Properties

 Label 23T3 Order $$253$$ n $$23$$ Cyclic No Abelian No Solvable Yes Primitive Yes $p$-group No Group: $C_{23}:C_{11}$

Related objects

Group action invariants

 Degree $n$ : $23$ Transitive number $t$ : $3$ Group : $C_{23}:C_{11}$ Parity: $1$ Primitive: Yes Nilpotency class: $-1$ (not nilpotent) Generators: (2,3,5,9,17,10,19,14,4,7,13)(6,11,21,18,12,23,22,20,16,8,15), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23) $|\Aut(F/K)|$: $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
11:  $C_{11}$

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - none

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

Group invariants

 Order: $253=11 \cdot 23$ Cyclic: No Abelian: No Solvable: Yes GAP id: [253, 1]
 Character table:  11 1 1 1 1 1 1 1 1 1 1 1 . . 23 1 . . . . . . . . . . 1 1 1a 11a 11b 11c 11d 11e 11f 11g 11h 11i 11j 23a 23b 2P 1a 11c 11f 11i 11h 11j 11g 11d 11e 11b 11a 23a 23b 3P 1a 11e 11c 11j 11f 11d 11i 11b 11g 11a 11h 23a 23b 5P 1a 11f 11h 11g 11a 11i 11e 11j 11c 11d 11b 23b 23a 7P 1a 11h 11a 11e 11b 11g 11c 11i 11f 11j 11d 23b 23a 11P 1a 1a 1a 1a 1a 1a 1a 1a 1a 1a 1a 23b 23a 13P 1a 11c 11f 11i 11h 11j 11g 11d 11e 11b 11a 23a 23b 17P 1a 11j 11i 11a 11g 11h 11b 11f 11d 11c 11e 23b 23a 19P 1a 11b 11d 11f 11j 11c 11h 11e 11a 11g 11i 23b 23a 23P 1a 11a 11b 11c 11d 11e 11f 11g 11h 11i 11j 1a 1a X.1 1 1 1 1 1 1 1 1 1 1 1 1 1 X.2 1 A /C B /B C E /A /D D /E 1 1 X.3 1 B E D /D /E /A /B C /C A 1 1 X.4 1 C B /E E /B D /C /A A /D 1 1 X.5 1 D /A /C C A /B /D /E E B 1 1 X.6 1 E /D /A A D C /E B /B /C 1 1 X.7 1 /E D A /A /D /C E /B B C 1 1 X.8 1 /D A C /C /A B D E /E /B 1 1 X.9 1 /C /B E /E B /D C A /A D 1 1 X.10 1 /B /E /D D E A B /C C /A 1 1 X.11 1 /A C /B B /C /E A D /D E 1 1 X.12 11 . . . . . . . . . . F /F X.13 11 . . . . . . . . . . /F F A = E(11)^10 B = E(11)^9 C = E(11)^8 D = E(11)^7 E = E(11)^6 F = E(23)^5+E(23)^7+E(23)^10+E(23)^11+E(23)^14+E(23)^15+E(23)^17+E(23)^19+E(23)^20+E(23)^21+E(23)^22 = (-1-Sqrt(-23))/2 = -1-b23