Properties

Label 44T1
Order \(44\)
n \(44\)
Cyclic Yes
Abelian Yes
Solvable Yes
Primitive No
$p$-group No
Group: $C_{44}$

Related objects

Learn more about

Group action invariants

Degree $n$ :  $44$
Transitive number $t$ :  $1$
Group :  $C_{44}$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $1$
Generators:  (1,31,18,4,33,19,5,35,22,7,38,24,10,40,26,12,41,28,13,43,30,15,2,32,17,3,34,20,6,36,21,8,37,23,9,39,25,11,42,27,14,44,29,16)
$|\Aut(F/K)|$:  $44$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
4:  $C_4$
11:  $C_{11}$
22:  22T1

Resolvents shown for degrees $\leq 29$

Subfields

Degree 2: $C_2$

Degree 4: $C_4$

Degree 11: $C_{11}$

Degree 22: 22T1

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

Group invariants

Order:  $44=2^{2} \cdot 11$
Cyclic:  Yes
Abelian:  Yes
Solvable:  Yes
GAP id:  [44, 2]
Character table: Data not available.