# Properties

 Label 14T30 Order $$1092$$ n $$14$$ Cyclic No Abelian No Solvable No Primitive Yes $p$-group No Group: $\PSL(2,13)$

# Related objects

## Group action invariants

 Degree $n$ : $14$ Transitive number $t$ : $30$ Group : $\PSL(2,13)$ CHM label : $L(14)=PSL(2,13)$ Parity: $1$ Primitive: Yes Nilpotency class: $-1$ (not nilpotent) Generators: (1,12)(2,6)(3,4)(7,11)(9,10)(13,14), (1,4,3,12,9,10)(2,8,6,11,5,7), (1,2,3,4,5,6,7,8,9,10,11,12,14) $|\Aut(F/K)|$: $1$

## Low degree resolvents

None

Resolvents shown for degrees $\leq 47$

Degree 2: None

Degree 7: None

## Low degree siblings

28T120, 42T176

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 $1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $1$ $1$ $()$ $3, 3, 3, 3, 1, 1$ $182$ $3$ $( 1, 4, 7)( 2,14, 9)( 3, 5,13)( 6,12, 8)$ $2, 2, 2, 2, 2, 2, 1, 1$ $91$ $2$ $( 1, 5)( 2,12)( 3, 7)( 4,13)( 6, 9)( 8,14)$ $6, 6, 1, 1$ $182$ $6$ $( 1, 3, 4, 5, 7,13)( 2, 6,14,12, 9, 8)$ $7, 7$ $156$ $7$ $( 1,10, 3, 9, 5, 6,14)( 2, 7,13,12, 4, 8,11)$ $7, 7$ $156$ $7$ $( 1, 5,10, 6, 3,14, 9)( 2, 4, 7, 8,13,11,12)$ $7, 7$ $156$ $7$ $( 1, 3, 5,14,10, 9, 6)( 2,13, 4,11, 7,12, 8)$ $13, 1$ $84$ $13$ $( 1,13,11, 2,12, 4, 7, 9, 3, 5, 8,14,10)$ $13, 1$ $84$ $13$ $( 1, 3, 2,14, 7,13, 5,12,10, 9,11, 8, 4)$

## Group invariants

 Order: $1092=2^{2} \cdot 3 \cdot 7 \cdot 13$ Cyclic: No Abelian: No Solvable: No GAP id: [1092, 25]
 Character table:  2 2 . . . 1 2 1 . . 3 1 . . . 1 1 1 . . 7 1 1 1 1 . . . . . 13 1 . . . . . . 1 1 1a 7a 7b 7c 3a 2a 6a 13a 13b 2P 1a 7c 7a 7b 3a 1a 3a 13b 13a 3P 1a 7b 7c 7a 1a 2a 2a 13a 13b 5P 1a 7c 7a 7b 3a 2a 6a 13b 13a 7P 1a 1a 1a 1a 3a 2a 6a 13b 13a 11P 1a 7b 7c 7a 3a 2a 6a 13b 13a 13P 1a 7a 7b 7c 3a 2a 6a 1a 1a X.1 1 1 1 1 1 1 1 1 1 X.2 7 . . . 1 -1 -1 D *D X.3 7 . . . 1 -1 -1 *D D X.4 12 A B C . . . -1 -1 X.5 12 B C A . . . -1 -1 X.6 12 C A B . . . -1 -1 X.7 13 -1 -1 -1 1 1 1 . . X.8 14 . . . -1 2 -1 1 1 X.9 14 . . . -1 -2 1 1 1 A = -E(7)^3-E(7)^4 B = -E(7)^2-E(7)^5 C = -E(7)-E(7)^6 D = -E(13)-E(13)^3-E(13)^4-E(13)^9-E(13)^10-E(13)^12 = (1-Sqrt(13))/2 = -b13