,42,26,31,37,43,27,34,39)(24,30,35,41,25,32,38,44,28,33,40)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 6, 9,13,18,22, 4, 7,12,15,19)( 2, 5,10,14,17,21, 3, 8,11,16,20) (23,31,39,26,34,42,27,36,43,29,37)(24,32,40,25,33,41,28,35,44,30,38)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 6, 9,13,18,22, 4, 7,12,15,19)( 2, 5,10,14,17,21, 3, 8,11,16,20) (23,37,29,43,36,27,42,34,26,39,31)(24,38,30,44,35,28,41,33,25,40,32)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 6, 9,13,18,22, 4, 7,12,15,19)( 2, 5,10,14,17,21, 3, 8,11,16,20) (23,39,34,27,43,37,31,26,42,36,29)(24,40,33,28,44,38,32,25,41,35,30)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 6, 9,13,18,22, 4, 7,12,15,19)( 2, 5,10,14,17,21, 3, 8,11,16,20) (23,42,37,34,29,26,43,39,36,31,27)(24,41,38,33,30,25,44,40,35,32,28)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 7,13,19, 4, 9,15,22, 6,12,18)( 2, 8,14,20, 3,10,16,21, 5,11,17) (23,27,31,36,39,43,26,29,34,37,42)(24,28,32,35,40,44,25,30,33,38,41)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 7,13,19, 4, 9,15,22, 6,12,18)( 2, 8,14,20, 3,10,16,21, 5,11,17) (23,29,36,42,26,31,37,43,27,34,39)(24,30,35,41,25,32,38,44,28,33,40)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 7,13,19, 4, 9,15,22, 6,12,18)( 2, 8,14,20, 3,10,16,21, 5,11,17) (23,31,39,26,34,42,27,36,43,29,37)(24,32,40,25,33,41,28,35,44,30,38)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 7,13,19, 4, 9,15,22, 6,12,18)( 2, 8,14,20, 3,10,16,21, 5,11,17) (23,39,34,27,43,37,31,26,42,36,29)(24,40,33,28,44,38,32,25,41,35,30)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 7,13,19, 4, 9,15,22, 6,12,18)( 2, 8,14,20, 3,10,16,21, 5,11,17) (23,42,37,34,29,26,43,39,36,31,27)(24,41,38,33,30,25,44,40,35,32,28)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 9,18, 4,12,19, 6,13,22, 7,15)( 2,10,17, 3,11,20, 5,14,21, 8,16) (23,27,31,36,39,43,26,29,34,37,42)(24,28,32,35,40,44,25,30,33,38,41)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 9,18, 4,12,19, 6,13,22, 7,15)( 2,10,17, 3,11,20, 5,14,21, 8,16) (23,29,36,42,26,31,37,43,27,34,39)(24,30,35,41,25,32,38,44,28,33,40)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1, 9,18, 4,12,19, 6,13,22, 7,15)( 2,10,17, 3,11,20, 5,14,21, 8,16) (23,39,34,27,43,37,31,26,42,36,29)(24,40,33,28,44,38,32,25,41,35,30)$
$ 11, 11, 11, 11 $ $4$ $11$ $( 1,12,22, 9,19, 7,18, 6,15, 4,13)( 2,11,21,10,20, 8,17, 5,16, 3,14) (23,29,36,42,26,31,37,43,27,34,39)(24,30,35,41,25,32,38,44,28,33,40)$
$ 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 $ $121$ $4$ $( 1,23, 2,24)( 3,33,22,36)( 4,34,21,35)( 5,44,19,26)( 6,43,20,25)( 7,31,17,38) ( 8,32,18,37)( 9,42,16,28)(10,41,15,27)(11,30,13,39)(12,29,14,40)$
$ 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 $ $121$ $4$ $( 1,24, 2,23)( 3,36,22,33)( 4,35,21,34)( 5,26,19,44)( 6,25,20,43)( 7,38,17,31) ( 8,37,18,32)( 9,28,16,42)(10,27,15,41)(11,39,13,30)(12,40,14,29)$

Group invariants

Order:  $484=2^{2} \cdot 11^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [484, 8]
Character table: Data not available.