Properties

Label 44T42
Order \(968\)
n \(44\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
4:  $C_4$
8:  $C_8$

Resolvents shown for degrees $\leq 29$

Subfields

Degree 2: $C_2$

Degree 4: $C_4$

Degree 11: None

Degree 22: None

Low degree siblings

There are no siblings 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, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $8$ $11$ $(12,20,17,14,22,19,16,13,21,18,15)(23,30,26,33,29,25,32,28,24,31,27) (34,38,42,35,39,43,36,40,44,37,41)$
$ 11, 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $8$ $11$ $(12,17,22,16,21,15,20,14,19,13,18)(23,26,29,32,24,27,30,33,25,28,31) (34,42,39,36,44,41,38,35,43,40,37)$
$ 11, 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $8$ $11$ $(12,22,21,20,19,18,17,16,15,14,13)(23,29,24,30,25,31,26,32,27,33,28) (34,39,44,38,43,37,42,36,41,35,40)$
$ 11, 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $8$ $11$ $(12,21,19,17,15,13,22,20,18,16,14)(23,24,25,26,27,28,29,30,31,32,33) (34,44,43,42,41,40,39,38,37,36,35)$
$ 11, 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $8$ $11$ $(12,19,15,22,18,14,21,17,13,20,16)(23,25,27,29,31,33,24,26,28,30,32) (34,43,41,39,37,35,44,42,40,38,36)$
$ 11, 11, 11, 11 $ $8$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,20,17,14,22,19,16,13,21,18,15) (23,25,27,29,31,33,24,26,28,30,32)(34,37,40,43,35,38,41,44,36,39,42)$
$ 11, 11, 11, 11 $ $8$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,17,22,16,21,15,20,14,19,13,18) (23,32,30,28,26,24,33,31,29,27,25)(34,41,37,44,40,36,43,39,35,42,38)$
$ 11, 11, 11, 11 $ $8$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,21,19,17,15,13,22,20,18,16,14) (23,30,26,33,29,25,32,28,24,31,27)(34,43,41,39,37,35,44,42,40,38,36)$
$ 11, 11, 11, 11 $ $8$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,19,15,22,18,14,21,17,13,20,16) (23,31,28,25,33,30,27,24,32,29,26)(34,42,39,36,44,41,38,35,43,40,37)$
$ 11, 11, 11, 11 $ $8$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,18,13,19,14,20,15,21,16,22,17) (23,26,29,32,24,27,30,33,25,28,31)(34,36,38,40,42,44,35,37,39,41,43)$
$ 11, 11, 11, 11 $ $8$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,16,20,13,17,21,14,18,22,15,19) (23,27,31,24,28,32,25,29,33,26,30)(34,35,36,37,38,39,40,41,42,43,44)$
$ 11, 11, 11, 11 $ $8$ $11$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,17,22,16,21,15,20,14,19,13,18) (23,27,31,24,28,32,25,29,33,26,30)(34,40,35,41,36,42,37,43,38,44,39)$
$ 11, 11, 11, 11 $ $8$ $11$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,22,21,20,19,18,17,16,15,14,13) (23,30,26,33,29,25,32,28,24,31,27)(34,37,40,43,35,38,41,44,36,39,42)$
$ 11, 11, 11, 11 $ $8$ $11$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,22,21,20,19,18,17,16,15,14,13) (23,31,28,25,33,30,27,24,32,29,26)(34,35,36,37,38,39,40,41,42,43,44)$
$ 11, 11, 11, 11 $ $8$ $11$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,21,19,17,15,13,22,20,18,16,14) (23,26,29,32,24,27,30,33,25,28,31)(34,40,35,41,36,42,37,43,38,44,39)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1 $ $121$ $2$ $( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)(17,18)(23,27) (24,26)(28,33)(29,32)(30,31)(34,43)(35,42)(36,41)(37,40)(38,39)$
$ 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2 $ $121$ $4$ $( 1,29, 9,25)( 2,23, 8,31)( 3,28, 7,26)( 4,33, 6,32)( 5,27)(10,30,11,24) (12,40,18,37)(13,34,17,43)(14,39,16,38)(15,44)(19,42,22,35)(20,36,21,41)$
$ 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2 $ $121$ $4$ $( 1,32, 9,25)( 2,27, 8,30)( 3,33, 7,24)( 4,28, 6,29)( 5,23)(10,31,11,26) (12,37)(13,43,22,42)(14,38,21,36)(15,44,20,41)(16,39,19,35)(17,34,18,40)$
$ 8, 8, 8, 8, 8, 4 $ $121$ $8$ $( 1,14,29,39, 9,16,25,38)( 2,17,23,43, 8,13,31,34)( 3,20,28,36, 7,21,26,41) ( 4,12,33,40, 6,18,32,37)( 5,15,27,44)(10,19,30,42,11,22,24,35)$
$ 8, 8, 8, 8, 8, 4 $ $121$ $8$ $( 1,21,24,42, 2,18,29,38)( 3,15,23,34,11,13,30,35)( 4,12,28,41,10,16,25,39) ( 5,20,33,37, 9,19,31,43)( 6,17,27,44, 8,22,26,36)( 7,14,32,40)$
$ 8, 8, 8, 8, 8, 4 $ $121$ $8$ $( 1,39,25,14, 9,38,29,16)( 2,43,31,17, 8,34,23,13)( 3,36,26,20, 7,41,28,21) ( 4,40,32,12, 6,37,33,18)( 5,44,27,15)(10,42,24,19,11,35,30,22)$
$ 8, 8, 8, 8, 8, 4 $ $121$ $8$ $( 1,38,32,12, 7,36,24,16)( 2,34,27,20, 6,40,29,19)( 3,41,33,17, 5,44,23,22) ( 4,37,28,14)( 8,43,30,13,11,42,26,15)( 9,39,25,21,10,35,31,18)$

Group invariants

Order:  $968=2^{3} \cdot 11^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [968, 35]
Character table: Data not available.