Properties

Label 26T14
Order \(1014\)
n \(26\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

Degree $n$ :  $26$
Transitive number $t$ :  $14$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,11,10)(2,7,13)(4,12,6)(5,8,9)(14,22,20)(15,25,16)(17,18,21)(19,24,26), (1,16,4,15,7,14,10,26,13,25,3,24,6,23,9,22,12,21,2,20,5,19,8,18,11,17)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
6:  $S_3$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 13: None

Low degree siblings

39T26, 39T27

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 $ $1$ $1$ $()$
$ 13, 13 $ $6$ $13$ $( 1, 9, 4,12, 7, 2,10, 5,13, 8, 3,11, 6)(14,24,21,18,15,25,22,19,16,26,23,20, 17)$
$ 13, 13 $ $6$ $13$ $( 1, 4, 7,10,13, 3, 6, 9,12, 2, 5, 8,11)(14,21,15,22,16,23,17,24,18,25,19,26, 20)$
$ 13, 13 $ $6$ $13$ $( 1, 7,13, 6,12, 5,11, 4,10, 3, 9, 2, 8)(14,15,16,17,18,19,20,21,22,23,24,25, 26)$
$ 13, 13 $ $6$ $13$ $( 1,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(14,16,18,20,22,24,26,15,17,19,21,23, 25)$
$ 13, 13 $ $6$ $13$ $( 1,12,10, 8, 6, 4, 2,13,11, 9, 7, 5, 3)(14,18,22,26,17,21,25,16,20,24,15,19, 23)$
$ 13, 13 $ $6$ $13$ $( 1,10, 6, 2,11, 7, 3,12, 8, 4,13, 9, 5)(14,22,17,25,20,15,23,18,26,21,16,24, 19)$
$ 13, 13 $ $6$ $13$ $( 1, 6,11, 3, 8,13, 5,10, 2, 7,12, 4, 9)(14,17,20,23,26,16,19,22,25,15,18,21, 24)$
$ 13, 13 $ $6$ $13$ $( 1,11, 8, 5, 2,12, 9, 6, 3,13,10, 7, 4)(14,20,26,19,25,18,24,17,23,16,22,15, 21)$
$ 13, 13 $ $6$ $13$ $( 1, 8, 2, 9, 3,10, 4,11, 5,12, 6,13, 7)(14,26,25,24,23,22,21,20,19,18,17,16, 15)$
$ 13, 13 $ $6$ $13$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13)(14,25,23,21,19,17,15,26,24,22,20,18, 16)$
$ 13, 13 $ $6$ $13$ $( 1, 3, 5, 7, 9,11,13, 2, 4, 6, 8,10,12)(14,23,19,15,24,20,16,25,21,17,26,22, 18)$
$ 13, 13 $ $6$ $13$ $( 1, 5, 9,13, 4, 8,12, 3, 7,11, 2, 6,10)(14,19,24,16,21,26,18,23,15,20,25,17, 22)$
$ 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $13$ $(14,19,24,16,21,26,18,23,15,20,25,17,22)$
$ 13, 13 $ $3$ $13$ $( 1, 9, 4,12, 7, 2,10, 5,13, 8, 3,11, 6)(14,16,18,20,22,24,26,15,17,19,21,23, 25)$
$ 13, 13 $ $3$ $13$ $( 1, 4, 7,10,13, 3, 6, 9,12, 2, 5, 8,11)(14,26,25,24,23,22,21,20,19,18,17,16, 15)$
$ 13, 13 $ $6$ $13$ $( 1, 7,13, 6,12, 5,11, 4,10, 3, 9, 2, 8)(14,20,26,19,25,18,24,17,23,16,22,15, 21)$
$ 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $13$ $( 1,10, 6, 2,11, 7, 3,12, 8, 4,13, 9, 5)$
$ 13, 13 $ $3$ $13$ $( 1, 6,11, 3, 8,13, 5,10, 2, 7,12, 4, 9)(14,22,17,25,20,15,23,18,26,21,16,24, 19)$
$ 13, 13 $ $6$ $13$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13)(14,17,20,23,26,16,19,22,25,15,18,21, 24)$
$ 13, 13 $ $6$ $13$ $( 1, 5, 9,13, 4, 8,12, 3, 7,11, 2, 6,10)(14,24,21,18,15,25,22,19,16,26,23,20, 17)$
$ 13, 13 $ $6$ $13$ $( 1, 9, 4,12, 7, 2,10, 5,13, 8, 3,11, 6)(14,21,15,22,16,23,17,24,18,25,19,26, 20)$
$ 13, 13 $ $3$ $13$ $( 1, 4, 7,10,13, 3, 6, 9,12, 2, 5, 8,11)(14,18,22,26,17,21,25,16,20,24,15,19, 23)$
$ 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $13$ $( 1, 6,11, 3, 8,13, 5,10, 2, 7,12, 4, 9)$
$ 13, 13 $ $3$ $13$ $( 1,11, 8, 5, 2,12, 9, 6, 3,13,10, 7, 4)(14,17,20,23,26,16,19,22,25,15,18,21, 24)$
$ 13, 13 $ $6$ $13$ $( 1, 3, 5, 7, 9,11,13, 2, 4, 6, 8,10,12)(14,20,26,19,25,18,24,17,23,16,22,15, 21)$
$ 13, 13 $ $3$ $13$ $( 1, 7,13, 6,12, 5,11, 4,10, 3, 9, 2, 8)(14,22,17,25,20,15,23,18,26,21,16,24, 19)$
$ 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $13$ $( 1,11, 8, 5, 2,12, 9, 6, 3,13,10, 7, 4)$
$ 13, 13 $ $6$ $13$ $( 1, 5, 9,13, 4, 8,12, 3, 7,11, 2, 6,10)(14,26,25,24,23,22,21,20,19,18,17,16, 15)$
$ 13, 13 $ $3$ $13$ $( 1,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(14,17,20,23,26,16,19,22,25,15,18,21, 24)$
$ 13, 13 $ $3$ $13$ $( 1,12,10, 8, 6, 4, 2,13,11, 9, 7, 5, 3)(14,20,26,19,25,18,24,17,23,16,22,15, 21)$
$ 13, 13 $ $3$ $13$ $( 1,10, 6, 2,11, 7, 3,12, 8, 4,13, 9, 5)(14,26,25,24,23,22,21,20,19,18,17,16, 15)$
$ 13, 13 $ $3$ $13$ $( 1, 6,11, 3, 8,13, 5,10, 2, 7,12, 4, 9)(14,25,23,21,19,17,15,26,24,22,20,18, 16)$
$ 13, 13 $ $3$ $13$ $( 1,11, 8, 5, 2,12, 9, 6, 3,13,10, 7, 4)(14,23,19,15,24,20,16,25,21,17,26,22, 18)$
$ 13, 13 $ $3$ $13$ $( 1, 8, 2, 9, 3,10, 4,11, 5,12, 6,13, 7)(14,19,24,16,21,26,18,23,15,20,25,17, 22)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 1, 1 $ $338$ $3$ $( 2,10, 4)( 3, 6, 7)( 5,11,13)( 8,12, 9)(15,17,23)(16,20,19)(18,26,24) (21,22,25)$
$ 26 $ $39$ $26$ $( 1,16, 4,15, 7,14,10,26,13,25, 3,24, 6,23, 9,22,12,21, 2,20, 5,19, 8,18,11,17 )$
$ 26 $ $39$ $26$ $( 1,26, 8,15, 2,17, 9,19, 3,21,10,23, 4,25,11,14, 5,16,12,18, 6,20,13,22, 7,24 )$
$ 26 $ $39$ $26$ $( 1,23,12,15,10,20, 8,25, 6,17, 4,22, 2,14,13,19,11,24, 9,16, 7,21, 5,26, 3,18 )$
$ 26 $ $39$ $26$ $( 1,17, 7,15,13,26, 6,24,12,22, 5,20,11,18, 4,16,10,14, 3,25, 9,23, 2,21, 8,19 )$
$ 26 $ $39$ $26$ $( 1,18,10,15, 6,25, 2,22,11,19, 7,16, 3,26,12,23, 8,20, 4,17,13,14, 9,24, 5,21 )$
$ 26 $ $39$ $26$ $( 1,20, 3,15, 5,23, 7,18, 9,26,11,21,13,16, 2,24, 4,19, 6,14, 8,22,10,17,12,25 )$
$ 26 $ $39$ $26$ $( 1,24, 2,15, 3,19, 4,23, 5,14, 6,18, 7,22, 8,26, 9,17,10,21,11,25,12,16,13,20 )$
$ 26 $ $39$ $26$ $( 1,19,13,15,12,24,11,20,10,16, 9,25, 8,21, 7,17, 6,26, 5,22, 4,18, 3,14, 2,23 )$
$ 26 $ $39$ $26$ $( 1,22, 9,15, 4,21,12,14, 7,20, 2,26,10,19, 5,25,13,18, 8,24, 3,17,11,23, 6,16 )$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $39$ $2$ $( 1,15)( 2,19)( 3,23)( 4,14)( 5,18)( 6,22)( 7,26)( 8,17)( 9,21)(10,25)(11,16) (12,20)(13,24)$
$ 26 $ $39$ $26$ $( 1,14,11,15, 8,16, 5,17, 2,18,12,19, 9,20, 6,21, 3,22,13,23,10,24, 7,25, 4,26 )$
$ 26 $ $39$ $26$ $( 1,25, 5,15, 9,18,13,21, 4,24, 8,14,12,17, 3,20, 7,23,11,26, 2,16, 6,19,10,22 )$
$ 26 $ $39$ $26$ $( 1,21, 6,15,11,22, 3,16, 8,23,13,17, 5,24,10,18, 2,25, 7,19,12,26, 4,20, 9,14 )$

Group invariants

Order:  $1014=2 \cdot 3 \cdot 13^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [1014, 7]
Character table: Data not available.