# Properties

 Label 14T42 Order $$2688$$ n $$14$$ Cyclic No Abelian No Solvable No Primitive No $p$-group No

# Related objects

## Group action invariants

 Degree $n$ : $14$ Transitive number $t$ : $42$ CHM label : $2^{4}`L_{7}(14)$ Parity: $-1$ Primitive: No Nilpotency class: $-1$ (not nilpotent) Generators: (1,9,11)(2,4,8)(3,13,5)(6,12,10), (1,8)(2,9)(4,11), (1,8)(2,11)(3,10)(4,9)(5,6)(12,13), (1,3,5,7,9,11,13)(2,4,6,8,10,12,14) $|\Aut(F/K)|$: $2$

## Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
168:  $\GL(3,2)$
336:  14T17
1344:  14T33

Resolvents shown for degrees $\leq 47$

## Subfields

Degree 2: None

Degree 7: $\GL(3,2)$

## Low degree siblings

14T42, 28T229 x 2, 28T230, 28T231 x 2, 42T327 x 2, 42T330 x 2

Siblings are shown with degree $\leq 47$

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

## Conjugacy Classes

 Cycle Type Size Order Representative $1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $1$ $1$ $()$ $2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1$ $7$ $2$ $( 4,11)( 5,12)( 7,14)$ $2, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $7$ $2$ $( 2, 9)( 4,11)( 5,12)( 6,13)$ $2, 2, 2, 2, 2, 2, 2$ $1$ $2$ $( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14)$ $4, 4, 2, 2, 2$ $42$ $4$ $( 1, 8)( 2, 9)( 3, 5,10,12)( 4,11)( 6, 7,13,14)$ $2, 2, 2, 2, 2, 2, 1, 1$ $84$ $2$ $( 1, 8)( 2, 9)( 3,12)( 5,10)( 6,14)( 7,13)$ $4, 4, 2, 2, 1, 1$ $42$ $4$ $( 1, 8)( 3, 5,10,12)( 4,11)( 6,14,13, 7)$ $2, 2, 2, 2, 2, 1, 1, 1, 1$ $84$ $2$ $( 1, 8)( 3,12)( 5,10)( 6, 7)(13,14)$ $4, 4, 2, 1, 1, 1, 1$ $42$ $4$ $( 2, 9)( 3,12,10, 5)( 6, 7,13,14)$ $4, 4, 1, 1, 1, 1, 1, 1$ $42$ $4$ $( 3,12,10, 5)( 6,14,13, 7)$ $8, 4, 2$ $168$ $8$ $( 1, 8)( 2,10, 4,14, 9, 3,11, 7)( 5, 6,12,13)$ $8, 2, 2, 2$ $168$ $8$ $( 1, 8)( 2,10,11,14, 9, 3, 4, 7)( 5, 6)(12,13)$ $8, 4, 1, 1$ $168$ $8$ $( 2, 3,11,14, 9,10, 4, 7)( 5, 6,12,13)$ $8, 2, 2, 1, 1$ $168$ $8$ $( 2, 3, 4,14, 9,10,11, 7)( 5, 6)(12,13)$ $3, 3, 3, 3, 1, 1$ $224$ $3$ $( 2, 3,12)( 4, 7, 6)( 5, 9,10)(11,14,13)$ $6, 3, 3, 1, 1$ $224$ $6$ $( 2, 3, 5, 9,10,12)( 4,14,13)( 6,11, 7)$ $6, 6, 2$ $224$ $6$ $( 1, 8)( 2,10, 5, 9, 3,12)( 4,14,13,11, 7, 6)$ $6, 3, 3, 2$ $224$ $6$ $( 1, 8)( 2,10,12)( 3, 5, 9)( 4, 7, 6,11,14,13)$ $7, 7$ $192$ $7$ $( 1, 2, 3, 4,12, 6, 7)( 5,13,14, 8, 9,10,11)$ $14$ $192$ $14$ $( 1, 2, 3,11,12, 6,14, 8, 9,10, 4, 5,13, 7)$ $14$ $192$ $14$ $( 1, 9, 3,14,13,11,12, 8, 2,10, 7, 6, 4, 5)$ $7, 7$ $192$ $7$ $( 1, 9, 3, 7, 6,11, 5)( 2,10,14,13, 4,12, 8)$

## Group invariants

 Order: $2688=2^{7} \cdot 3 \cdot 7$ Cyclic: No Abelian: No Solvable: No GAP id: Data not available
 Character table: Data not available.