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Properties

Label 45T9
45T9 1 12 1->12 41 1->41 2 11 2->11 42 2->42 3 10 3->10 40 3->40 4 29 4->29 44 4->44 5 30 5->30 43 5->43 6 28 6->28 45 6->45 7 17 7->17 32 7->32 8 18 8->18 33 8->33 9 16 9->16 31 9->31 10->5 19 10->19 11->6 21 11->21 12->4 20 12->20 13 13->7 37 13->37 14 14->8 39 14->39 15 15->9 38 15->38 27 16->27 16->41 26 17->26 17->40 25 18->25 18->42 19->15 19->30 20->13 20->29 21->14 21->28 22 22->1 22->16 23 23->3 23->17 24 24->2 24->18 25->4 34 25->34 26->6 36 26->36 27->5 35 27->35 28->22 28->39 29->24 29->37 30->23 30->38 31->10 31->27 32->11 32->26 33->12 33->25 34->14 34->44 35->13 35->43 36->15 36->45 37->2 37->32 38->3 38->31 39->1 39->33 40->19 40->36 41->20 41->35 42->21 42->34 43->7 43->23 44->8 44->24 45->9 45->22
Degree $45$
Order $90$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_5\times D_9$

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Copy content magma:G := TransitiveGroup(45, 9);
 

Group invariants

Abstract group:  $C_5\times D_9$
Copy content magma:IdentifyGroup(G);
 
Order:  $90=2 \cdot 3^{2} \cdot 5$
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  yes
Copy content magma:IsSolvable(G);
 
Nilpotency class:   not nilpotent
Copy content magma:NilpotencyClass(G);
 

Group action invariants

Degree $n$:  $45$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $9$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $5$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,41,20,13,37,32,11,6,28,22)(2,42,21,14,39,33,12,4,29,24)(3,40,19,15,38,31,10,5,30,23)(7,17,26,36,45,9,16,27,35,43)(8,18,25,34,44)$, $(1,12,20,29,37,2,11,21,28,39)(3,10,19,30,38)(4,44,24,18,42,34,14,8,33,25)(5,43,23,17,40,36,15,9,31,27)(6,45,22,16,41,35,13,7,32,26)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$5$:  $C_5$
$6$:  $S_3$
$10$:  $C_{10}$
$18$:  $D_{9}$
$30$:  $S_3 \times C_5$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 5: $C_5$

Degree 9: $D_{9}$

Degree 15: $S_3 \times C_5$

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 $1^{45}$ $1$ $1$ $0$ $()$
2A $2^{20},1^{5}$ $9$ $2$ $20$ $( 2, 3)( 4,35)( 5,34)( 6,36)( 7,24)( 8,23)( 9,22)(10,12)(13,43)(14,45)(15,44)(16,33)(17,32)(18,31)(19,21)(25,40)(26,42)(27,41)(29,30)(38,39)$
3A $3^{15}$ $2$ $3$ $30$ $( 1, 2, 3)( 4, 6, 5)( 7, 8, 9)(10,11,12)(13,15,14)(16,18,17)(19,20,21)(22,23,24)(25,27,26)(28,29,30)(31,33,32)(34,36,35)(37,39,38)(40,42,41)(43,45,44)$
5A1 $5^{9}$ $1$ $5$ $36$ $( 1,37,28,20,11)( 2,39,29,21,12)( 3,38,30,19,10)( 4,42,33,24,14)( 5,40,31,23,15)( 6,41,32,22,13)( 7,45,35,26,16)( 8,44,34,25,18)( 9,43,36,27,17)$
5A-1 $5^{9}$ $1$ $5$ $36$ $( 1,11,20,28,37)( 2,12,21,29,39)( 3,10,19,30,38)( 4,14,24,33,42)( 5,15,23,31,40)( 6,13,22,32,41)( 7,16,26,35,45)( 8,18,25,34,44)( 9,17,27,36,43)$
5A2 $5^{9}$ $1$ $5$ $36$ $( 1,28,11,37,20)( 2,29,12,39,21)( 3,30,10,38,19)( 4,33,14,42,24)( 5,31,15,40,23)( 6,32,13,41,22)( 7,35,16,45,26)( 8,34,18,44,25)( 9,36,17,43,27)$
5A-2 $5^{9}$ $1$ $5$ $36$ $( 1,20,37,11,28)( 2,21,39,12,29)( 3,19,38,10,30)( 4,24,42,14,33)( 5,23,40,15,31)( 6,22,41,13,32)( 7,26,45,16,35)( 8,25,44,18,34)( 9,27,43,17,36)$
9A1 $9^{5}$ $2$ $9$ $40$ $( 1,31,17, 2,33,16, 3,32,18)( 4,35,19, 6,34,20, 5,36,21)( 7,38,22, 8,37,23, 9,39,24)(10,41,25,11,40,27,12,42,26)(13,44,28,15,43,29,14,45,30)$
9A2 $9^{5}$ $2$ $9$ $40$ $( 1,17,33, 3,18,31, 2,16,32)( 4,19,34, 5,21,35, 6,20,36)( 7,22,37, 9,24,38, 8,23,39)(10,25,40,12,26,41,11,27,42)(13,28,43,14,30,44,15,29,45)$
9A4 $9^{5}$ $2$ $9$ $40$ $( 1,33,18, 2,32,17, 3,31,16)( 4,34,21, 6,36,19, 5,35,20)( 7,37,24, 8,39,22, 9,38,23)(10,40,26,11,42,25,12,41,27)(13,43,30,15,45,28,14,44,29)$
10A1 $10^{4},5$ $9$ $10$ $40$ $( 1,20,37,11,28)( 2,19,39,10,29, 3,21,38,12,30)( 4, 7,42,45,33,35,24,26,14,16)( 5, 8,40,44,31,34,23,25,15,18)( 6, 9,41,43,32,36,22,27,13,17)$
10A-1 $10^{4},5$ $9$ $10$ $40$ $( 1,43,11, 9,20,17,28,27,37,36)( 2,44,12, 8,21,18,29,25,39,34)( 3,45,10, 7,19,16,30,26,38,35)( 4,32,14,41,24, 6,33,13,42,22)( 5,31,15,40,23)$
10A3 $10^{4},5$ $9$ $10$ $40$ $( 1,42,20,14,37,33,11, 4,28,24)( 2,40,21,15,39,31,12, 5,29,23)( 3,41,19,13,38,32,10, 6,30,22)( 7,18,26,34,45, 8,16,25,35,44)( 9,17,27,36,43)$
10A-3 $10^{4},5$ $9$ $10$ $40$ $( 1,38,28,19,11, 3,37,30,20,10)( 2,39,29,21,12)( 4,27,33, 9,14,36,42,17,24,43)( 5,26,31, 7,15,35,40,16,23,45)( 6,25,32, 8,13,34,41,18,22,44)$
15A1 $15^{3}$ $2$ $15$ $42$ $( 1,38,29,20,10, 2,37,30,21,11, 3,39,28,19,12)( 4,40,32,24,15, 6,42,31,22,14, 5,41,33,23,13)( 7,43,34,26,17, 8,45,36,25,16, 9,44,35,27,18)$
15A-1 $15^{3}$ $2$ $15$ $42$ $( 1,12,19,28,39, 3,11,21,30,37, 2,10,20,29,38)( 4,13,23,33,41, 5,14,22,31,42, 6,15,24,32,40)( 7,18,27,35,44, 9,16,25,36,45, 8,17,26,34,43)$
15A2 $15^{3}$ $2$ $15$ $42$ $( 1,29,10,37,21, 3,28,12,38,20, 2,30,11,39,19)( 4,32,15,42,22, 5,33,13,40,24, 6,31,14,41,23)( 7,34,17,45,25, 9,35,18,43,26, 8,36,16,44,27)$
15A-2 $15^{3}$ $2$ $15$ $42$ $( 1,19,39,11,30, 2,20,38,12,28, 3,21,37,10,29)( 4,23,41,14,31, 6,24,40,13,33, 5,22,42,15,32)( 7,27,44,16,36, 8,26,43,18,35, 9,25,45,17,34)$
45A1 $45$ $2$ $45$ $44$ $( 1,43,42,38,34,31,29,26,22,20,17,14,10, 8, 5, 2,45,41,37,36,33,30,25,23,21,16,13,11, 9, 4, 3,44,40,39,35,32,28,27,24,19,18,15,12, 7, 6)$
45A-1 $45$ $2$ $45$ $44$ $( 1,36,24,10,44,31,21, 7,41,28,17, 4,38,25,15, 2,35,22,11,43,33,19, 8,40,29,16, 6,37,27,14, 3,34,23,12,45,32,20, 9,42,30,18, 5,39,26,13)$
45A2 $45$ $2$ $45$ $44$ $( 1,42,34,29,22,17,10, 5,45,37,33,25,21,13, 9, 3,40,35,28,24,18,12, 6,43,38,31,26,20,14, 8, 2,41,36,30,23,16,11, 4,44,39,32,27,19,15, 7)$
45A-2 $45$ $2$ $45$ $44$ $( 1,24,44,21,41,17,38,15,35,11,33, 8,29, 6,27, 3,23,45,20,42,18,39,13,36,10,31, 7,28, 4,25, 2,22,43,19,40,16,37,14,34,12,32, 9,30, 5,26)$
45A4 $45$ $2$ $45$ $44$ $( 1,34,22,10,45,33,21, 9,40,28,18, 6,38,26,14, 2,36,23,11,44,32,19, 7,42,29,17, 5,37,25,13, 3,35,24,12,43,31,20, 8,41,30,16, 4,39,27,15)$
45A-4 $45$ $2$ $45$ $44$ $( 1,44,41,38,35,33,29,27,23,20,18,13,10, 7, 4, 2,43,40,37,34,32,30,26,24,21,17,15,11, 8, 6, 3,45,42,39,36,31,28,25,22,19,16,14,12, 9, 5)$
45A8 $45$ $2$ $45$ $44$ $( 1, 9,14,19,25,31,39,45, 6,11,17,24,30,34,40, 2, 7,13,20,27,33,38,44, 5,12,16,22,28,36,42, 3, 8,15,21,26,32,37,43, 4,10,18,23,29,35,41)$
45A-8 $45$ $2$ $45$ $44$ $( 1,27, 4,30, 8,31,12,35,13,37,17,42,19,44,23, 2,26, 6,28, 9,33,10,34,15,39,16,41,20,43,24, 3,25, 5,29, 7,32,11,36,14,38,18,40,21,45,22)$
45A11 $45$ $2$ $45$ $44$ $( 1,14,25,39, 6,17,30,40, 7,20,33,44,12,22,36, 3,15,26,37, 4,18,29,41, 9,19,31,45,11,24,34, 2,13,27,38, 5,16,28,42, 8,21,32,43,10,23,35)$
45A-11 $45$ $2$ $45$ $44$ $( 1, 4, 8,12,13,17,19,23,26,28,33,34,39,41,43, 3, 5, 7,11,14,18,21,22,27,30,31,35,37,42,44, 2, 6, 9,10,15,16,20,24,25,29,32,36,38,40,45)$
45A13 $45$ $2$ $45$ $44$ $( 1, 8,13,19,26,33,39,43, 5,11,18,22,30,35,42, 2, 9,15,20,25,32,38,45, 4,12,17,23,28,34,41, 3, 7,14,21,27,31,37,44, 6,10,16,24,29,36,40)$
45A-13 $45$ $2$ $45$ $44$ $( 1,25, 6,30, 7,33,12,36,15,37,18,41,19,45,24, 2,27, 5,28, 8,32,10,35,14,39,17,40,20,44,22, 3,26, 4,29, 9,31,11,34,13,38,16,42,21,43,23)$

Malle's constant $a(G)$:     $1/20$

Copy content magma:ConjugacyClasses(G);
 

Character table

1A 2A 3A 5A1 5A-1 5A2 5A-2 9A1 9A2 9A4 10A1 10A-1 10A3 10A-3 15A1 15A-1 15A2 15A-2 45A1 45A-1 45A2 45A-2 45A4 45A-4 45A8 45A-8 45A11 45A-11 45A13 45A-13
Size 1 9 2 1 1 1 1 2 2 2 9 9 9 9 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 P 1A 1A 3A 5A2 5A-2 5A-1 5A1 9A2 9A4 9A1 5A1 5A-1 5A-2 5A2 15A2 15A-2 15A-1 15A1 45A2 45A-2 45A4 45A-4 45A8 45A-8 45A11 45A-11 45A-13 45A13 45A1 45A-1
3 P 1A 2A 1A 5A-2 5A2 5A1 5A-1 3A 3A 3A 10A3 10A-3 10A-1 10A1 5A-2 5A2 5A1 5A-1 15A1 15A-1 15A2 15A-2 15A-1 15A1 15A-2 15A2 15A1 15A-1 15A-2 15A2
5 P 1A 2A 3A 1A 1A 1A 1A 9A4 9A1 9A2 2A 2A 2A 2A 3A 3A 3A 3A 9A1 9A1 9A2 9A2 9A4 9A4 9A1 9A1 9A2 9A2 9A4 9A4
Type
90.1.1a 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 1 1 1 1 1
90.1.1b 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 1 1 1 1 1
90.1.1c1 C 1 1 1 ζ5−2 ζ52 ζ5 ζ5−1 1 1 1 ζ5−2 ζ5−1 ζ52 ζ5 ζ5 ζ5−2 ζ52 ζ5−1 ζ52 ζ5−2 ζ52 ζ5 ζ5−1 ζ5 ζ5 ζ5−2 ζ52 ζ5−1 ζ5−1 ζ5−2
90.1.1c2 C 1 1 1 ζ52 ζ5−2 ζ5−1 ζ5 1 1 1 ζ52 ζ5 ζ5−2 ζ5−1 ζ5−1 ζ52 ζ5−2 ζ5 ζ5−2 ζ52 ζ5−2 ζ5−1 ζ5 ζ5−1 ζ5−1 ζ52 ζ5−2 ζ5 ζ5 ζ52
90.1.1c3 C 1 1 1 ζ5−1 ζ5 ζ5−2 ζ52 1 1 1 ζ5−1 ζ52 ζ5 ζ5−2 ζ5−2 ζ5−1 ζ5 ζ52 ζ5 ζ5−1 ζ5 ζ5−2 ζ52 ζ5−2 ζ5−2 ζ5−1 ζ5 ζ52 ζ52 ζ5−1
90.1.1c4 C 1 1 1 ζ5 ζ5−1 ζ52 ζ5−2 1 1 1 ζ5 ζ5−2 ζ5−1 ζ52 ζ52 ζ5 ζ5−1 ζ5−2 ζ5−1 ζ5 ζ5−1 ζ52 ζ5−2 ζ52 ζ52 ζ5 ζ5−1 ζ5−2 ζ5−2 ζ5
90.1.1d1 C 1 −1 1 ζ5−2 ζ52 ζ5 ζ5−1 1 1 1 −ζ5−2 −ζ5−1 −ζ52 −ζ5 ζ5 ζ5−2 ζ52 ζ5−1 ζ52 ζ5−2 ζ52 ζ5 ζ5−1 ζ5 ζ5 ζ5−2 ζ52 ζ5−1 ζ5−1 ζ5−2
90.1.1d2 C 1 −1 1 ζ52 ζ5−2 ζ5−1 ζ5 1 1 1 −ζ52 −ζ5 −ζ5−2 −ζ5−1 ζ5−1 ζ52 ζ5−2 ζ5 ζ5−2 ζ52 ζ5−2 ζ5−1 ζ5 ζ5−1 ζ5−1 ζ52 ζ5−2 ζ5 ζ5 ζ52
90.1.1d3 C 1 −1 1 ζ5−1 ζ5 ζ5−2 ζ52 1 1 1 −ζ5−1 −ζ52 −ζ5 −ζ5−2 ζ5−2 ζ5−1 ζ5 ζ52 ζ5 ζ5−1 ζ5 ζ5−2 ζ52 ζ5−2 ζ5−2 ζ5−1 ζ5 ζ52 ζ52 ζ5−1
90.1.1d4 C 1 −1 1 ζ5 ζ5−1 ζ52 ζ5−2 1 1 1 −ζ5 −ζ5−2 −ζ5−1 −ζ52 ζ52 ζ5 ζ5−1 ζ5−2 ζ5−1 ζ5 ζ5−1 ζ52 ζ5−2 ζ52 ζ52 ζ5 ζ5−1 ζ5−2 ζ5−2 ζ5
90.1.2a R 2 0 2 2 2 2 2 −1 −1 −1 0 0 0 0 2 2 2 2 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1
90.1.2b1 R 2 0 −1 2 2 2 2 ζ9−4+ζ94 ζ9−1+ζ9 ζ9−2+ζ92 0 0 0 0 −1 −1 −1 −1 ζ9−4+ζ94 ζ9−4+ζ94 ζ9−2+ζ92 ζ9−1+ζ9 ζ9−1+ζ9 ζ9−4+ζ94 ζ9−2+ζ92 ζ9−1+ζ9 ζ9−1+ζ9 ζ9−2+ζ92 ζ9−4+ζ94 ζ9−2+ζ92
90.1.2b2 R 2 0 −1 2 2 2 2 ζ9−2+ζ92 ζ9−4+ζ94 ζ9−1+ζ9 0 0 0 0 −1 −1 −1 −1 ζ9−2+ζ92 ζ9−2+ζ92 ζ9−1+ζ9 ζ9−4+ζ94 ζ9−4+ζ94 ζ9−2+ζ92 ζ9−1+ζ9 ζ9−4+ζ94 ζ9−4+ζ94 ζ9−1+ζ9 ζ9−2+ζ92 ζ9−1+ζ9
90.1.2b3 R 2 0 −1 2 2 2 2 ζ9−1+ζ9 ζ9−2+ζ92 ζ9−4+ζ94 0 0 0 0 −1 −1 −1 −1 ζ9−1+ζ9 ζ9−1+ζ9 ζ9−4+ζ94 ζ9−2+ζ92 ζ9−2+ζ92 ζ9−1+ζ9 ζ9−4+ζ94 ζ9−2+ζ92 ζ9−2+ζ92 ζ9−4+ζ94 ζ9−1+ζ9 ζ9−4+ζ94
90.1.2c1 C 2 0 2 2ζ5−2 2ζ52 2ζ5 2ζ5−1 −1 −1 −1 0 0 0 0 2ζ5 2ζ5−2 2ζ52 2ζ5−1 −ζ52 −ζ5−2 −ζ52 −ζ5 −ζ5−1 −ζ5 −ζ5 −ζ5−2 −ζ52 −ζ5−1 −ζ5−1 −ζ5−2
90.1.2c2 C 2 0 2 2ζ52 2ζ5−2 2ζ5−1 2ζ5 −1 −1 −1 0 0 0 0 2ζ5−1 2ζ52 2ζ5−2 2ζ5 −ζ5−2 −ζ52 −ζ5−2 −ζ5−1 −ζ5 −ζ5−1 −ζ5−1 −ζ52 −ζ5−2 −ζ5 −ζ5 −ζ52
90.1.2c3 C 2 0 2 2ζ5−1 2ζ5 2ζ5−2 2ζ52 −1 −1 −1 0 0 0 0 2ζ5−2 2ζ5−1 2ζ5 2ζ52 −ζ5 −ζ5−1 −ζ5 −ζ5−2 −ζ52 −ζ5−2 −ζ5−2 −ζ5−1 −ζ5 −ζ52 −ζ52 −ζ5−1
90.1.2c4 C 2 0 2 2ζ5 2ζ5−1 2ζ52 2ζ5−2 −1 −1 −1 0 0 0 0 2ζ52 2ζ5 2ζ5−1 2ζ5−2 −ζ5−1 −ζ5 −ζ5−1 −ζ52 −ζ5−2 −ζ52 −ζ52 −ζ5 −ζ5−1 −ζ5−2 −ζ5−2 −ζ5
90.1.2d1 C 2 0 −1 2ζ45−18 2ζ4518 2ζ459 2ζ45−9 ζ45−20+ζ4520 ζ45−5+ζ455 ζ45−10+ζ4510 0 0 0 0 −ζ459 −ζ45−18 −ζ4518 −ζ45−9 −ζ45−22+ζ45−ζ457−ζ458+ζ4510−ζ4513+ζ4519−ζ4522 ζ452+ζ457 −ζ45+ζ457+ζ458−ζ4510−ζ4519+ζ4522 ζ454+ζ4514 −ζ45−22−ζ45+ζ452−ζ455−ζ4514−ζ4516+ζ4517 ζ45−22−ζ452−ζ454+ζ458−ζ4511−ζ4519−ζ4520 −ζ45−22+ζ452−ζ458+ζ4511−ζ4514+ζ4519+ζ4520 −ζ452−ζ4517+ζ4522 ζ45−22+ζ4513 ζ45−22+ζ45−ζ452+ζ455−ζ4511+ζ4514−ζ4517 ζ4511+ζ4516 −ζ457+ζ4517−ζ4522
90.1.2d2 C 2 0 −1 2ζ4518 2ζ45−18 2ζ45−9 2ζ459 ζ45−20+ζ4520 ζ45−5+ζ455 ζ45−10+ζ4510 0 0 0 0 −ζ45−9 −ζ4518 −ζ45−18 −ζ459 ζ452+ζ457 −ζ45−22+ζ45−ζ457−ζ458+ζ4510−ζ4513+ζ4519−ζ4522 −ζ457+ζ4517−ζ4522 −ζ45−22−ζ45+ζ452−ζ455−ζ4514−ζ4516+ζ4517 ζ454+ζ4514 ζ4511+ζ4516 ζ45−22+ζ45−ζ452+ζ455−ζ4511+ζ4514−ζ4517 ζ45−22+ζ4513 −ζ452−ζ4517+ζ4522 −ζ45−22+ζ452−ζ458+ζ4511−ζ4514+ζ4519+ζ4520 ζ45−22−ζ452−ζ454+ζ458−ζ4511−ζ4519−ζ4520 −ζ45+ζ457+ζ458−ζ4510−ζ4519+ζ4522
90.1.2d3 C 2 0 −1 2ζ45−18 2ζ4518 2ζ459 2ζ45−9 ζ45−10+ζ4510 ζ45−20+ζ4520 ζ45−5+ζ455 0 0 0 0 −ζ459 −ζ45−18 −ζ4518 −ζ45−9 −ζ45+ζ457+ζ458−ζ4510−ζ4519+ζ4522 −ζ457+ζ4517−ζ4522 ζ45−22+ζ4513 ζ45−22−ζ452−ζ454+ζ458−ζ4511−ζ4519−ζ4520 ζ4511+ζ4516 −ζ45−22+ζ452−ζ458+ζ4511−ζ4514+ζ4519+ζ4520 ζ454+ζ4514 ζ452+ζ457 −ζ45−22+ζ45−ζ457−ζ458+ζ4510−ζ4513+ζ4519−ζ4522 −ζ45−22−ζ45+ζ452−ζ455−ζ4514−ζ4516+ζ4517 ζ45−22+ζ45−ζ452+ζ455−ζ4511+ζ4514−ζ4517 −ζ452−ζ4517+ζ4522
90.1.2d4 C 2 0 −1 2ζ4518 2ζ45−18 2ζ45−9 2ζ459 ζ45−10+ζ4510 ζ45−20+ζ4520 ζ45−5+ζ455 0 0 0 0 −ζ45−9 −ζ4518 −ζ45−18 −ζ459 −ζ457+ζ4517−ζ4522 −ζ45+ζ457+ζ458−ζ4510−ζ4519+ζ4522 −ζ452−ζ4517+ζ4522 ζ4511+ζ4516 ζ45−22−ζ452−ζ454+ζ458−ζ4511−ζ4519−ζ4520 ζ45−22+ζ45−ζ452+ζ455−ζ4511+ζ4514−ζ4517 −ζ45−22−ζ45+ζ452−ζ455−ζ4514−ζ4516+ζ4517 −ζ45−22+ζ45−ζ457−ζ458+ζ4510−ζ4513+ζ4519−ζ4522 ζ452+ζ457 ζ454+ζ4514 −ζ45−22+ζ452−ζ458+ζ4511−ζ4514+ζ4519+ζ4520 ζ45−22+ζ4513
90.1.2d5 C 2 0 −1 2ζ45−18 2ζ4518 2ζ459 2ζ45−9 ζ45−5+ζ455 ζ45−10+ζ4510 ζ45−20+ζ4520 0 0 0 0 −ζ459 −ζ45−18 −ζ4518 −ζ45−9 ζ45−22+ζ4513 −ζ452−ζ4517+ζ4522 −ζ45−22+ζ45−ζ457−ζ458+ζ4510−ζ4513+ζ4519−ζ4522 −ζ45−22+ζ452−ζ458+ζ4511−ζ4514+ζ4519+ζ4520 ζ45−22+ζ45−ζ452+ζ455−ζ4511+ζ4514−ζ4517 ζ454+ζ4514 ζ45−22−ζ452−ζ454+ζ458−ζ4511−ζ4519−ζ4520 −ζ457+ζ4517−ζ4522 −ζ45+ζ457+ζ458−ζ4510−ζ4519+ζ4522 ζ4511+ζ4516 −ζ45−22−ζ45+ζ452−ζ455−ζ4514−ζ4516+ζ4517 ζ452+ζ457
90.1.2d6 C 2 0 −1 2ζ4518 2ζ45−18 2ζ45−9 2ζ459 ζ45−5+ζ455 ζ45−10+ζ4510 ζ45−20+ζ4520 0 0 0 0 −ζ45−9 −ζ4518 −ζ45−18 −ζ459 −ζ452−ζ4517+ζ4522 ζ45−22+ζ4513 ζ452+ζ457 ζ45−22+ζ45−ζ452+ζ455−ζ4511+ζ4514−ζ4517 −ζ45−22+ζ452−ζ458+ζ4511−ζ4514+ζ4519+ζ4520 −ζ45−22−ζ45+ζ452−ζ455−ζ4514−ζ4516+ζ4517 ζ4511+ζ4516 −ζ45+ζ457+ζ458−ζ4510−ζ4519+ζ4522 −ζ457+ζ4517−ζ4522 ζ45−22−ζ452−ζ454+ζ458−ζ4511−ζ4519−ζ4520 ζ454+ζ4514 −ζ45−22+ζ45−ζ457−ζ458+ζ4510−ζ4513+ζ4519−ζ4522
90.1.2d7 C 2 0 −1 2ζ45−9 2ζ459 2ζ45−18 2ζ4518 ζ45−20+ζ4520 ζ45−5+ζ455 ζ45−10+ζ4510 0 0 0 0 −ζ45−18 −ζ45−9 −ζ459 −ζ4518 ζ45−22−ζ452−ζ454+ζ458−ζ4511−ζ4519−ζ4520 ζ4511+ζ4516 −ζ45−22+ζ452−ζ458+ζ4511−ζ4514+ζ4519+ζ4520 −ζ452−ζ4517+ζ4522 ζ45−22+ζ4513 ζ452+ζ457 −ζ457+ζ4517−ζ4522 −ζ45−22−ζ45+ζ452−ζ455−ζ4514−ζ4516+ζ4517 ζ454+ζ4514 −ζ45+ζ457+ζ458−ζ4510−ζ4519+ζ4522 −ζ45−22+ζ45−ζ457−ζ458+ζ4510−ζ4513+ζ4519−ζ4522 ζ45−22+ζ45−ζ452+ζ455−ζ4511+ζ4514−ζ4517
90.1.2d8 C 2 0 −1 2ζ459 2ζ45−9 2ζ4518 2ζ45−18 ζ45−20+ζ4520 ζ45−5+ζ455 ζ45−10+ζ4510 0 0 0 0 −ζ4518 −ζ459 −ζ45−9 −ζ45−18 ζ4511+ζ4516 ζ45−22−ζ452−ζ454+ζ458−ζ4511−ζ4519−ζ4520 ζ45−22+ζ45−ζ452+ζ455−ζ4511+ζ4514−ζ4517 ζ45−22+ζ4513 −ζ452−ζ4517+ζ4522 −ζ45−22+ζ45−ζ457−ζ458+ζ4510−ζ4513+ζ4519−ζ4522 −ζ45+ζ457+ζ458−ζ4510−ζ4519+ζ4522 ζ454+ζ4514 −ζ45−22−ζ45+ζ452−ζ455−ζ4514−ζ4516+ζ4517 −ζ457+ζ4517−ζ4522 ζ452+ζ457 −ζ45−22+ζ452−ζ458+ζ4511−ζ4514+ζ4519+ζ4520
90.1.2d9 C 2 0 −1 2ζ45−9 2ζ459 2ζ45−18 2ζ4518 ζ45−10+ζ4510 ζ45−20+ζ4520 ζ45−5+ζ455 0 0 0 0 −ζ45−18 −ζ45−9 −ζ459 −ζ4518 −ζ45−22+ζ452−ζ458+ζ4511−ζ4514+ζ4519+ζ4520 ζ45−22+ζ45−ζ452+ζ455−ζ4511+ζ4514−ζ4517 ζ454+ζ4514 ζ452+ζ457 −ζ45−22+ζ45−ζ457−ζ458+ζ4510−ζ4513+ζ4519−ζ4522 −ζ457+ζ4517−ζ4522 −ζ452−ζ4517+ζ4522 ζ4511+ζ4516 ζ45−22−ζ452−ζ454+ζ458−ζ4511−ζ4519−ζ4520 ζ45−22+ζ4513 −ζ45+ζ457+ζ458−ζ4510−ζ4519+ζ4522 −ζ45−22−ζ45+ζ452−ζ455−ζ4514−ζ4516+ζ4517
90.1.2d10 C 2 0 −1 2ζ459 2ζ45−9 2ζ4518 2ζ45−18 ζ45−10+ζ4510 ζ45−20+ζ4520 ζ45−5+ζ455 0 0 0 0 −ζ4518 −ζ459 −ζ45−9 −ζ45−18 ζ45−22+ζ45−ζ452+ζ455−ζ4511+ζ4514−ζ4517 −ζ45−22+ζ452−ζ458+ζ4511−ζ4514+ζ4519+ζ4520 −ζ45−22−ζ45+ζ452−ζ455−ζ4514−ζ4516+ζ4517 −ζ45−22+ζ45−ζ457−ζ458+ζ4510−ζ4513+ζ4519−ζ4522 ζ452+ζ457 −ζ45+ζ457+ζ458−ζ4510−ζ4519+ζ4522 ζ45−22+ζ4513 ζ45−22−ζ452−ζ454+ζ458−ζ4511−ζ4519−ζ4520 ζ4511+ζ4516 −ζ452−ζ4517+ζ4522 −ζ457+ζ4517−ζ4522 ζ454+ζ4514
90.1.2d11 C 2 0 −1 2ζ45−9 2ζ459 2ζ45−18 2ζ4518 ζ45−5+ζ455 ζ45−10+ζ4510 ζ45−20+ζ4520 0 0 0 0 −ζ45−18 −ζ45−9 −ζ459 −ζ4518 ζ454+ζ4514 −ζ45−22−ζ45+ζ452−ζ455−ζ4514−ζ4516+ζ4517 ζ45−22−ζ452−ζ454+ζ458−ζ4511−ζ4519−ζ4520 −ζ457+ζ4517−ζ4522 −ζ45+ζ457+ζ458−ζ4510−ζ4519+ζ4522 −ζ452−ζ4517+ζ4522 ζ452+ζ457 ζ45−22+ζ45−ζ452+ζ455−ζ4511+ζ4514−ζ4517 −ζ45−22+ζ452−ζ458+ζ4511−ζ4514+ζ4519+ζ4520 −ζ45−22+ζ45−ζ457−ζ458+ζ4510−ζ4513+ζ4519−ζ4522 ζ45−22+ζ4513 ζ4511+ζ4516
90.1.2d12 C 2 0 −1 2ζ459 2ζ45−9 2ζ4518 2ζ45−18 ζ45−5+ζ455 ζ45−10+ζ4510 ζ45−20+ζ4520 0 0 0 0 −ζ4518 −ζ459 −ζ45−9 −ζ45−18 −ζ45−22−ζ45+ζ452−ζ455−ζ4514−ζ4516+ζ4517 ζ454+ζ4514 ζ4511+ζ4516 −ζ45+ζ457+ζ458−ζ4510−ζ4519+ζ4522 −ζ457+ζ4517−ζ4522 ζ45−22+ζ4513 −ζ45−22+ζ45−ζ457−ζ458+ζ4510−ζ4513+ζ4519−ζ4522 −ζ45−22+ζ452−ζ458+ζ4511−ζ4514+ζ4519+ζ4520 ζ45−22+ζ45−ζ452+ζ455−ζ4511+ζ4514−ζ4517 ζ452+ζ457 −ζ452−ζ4517+ζ4522 ζ45−22−ζ452−ζ454+ζ458−ζ4511−ζ4519−ζ4520

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Regular extensions

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