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Properties

Label 34T18
Degree $34$
Order $4352$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^8:C_{17}$

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Show commands: Magma

magma: G := TransitiveGroup(34, 18);
 

Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$17$:  $C_{17}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 17: $C_{17}$

Low degree siblings

34T18 x 14

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

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 $ $1$ $1$ $()$
$ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $17$ $2$ $( 5, 6)( 9,10)(11,12)(15,16)(21,22)(23,24)(31,32)(33,34)$
$ 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $17$ $2$ $( 5, 6)( 7, 8)(11,12)(19,20)(23,24)(25,26)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $17$ $2$ $( 1, 2)( 5, 6)( 9,10)(11,12)(17,18)(23,24)(29,30)(31,32)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $17$ $2$ $( 1, 2)( 5, 6)( 7, 8)(11,12)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(29,30) (33,34)$
$ 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $17$ $2$ $( 9,10)(13,14)(17,18)(21,22)(31,32)(33,34)$
$ 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $17$ $2$ $( 5, 6)(11,12)(13,14)(15,16)(17,18)(23,24)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $17$ $2$ $( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(17,18)(19,20)(21,22)(23,24)(25,26)(31,32) (33,34)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $17$ $2$ $( 3, 4)(11,12)(17,18)(21,22)(23,24)(25,26)(27,28)(31,32)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $17$ $2$ $( 3, 4)( 7, 8)( 9,10)(11,12)(15,16)(17,18)(19,20)(23,24)(27,28)(33,34)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $17$ $2$ $( 3, 4)( 5, 6)( 7, 8)(17,18)(19,20)(21,22)(27,28)(31,32)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $17$ $2$ $( 1, 2)( 3, 4)(11,12)(15,16)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $17$ $2$ $( 1, 2)( 3, 4)( 5, 6)( 9,10)(21,22)(25,26)(27,28)(29,30)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $17$ $2$ $( 1, 2)( 3, 4)( 7, 8)( 9,10)(11,12)(19,20)(21,22)(23,24)(27,28)(29,30)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $17$ $2$ $(11,12)(13,14)(15,16)(17,18)(21,22)(23,24)(27,28)(29,30)(31,32)(33,34)$
$ 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $17$ $2$ $( 1, 2)( 3, 4)(11,12)(21,22)(29,30)(31,32)$
$ 17, 17 $ $256$ $17$ $( 1,11,21,31, 7,18,28, 3,13,23,33, 9,19,30, 5,15,25)( 2,12,22,32, 8,17,27, 4, 14,24,34,10,20,29, 6,16,26)$
$ 17, 17 $ $256$ $17$ $( 1,31,28,23,19,15,11, 7, 3,33,30,25,21,18,13, 9, 5)( 2,32,27,24,20,16,12, 8, 4,34,29,26,22,17,14,10, 6)$
$ 17, 17 $ $256$ $17$ $( 1,23,11,33,21, 9,31,19, 7,30,18, 5,28,15, 3,25,13)( 2,24,12,34,22,10,32,20, 8,29,17, 6,27,16, 4,26,14)$
$ 17, 17 $ $256$ $17$ $( 1,33,31,30,28,25,23,21,19,18,15,13,11, 9, 7, 5, 3)( 2,34,32,29,27,26,24,22, 20,17,16,14,12,10, 8, 6, 4)$
$ 17, 17 $ $256$ $17$ $( 1,30,23,18,11, 5,33,28,21,15, 9, 3,31,25,19,13, 7)( 2,29,24,17,12, 6,34,27, 22,16,10, 4,32,26,20,14, 8)$
$ 17, 17 $ $256$ $17$ $( 1,18,33,15,31,13,30,11,28, 9,25, 7,23, 5,21, 3,19)( 2,17,34,16,32,14,29,12, 27,10,26, 8,24, 6,22, 4,20)$
$ 17, 17 $ $256$ $17$ $( 1,15,30, 9,23, 3,18,31,11,25, 5,19,33,13,28, 7,21)( 2,16,29,10,24, 4,17,32, 12,26, 6,20,34,14,27, 8,22)$
$ 17, 17 $ $256$ $17$ $( 1, 9,18,25,33, 7,15,23,31, 5,13,21,30, 3,11,19,28)( 2,10,17,26,34, 8,16,24, 32, 6,14,22,29, 4,12,20,27)$
$ 17, 17 $ $256$ $17$ $( 1,25,15, 5,30,19, 9,33,23,13, 3,28,18, 7,31,21,11)( 2,26,16, 6,29,20,10,34, 24,14, 4,27,17, 8,32,22,12)$
$ 17, 17 $ $256$ $17$ $( 1, 5, 9,13,18,21,25,30,33, 3, 7,11,15,19,23,28,31)( 2, 6,10,14,17,22,26,29, 34, 4, 8,12,16,20,24,27,32)$
$ 17, 17 $ $256$ $17$ $( 1,13,25, 3,15,28, 5,18,30, 7,19,31, 9,21,33,11,23)( 2,14,26, 4,16,27, 6,17, 29, 8,20,32,10,22,34,12,24)$
$ 17, 17 $ $256$ $17$ $( 1, 3, 5, 7, 9,11,13,15,18,19,21,23,25,28,30,31,33)( 2, 4, 6, 8,10,12,14,16, 17,20,22,24,26,27,29,32,34)$
$ 17, 17 $ $256$ $17$ $( 1, 7,13,19,25,31, 3, 9,15,21,28,33, 5,11,18,23,30)( 2, 8,14,20,26,32, 4,10, 16,22,27,34, 6,12,17,24,29)$
$ 17, 17 $ $256$ $17$ $( 1,19, 3,21, 5,23, 7,25, 9,28,11,30,13,31,15,33,18)( 2,20, 4,22, 6,24, 8,26, 10,27,12,29,14,32,16,34,17)$
$ 17, 17 $ $256$ $17$ $( 1,21, 7,28,13,33,19, 5,25,11,31,18, 3,23, 9,30,15)( 2,22, 8,27,14,34,20, 6, 26,12,32,17, 4,24,10,29,16)$
$ 17, 17 $ $256$ $17$ $( 1,28,19,11, 3,30,21,13, 5,31,23,15, 7,33,25,18, 9)( 2,27,20,12, 4,29,22,14, 6,32,24,16, 8,34,26,17,10)$

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $4352=2^{8} \cdot 17$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  4352.1118911
magma: IdentifyGroup(G);
 
Character table: not available.

magma: CharacterTable(G);