Properties

 Label 44T2 Degree $44$ Order $44$ Cyclic no Abelian yes Solvable yes Primitive no $p$-group no Group: $C_2\times C_{22}$

Related objects

Show commands: Magma

magma: G := TransitiveGroup(44, 2);

Group action invariants

 Degree $n$: $44$ magma: t, n := TransitiveGroupIdentification(G); n; Transitive number $t$: $2$ magma: t, n := TransitiveGroupIdentification(G); t; Group: $C_2\times C_{22}$ Parity: $1$ magma: IsEven(G); Primitive: no magma: IsPrimitive(G); Nilpotency class: $1$ magma: NilpotencyClass(G); $\card{\Aut(F/K)}$: $44$ magma: Order(Centralizer(SymmetricGroup(n), G)); Generators: (1,4,6,7,10,11,14,15,18,19,21,23,26,27,29,32,34,35,37,39,41,43)(2,3,5,8,9,12,13,16,17,20,22,24,25,28,30,31,33,36,38,40,42,44), (1,5,10,13,18,22,26,30,34,38,41,2,6,9,14,17,21,25,29,33,37,42)(3,7,12,15,20,23,28,32,36,39,44,4,8,11,16,19,24,27,31,35,40,43) magma: Generators(G);

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$11$:  $C_{11}$
$22$:  22T1 x 3

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$ x 3

Degree 4: $C_2^2$

Degree 11: $C_{11}$

Degree 22: 22T1 x 3

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

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

magma: ConjugacyClasses(G);

Group invariants

 Order: $44=2^{2} \cdot 11$ magma: Order(G); Cyclic: no magma: IsCyclic(G); Abelian: yes magma: IsAbelian(G); Solvable: yes magma: IsSolvable(G); Label: 44.4 magma: IdentifyGroup(G);
 Character table: not available.

magma: CharacterTable(G);