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Properties

Label 47T3
Degree $47$
Order $1081$
Cyclic no
Abelian no
Solvable yes
Primitive yes
$p$-group no
Group: $C_{47}:C_{23}$

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Show commands: Magma

magma: G := TransitiveGroup(47, 3);
 

Group action invariants

Degree $n$:  $47$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $3$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $C_{47}:C_{23}$
Parity:  $1$
magma: IsEven(G);
 
Primitive:  yes
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $1$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47), (1,25,14,21,8,12,18,27,17,2,3,28,42,16,24,36,7,34,4,6,9,37,32)(5,31,23,11,40,13,43,41,38,10,15,46,22,33,26,39,35,29,20,30,45,44,19)
magma: Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$23$:  $C_{23}$

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

LabelCycle TypeSizeOrderIndexRepresentative
1A $1^{47}$ $1$ $1$ $0$ $()$
23A1 $23^{2},1$ $47$ $23$ $44$ $( 2, 7,37,29,28,22,33, 5,25, 4,19,15,38,35,17, 3,13,26,10, 8,43,18, 9)( 6,31,40,47,42,12,20,21,27,16,44,24,45,30,34,11,14,32,46,36,23,39,41)$
23A-1 $23^{2},1$ $47$ $23$ $44$ $( 2,13, 4,37,10,15,28,43,35,33, 9, 3,25, 7,26,19,29, 8,38,22,18,17, 5)( 6,14,16,40,46,24,42,23,30,20,41,11,27,31,32,44,47,36,45,12,39,34,21)$
23A2 $23^{2},1$ $47$ $23$ $44$ $( 2,25,13, 7, 4,26,37,19,10,29,15, 8,28,38,43,22,35,18,33,17, 9, 5, 3)( 6,27,14,31,16,32,40,44,46,47,24,36,42,45,23,12,30,39,20,34,41,21,11)$
23A-2 $23^{2},1$ $47$ $23$ $44$ $( 2,29,33, 4,38, 3,10,18, 7,28, 5,19,35,13, 8, 9,37,22,25,15,17,26,43)( 6,47,20,16,45,11,46,39,31,42,21,44,30,14,36,41,40,12,27,24,34,32,23)$
23A3 $23^{2},1$ $47$ $23$ $44$ $( 2,18, 8,26, 3,35,15, 4, 5,22,29, 7, 9,43,10,13,17,38,19,25,33,28,37)( 6,39,36,32,11,30,24,16,21,12,47,31,41,23,46,14,34,45,44,27,20,42,40)$
23A-3 $23^{2},1$ $47$ $23$ $44$ $( 2,35,29,13,33, 8, 4, 9,38,37, 3,22,10,25,18,15, 7,17,28,26, 5,43,19)( 6,30,47,14,20,36,16,41,45,40,11,12,46,27,39,24,31,34,42,32,21,23,44)$
23A4 $23^{2},1$ $47$ $23$ $44$ $( 2,15, 9,19,18, 4,43,25, 8, 5,10,33,26,22,13,28, 3,29,17,37,35, 7,38)( 6,24,41,44,39,16,23,27,36,21,46,20,32,12,14,42,11,47,34,40,30,31,45)$
23A-4 $23^{2},1$ $47$ $23$ $44$ $( 2,26,15,22, 9,13,19,28,18, 3, 4,29,43,17,25,37, 8,35, 5, 7,10,38,33)( 6,32,24,12,41,14,44,42,39,11,16,47,23,34,27,40,36,30,21,31,46,45,20)$
23A5 $23^{2},1$ $47$ $23$ $44$ $( 2,22,19, 3,43,37, 5,38,26, 9,28, 4,17, 8, 7,33,15,13,18,29,25,35,10)( 6,12,44,11,23,40,21,45,32,41,42,16,34,36,31,20,24,14,39,47,27,30,46)$
23A-5 $23^{2},1$ $47$ $23$ $44$ $( 2, 8, 3,15, 5,29, 9,10,17,19,33,37,18,26,35, 4,22, 7,43,13,38,25,28)( 6,36,11,24,21,47,41,46,34,44,20,40,39,32,30,16,12,31,23,14,45,27,42)$
23A6 $23^{2},1$ $47$ $23$ $44$ $( 2, 3, 5, 9,17,33,18,35,22,43,38,28, 8,15,29,10,19,37,26, 4, 7,13,25)( 6,11,21,41,34,20,39,30,12,23,45,42,36,24,47,46,44,40,32,16,31,14,27)$
23A-6 $23^{2},1$ $47$ $23$ $44$ $( 2, 4,10,28,35, 9,25,26,29,38,18, 5,13,37,15,43,33, 3, 7,19, 8,22,17)( 6,16,46,42,30,41,27,32,47,45,39,21,14,40,24,23,20,11,31,44,36,12,34)$
23A7 $23^{2},1$ $47$ $23$ $44$ $( 2,37,28,33,25,19,38,17,13,10,43, 9, 7,29,22, 5, 4,15,35, 3,26, 8,18)( 6,40,42,20,27,44,45,34,14,46,23,41,31,47,12,21,16,24,30,11,32,36,39)$
23A-7 $23^{2},1$ $47$ $23$ $44$ $( 2, 9,18,43, 8,10,26,13, 3,17,35,38,15,19, 4,25, 5,33,22,28,29,37, 7)( 6,41,39,23,36,46,32,14,11,34,30,45,24,44,16,27,21,20,12,42,47,40,31)$
23A8 $23^{2},1$ $47$ $23$ $44$ $( 2,38, 7,35,37,17,29, 3,28,13,22,26,33,10, 5, 8,25,43, 4,18,19, 9,15)( 6,45,31,30,40,34,47,11,42,14,12,32,20,46,21,36,27,23,16,39,44,41,24)$
23A-8 $23^{2},1$ $47$ $23$ $44$ $( 2,33,38,10, 7, 5,35, 8,37,25,17,43,29, 4, 3,18,28,19,13, 9,22,15,26)( 6,20,45,46,31,21,30,36,40,27,34,23,47,16,11,39,42,44,14,41,12,24,32)$
23A9 $23^{2},1$ $47$ $23$ $44$ $( 2, 5,17,18,22,38, 8,29,19,26, 7,25, 3, 9,33,35,43,28,15,10,37, 4,13)( 6,21,34,39,12,45,36,47,44,32,31,27,11,41,20,30,23,42,24,46,40,16,14)$
23A-9 $23^{2},1$ $47$ $23$ $44$ $( 2,28,25,38,13,43, 7,22, 4,35,26,18,37,33,19,17,10, 9,29, 5,15, 3, 8)( 6,42,27,45,14,23,31,12,16,30,32,39,40,20,44,34,46,41,47,21,24,11,36)$
23A10 $23^{2},1$ $47$ $23$ $44$ $( 2,43,26,17,15,25,22,37, 9, 8,13,35,19, 5,28, 7,18,10, 3,38, 4,33,29)( 6,23,32,34,24,27,12,40,41,36,14,30,44,21,42,31,39,46,11,45,16,20,47)$
23A-10 $23^{2},1$ $47$ $23$ $44$ $( 2,17,22, 8,19, 7, 3,33,43,15,37,13, 5,18,38,29,26,25, 9,35,28,10, 4)( 6,34,12,36,44,31,11,20,23,24,40,14,21,39,45,47,32,27,41,30,42,46,16)$
23A11 $23^{2},1$ $47$ $23$ $44$ $( 2,19,43, 5,26,28,17, 7,15,18,25,10,22, 3,37,38, 9, 4, 8,33,13,29,35)( 6,44,23,21,32,42,34,31,24,39,27,46,12,11,40,45,41,16,36,20,14,47,30)$
23A-11 $23^{2},1$ $47$ $23$ $44$ $( 2,10,35,25,29,18,13,15,33, 7, 8,17, 4,28, 9,26,38, 5,37,43, 3,19,22)( 6,46,30,27,47,39,14,24,20,31,36,34,16,42,41,32,45,21,40,23,11,44,12)$
47A1 $47$ $23$ $47$ $46$ $( 1,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)$
47A-1 $47$ $23$ $47$ $46$ $( 1,43,38,33,28,23,18,13, 8, 3,45,40,35,30,25,20,15,10, 5,47,42,37,32,27,22,17,12, 7, 2,44,39,34,29,24,19,14, 9, 4,46,41,36,31,26,21,16,11, 6)$

Malle's constant $a(G)$:     $1/44$

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $1081=23 \cdot 47$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  1081.1
magma: IdentifyGroup(G);
 
Character table:

1A 23A1 23A-1 23A2 23A-2 23A3 23A-3 23A4 23A-4 23A5 23A-5 23A6 23A-6 23A7 23A-7 23A8 23A-8 23A9 23A-9 23A10 23A-10 23A11 23A-11 47A1 47A-1
Size 1 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 23 23
23 P 1A 23A11 23A-8 23A-4 23A10 23A1 23A5 23A6 23A3 23A9 23A2 23A4 23A7 23A-1 23A-11 23A-6 23A-3 23A8 23A-2 23A-10 23A-7 23A-5 23A-9 47A1 47A-1
47 P 1A 23A3 23A2 23A1 23A9 23A-6 23A-7 23A10 23A5 23A-8 23A11 23A-1 23A4 23A6 23A-3 23A-10 23A-5 23A-2 23A-11 23A-9 23A-4 23A7 23A8 47A-1 47A1
Type
1081.1.1a R 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
1081.1.1b1 C 1 ζ23−11 ζ2311 ζ23 ζ23−1 ζ23−10 ζ2310 ζ232 ζ23−2 ζ23−9 ζ239 ζ233 ζ23−3 ζ23−8 ζ238 ζ234 ζ23−4 ζ23−7 ζ237 ζ235 ζ23−5 ζ23−6 ζ236 1 1
1081.1.1b2 C 1 ζ2311 ζ23−11 ζ23−1 ζ23 ζ2310 ζ23−10 ζ23−2 ζ232 ζ239 ζ23−9 ζ23−3 ζ233 ζ238 ζ23−8 ζ23−4 ζ234 ζ237 ζ23−7 ζ23−5 ζ235 ζ236 ζ23−6 1 1
1081.1.1b3 C 1 ζ23−10 ζ2310 ζ233 ζ23−3 ζ23−7 ζ237 ζ236 ζ23−6 ζ23−4 ζ234 ζ239 ζ23−9 ζ23−1 ζ23 ζ23−11 ζ2311 ζ232 ζ23−2 ζ23−8 ζ238 ζ235 ζ23−5 1 1
1081.1.1b4 C 1 ζ2310 ζ23−10 ζ23−3 ζ233 ζ237 ζ23−7 ζ23−6 ζ236 ζ234 ζ23−4 ζ23−9 ζ239 ζ23 ζ23−1 ζ2311 ζ23−11 ζ23−2 ζ232 ζ238 ζ23−8 ζ23−5 ζ235 1 1
1081.1.1b5 C 1 ζ23−9 ζ239 ζ235 ζ23−5 ζ23−4 ζ234 ζ2310 ζ23−10 ζ23 ζ23−1 ζ23−8 ζ238 ζ236 ζ23−6 ζ23−3 ζ233 ζ2311 ζ23−11 ζ232 ζ23−2 ζ23−7 ζ237 1 1
1081.1.1b6 C 1 ζ239 ζ23−9 ζ23−5 ζ235 ζ234 ζ23−4 ζ23−10 ζ2310 ζ23−1 ζ23 ζ238 ζ23−8 ζ23−6 ζ236 ζ233 ζ23−3 ζ23−11 ζ2311 ζ23−2 ζ232 ζ237 ζ23−7 1 1
1081.1.1b7 C 1 ζ23−8 ζ238 ζ237 ζ23−7 ζ23−1 ζ23 ζ23−9 ζ239 ζ236 ζ23−6 ζ23−2 ζ232 ζ23−10 ζ2310 ζ235 ζ23−5 ζ23−3 ζ233 ζ23−11 ζ2311 ζ234 ζ23−4 1 1
1081.1.1b8 C 1 ζ238 ζ23−8 ζ23−7 ζ237 ζ23 ζ23−1 ζ239 ζ23−9 ζ23−6 ζ236 ζ232 ζ23−2 ζ2310 ζ23−10 ζ23−5 ζ235 ζ233 ζ23−3 ζ2311 ζ23−11 ζ23−4 ζ234 1 1
1081.1.1b9 C 1 ζ23−7 ζ237 ζ239 ζ23−9 ζ232 ζ23−2 ζ23−5 ζ235 ζ2311 ζ23−11 ζ234 ζ23−4 ζ23−3 ζ233 ζ23−10 ζ2310 ζ236 ζ23−6 ζ23−1 ζ23 ζ23−8 ζ238 1 1
1081.1.1b10 C 1 ζ237 ζ23−7 ζ23−9 ζ239 ζ23−2 ζ232 ζ235 ζ23−5 ζ23−11 ζ2311 ζ23−4 ζ234 ζ233 ζ23−3 ζ2310 ζ23−10 ζ23−6 ζ236 ζ23 ζ23−1 ζ238 ζ23−8 1 1
1081.1.1b11 C 1 ζ23−6 ζ236 ζ2311 ζ23−11 ζ235 ζ23−5 ζ23−1 ζ23 ζ23−7 ζ237 ζ2310 ζ23−10 ζ234 ζ23−4 ζ23−2 ζ232 ζ23−8 ζ238 ζ239 ζ23−9 ζ233 ζ23−3 1 1
1081.1.1b12 C 1 ζ236 ζ23−6 ζ23−11 ζ2311 ζ23−5 ζ235 ζ23 ζ23−1 ζ237 ζ23−7 ζ23−10 ζ2310 ζ23−4 ζ234 ζ232 ζ23−2 ζ238 ζ23−8 ζ23−9 ζ239 ζ23−3 ζ233 1 1
1081.1.1b13 C 1 ζ23−5 ζ235 ζ23−10 ζ2310 ζ238 ζ23−8 ζ233 ζ23−3 ζ23−2 ζ232 ζ23−7 ζ237 ζ2311 ζ23−11 ζ236 ζ23−6 ζ23 ζ23−1 ζ23−4 ζ234 ζ23−9 ζ239 1 1
1081.1.1b14 C 1 ζ235 ζ23−5 ζ2310 ζ23−10 ζ23−8 ζ238 ζ23−3 ζ233 ζ232 ζ23−2 ζ237 ζ23−7 ζ23−11 ζ2311 ζ23−6 ζ236 ζ23−1 ζ23 ζ234 ζ23−4 ζ239 ζ23−9 1 1
1081.1.1b15 C 1 ζ23−4 ζ234 ζ23−8 ζ238 ζ2311 ζ23−11 ζ237 ζ23−7 ζ233 ζ23−3 ζ23−1 ζ23 ζ23−5 ζ235 ζ23−9 ζ239 ζ2310 ζ23−10 ζ236 ζ23−6 ζ232 ζ23−2 1 1
1081.1.1b16 C 1 ζ234 ζ23−4 ζ238 ζ23−8 ζ23−11 ζ2311 ζ23−7 ζ237 ζ23−3 ζ233 ζ23 ζ23−1 ζ235 ζ23−5 ζ239 ζ23−9 ζ23−10 ζ2310 ζ23−6 ζ236 ζ23−2 ζ232 1 1
1081.1.1b17 C 1 ζ23−3 ζ233 ζ23−6 ζ236 ζ23−9 ζ239 ζ2311 ζ23−11 ζ238 ζ23−8 ζ235 ζ23−5 ζ232 ζ23−2 ζ23−1 ζ23 ζ23−4 ζ234 ζ23−7 ζ237 ζ23−10 ζ2310 1 1
1081.1.1b18 C 1 ζ233 ζ23−3 ζ236 ζ23−6 ζ239 ζ23−9 ζ23−11 ζ2311 ζ23−8 ζ238 ζ23−5 ζ235 ζ23−2 ζ232 ζ23 ζ23−1 ζ234 ζ23−4 ζ237 ζ23−7 ζ2310 ζ23−10 1 1
1081.1.1b19 C 1 ζ23−2 ζ232 ζ23−4 ζ234 ζ23−6 ζ236 ζ23−8 ζ238 ζ23−10 ζ2310 ζ2311 ζ23−11 ζ239 ζ23−9 ζ237 ζ23−7 ζ235 ζ23−5 ζ233 ζ23−3 ζ23 ζ23−1 1 1
1081.1.1b20 C 1 ζ232 ζ23−2 ζ234 ζ23−4 ζ236 ζ23−6 ζ238 ζ23−8 ζ2310 ζ23−10 ζ23−11 ζ2311 ζ23−9 ζ239 ζ23−7 ζ237 ζ23−5 ζ235 ζ23−3 ζ233 ζ23−1 ζ23 1 1
1081.1.1b21 C 1 ζ23−1 ζ23 ζ23−2 ζ232 ζ23−3 ζ233 ζ23−4 ζ234 ζ23−5 ζ235 ζ23−6 ζ236 ζ23−7 ζ237 ζ23−8 ζ238 ζ23−9 ζ239 ζ23−10 ζ2310 ζ23−11 ζ2311 1 1
1081.1.1b22 C 1 ζ23 ζ23−1 ζ232 ζ23−2 ζ233 ζ23−3 ζ234 ζ23−4 ζ235 ζ23−5 ζ236 ζ23−6 ζ237 ζ23−7 ζ238 ζ23−8 ζ239 ζ23−9 ζ2310 ζ23−10 ζ2311 ζ23−11 1 1
1081.1.23a1 C 23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 −ζ47−23−ζ47−22−ζ47−20−ζ47−19−ζ47−15−ζ47−13−ζ47−11−ζ47−10−ζ47−5−1−ζ47−ζ472−ζ473−ζ474−ζ476−ζ477−ζ478−ζ479−ζ4712−ζ4714−ζ4716−ζ4717−ζ4718−ζ4721 ζ47−23+ζ47−22+ζ47−20+ζ47−19+ζ47−15+ζ47−13+ζ47−11+ζ47−10+ζ47−5+ζ47+ζ472+ζ473+ζ474+ζ476+ζ477+ζ478+ζ479+ζ4712+ζ4714+ζ4716+ζ4717+ζ4718+ζ4721
1081.1.23a2 C 23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ζ47−23+ζ47−22+ζ47−20+ζ47−19+ζ47−15+ζ47−13+ζ47−11+ζ47−10+ζ47−5+ζ47+ζ472+ζ473+ζ474+ζ476+ζ477+ζ478+ζ479+ζ4712+ζ4714+ζ4716+ζ4717+ζ4718+ζ4721 −ζ47−23−ζ47−22−ζ47−20−ζ47−19−ζ47−15−ζ47−13−ζ47−11−ζ47−10−ζ47−5−1−ζ47−ζ472−ζ473−ζ474−ζ476−ζ477−ζ478−ζ479−ζ4712−ζ4714−ζ4716−ζ4717−ζ4718−ζ4721

magma: CharacterTable(G);