Properties

Label 30T1
30T1 1 29 1->29 2 30 2->30 3 3->2 4 4->1 5 5->4 6 6->3 7 7->6 8 8->5 9 9->8 10 10->7 11 11->9 12 12->10 13 13->11 14 14->12 15 15->14 16 16->13 17 17->15 18 18->16 19 19->18 20 20->17 21 21->19 22 22->20 23 23->21 24 24->22 25 25->24 26 26->23 27 27->25 28 28->26 29->27 30->28
Degree $30$
Order $30$
Cyclic yes
Abelian yes
Solvable yes
Transitivity $1$
Primitive no
$p$-group no
Group: $C_{30}$

Related objects

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Copy content comment:Define the Galois group
 
Copy content magma:G := TransitiveGroup(30, 1);
 
Copy content sage:G = TransitiveGroup(30, 1)
 
Copy content oscar:G = transitive_group(30, 1)
 
Copy content gap:G := TransitiveGroup(30, 1);
 

Group invariants

Abstract group:  $C_{30}$
Copy content comment:Abstract group ID
 
Copy content magma:IdentifyGroup(G);
 
Copy content sage:G.id()
 
Copy content oscar:small_group_identification(G)
 
Copy content gap:IdGroup(G);
 
Order:  $30=2 \cdot 3 \cdot 5$
Copy content comment:Order
 
Copy content magma:Order(G);
 
Copy content sage:G.order()
 
Copy content oscar:order(G)
 
Copy content gap:Order(G);
 
Cyclic:  yes
Copy content comment:Determine if group is cyclic
 
Copy content magma:IsCyclic(G);
 
Copy content sage:G.is_cyclic()
 
Copy content oscar:is_cyclic(G)
 
Copy content gap:IsCyclic(G);
 
Abelian:  yes
Copy content comment:Determine if group is abelian
 
Copy content magma:IsAbelian(G);
 
Copy content sage:G.is_abelian()
 
Copy content oscar:is_abelian(G)
 
Copy content gap:IsAbelian(G);
 
Solvable:  yes
Copy content comment:Determine if group is solvable
 
Copy content magma:IsSolvable(G);
 
Copy content sage:G.is_solvable()
 
Copy content oscar:is_solvable(G)
 
Copy content gap:IsSolvable(G);
 
Nilpotency class:  $1$
Copy content comment:Nilpotency class
 
Copy content magma:NilpotencyClass(G);
 
Copy content sage:libgap(G).NilpotencyClassOfGroup() if G.is_nilpotent() else -1
 
Copy content oscar:if is_nilpotent(G) nilpotency_class(G) end
 
Copy content gap:if IsNilpotentGroup(G) then NilpotencyClassOfGroup(G); fi;
 

Group action invariants

Degree $n$:  $30$
Copy content comment:Degree
 
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Copy content sage:G.degree()
 
Copy content oscar:degree(G)
 
Copy content gap:NrMovedPoints(G);
 
Transitive number $t$:  $1$
Copy content comment:Transitive number
 
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Copy content sage:G.transitive_number()
 
Copy content oscar:transitive_group_identification(G)[2]
 
Copy content gap:TransitiveIdentification(G);
 
Parity:  $-1$
Copy content comment:Parity
 
Copy content magma:IsEven(G);
 
Copy content sage:all(g.SignPerm() == 1 for g in libgap(G).GeneratorsOfGroup())
 
Copy content oscar:is_even(G)
 
Copy content gap:ForAll(GeneratorsOfGroup(G), g -> SignPerm(g) = 1);
 
Transitivity:  1
Primitive:  no
Copy content comment:Determine if group is primitive
 
Copy content magma:IsPrimitive(G);
 
Copy content sage:G.is_primitive()
 
Copy content oscar:is_primitive(G)
 
Copy content gap:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $30$
Copy content comment:Order of the centralizer of G in S_n
 
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Copy content sage:SymmetricGroup(30).centralizer(G).order()
 
Copy content oscar:order(centralizer(symmetric_group(30), G)[1])
 
Copy content gap:Order(Centralizer(SymmetricGroup(30), G));
 
Generators:  $(1,29,27,25,24,22,20,17,15,14,12,10,7,6,3,2,30,28,26,23,21,19,18,16,13,11,9,8,5,4)$
Copy content comment:Generators
 
Copy content magma:Generators(G);
 
Copy content sage:G.gens()
 
Copy content oscar:gens(G)
 
Copy content gap:GeneratorsOfGroup(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$5$:  $C_5$
$6$:  $C_6$
$10$:  $C_{10}$
$15$:  $C_{15}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 3: $C_3$

Degree 5: $C_5$

Degree 6: $C_6$

Degree 10: $C_{10}$

Degree 15: $C_{15}$

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 $1^{30}$ $1$ $1$ $0$ $()$
2A $2^{15}$ $1$ $2$ $15$ $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)$
3A1 $3^{10}$ $1$ $3$ $20$ $( 1,12,21)( 2,11,22)( 3,13,24)( 4,14,23)( 5,15,26)( 6,16,25)( 7,18,27)( 8,17,28)( 9,20,30)(10,19,29)$
3A-1 $3^{10}$ $1$ $3$ $20$ $( 1,21,12)( 2,22,11)( 3,24,13)( 4,23,14)( 5,26,15)( 6,25,16)( 7,27,18)( 8,28,17)( 9,30,20)(10,29,19)$
5A1 $5^{6}$ $1$ $5$ $24$ $( 1,20, 7,26,13)( 2,19, 8,25,14)( 3,21, 9,27,15)( 4,22,10,28,16)( 5,24,12,30,18)( 6,23,11,29,17)$
5A-1 $5^{6}$ $1$ $5$ $24$ $( 1,13,26, 7,20)( 2,14,25, 8,19)( 3,15,27, 9,21)( 4,16,28,10,22)( 5,18,30,12,24)( 6,17,29,11,23)$
5A2 $5^{6}$ $1$ $5$ $24$ $( 1, 7,13,20,26)( 2, 8,14,19,25)( 3, 9,15,21,27)( 4,10,16,22,28)( 5,12,18,24,30)( 6,11,17,23,29)$
5A-2 $5^{6}$ $1$ $5$ $24$ $( 1,26,20,13, 7)( 2,25,19,14, 8)( 3,27,21,15, 9)( 4,28,22,16,10)( 5,30,24,18,12)( 6,29,23,17,11)$
6A1 $6^{5}$ $1$ $6$ $25$ $( 1,22,12, 2,21,11)( 3,23,13, 4,24,14)( 5,25,15, 6,26,16)( 7,28,18, 8,27,17)( 9,29,20,10,30,19)$
6A-1 $6^{5}$ $1$ $6$ $25$ $( 1,11,21, 2,12,22)( 3,14,24, 4,13,23)( 5,16,26, 6,15,25)( 7,17,27, 8,18,28)( 9,19,30,10,20,29)$
10A1 $10^{3}$ $1$ $10$ $27$ $( 1,25,20,14, 7, 2,26,19,13, 8)( 3,28,21,16, 9, 4,27,22,15,10)( 5,29,24,17,12, 6,30,23,18,11)$
10A-1 $10^{3}$ $1$ $10$ $27$ $( 1, 8,13,19,26, 2, 7,14,20,25)( 3,10,15,22,27, 4, 9,16,21,28)( 5,11,18,23,30, 6,12,17,24,29)$
10A3 $10^{3}$ $1$ $10$ $27$ $( 1,14,26, 8,20, 2,13,25, 7,19)( 3,16,27,10,21, 4,15,28, 9,22)( 5,17,30,11,24, 6,18,29,12,23)$
10A-3 $10^{3}$ $1$ $10$ $27$ $( 1,19, 7,25,13, 2,20, 8,26,14)( 3,22, 9,28,15, 4,21,10,27,16)( 5,23,12,29,18, 6,24,11,30,17)$
15A1 $15^{2}$ $1$ $15$ $28$ $( 1,27,24,20,15,12, 7, 3,30,26,21,18,13, 9, 5)( 2,28,23,19,16,11, 8, 4,29,25,22,17,14,10, 6)$
15A-1 $15^{2}$ $1$ $15$ $28$ $( 1, 5, 9,13,18,21,26,30, 3, 7,12,15,20,24,27)( 2, 6,10,14,17,22,25,29, 4, 8,11,16,19,23,28)$
15A2 $15^{2}$ $1$ $15$ $28$ $( 1,24,15, 7,30,21,13, 5,27,20,12, 3,26,18, 9)( 2,23,16, 8,29,22,14, 6,28,19,11, 4,25,17,10)$
15A-2 $15^{2}$ $1$ $15$ $28$ $( 1, 9,18,26, 3,12,20,27, 5,13,21,30, 7,15,24)( 2,10,17,25, 4,11,19,28, 6,14,22,29, 8,16,23)$
15A4 $15^{2}$ $1$ $15$ $28$ $( 1,15,30,13,27,12,26, 9,24, 7,21, 5,20, 3,18)( 2,16,29,14,28,11,25,10,23, 8,22, 6,19, 4,17)$
15A-4 $15^{2}$ $1$ $15$ $28$ $( 1,18, 3,20, 5,21, 7,24, 9,26,12,27,13,30,15)( 2,17, 4,19, 6,22, 8,23,10,25,11,28,14,29,16)$
15A7 $15^{2}$ $1$ $15$ $28$ $( 1, 3, 5, 7, 9,12,13,15,18,20,21,24,26,27,30)( 2, 4, 6, 8,10,11,14,16,17,19,22,23,25,28,29)$
15A-7 $15^{2}$ $1$ $15$ $28$ $( 1,30,27,26,24,21,20,18,15,13,12, 9, 7, 5, 3)( 2,29,28,25,23,22,19,17,16,14,11,10, 8, 6, 4)$
30A1 $30$ $1$ $30$ $29$ $( 1,29,27,25,24,22,20,17,15,14,12,10, 7, 6, 3, 2,30,28,26,23,21,19,18,16,13,11, 9, 8, 5, 4)$
30A-1 $30$ $1$ $30$ $29$ $( 1, 4, 5, 8, 9,11,13,16,18,19,21,23,26,28,30, 2, 3, 6, 7,10,12,14,15,17,20,22,24,25,27,29)$
30A7 $30$ $1$ $30$ $29$ $( 1,17, 3,19, 5,22, 7,23, 9,25,12,28,13,29,15, 2,18, 4,20, 6,21, 8,24,10,26,11,27,14,30,16)$
30A-7 $30$ $1$ $30$ $29$ $( 1,16,30,14,27,11,26,10,24, 8,21, 6,20, 4,18, 2,15,29,13,28,12,25, 9,23, 7,22, 5,19, 3,17)$
30A11 $30$ $1$ $30$ $29$ $( 1,10,18,25, 3,11,20,28, 5,14,21,29, 7,16,24, 2, 9,17,26, 4,12,19,27, 6,13,22,30, 8,15,23)$
30A-11 $30$ $1$ $30$ $29$ $( 1,23,15, 8,30,22,13, 6,27,19,12, 4,26,17, 9, 2,24,16, 7,29,21,14, 5,28,20,11, 3,25,18,10)$
30A13 $30$ $1$ $30$ $29$ $( 1, 6, 9,14,18,22,26,29, 3, 8,12,16,20,23,27, 2, 5,10,13,17,21,25,30, 4, 7,11,15,19,24,28)$
30A-13 $30$ $1$ $30$ $29$ $( 1,28,24,19,15,11, 7, 4,30,25,21,17,13,10, 5, 2,27,23,20,16,12, 8, 3,29,26,22,18,14, 9, 6)$

Malle's constant $a(G)$:     $1/15$

Copy content comment:Conjugacy classes
 
Copy content magma:ConjugacyClasses(G);
 
Copy content sage:G.conjugacy_classes()
 
Copy content oscar:conjugacy_classes(G)
 
Copy content gap:ConjugacyClasses(G);
 

Character table

1A 2A 3A1 3A-1 5A1 5A-1 5A2 5A-2 6A1 6A-1 10A1 10A-1 10A3 10A-3 15A1 15A-1 15A2 15A-2 15A4 15A-4 15A7 15A-7 30A1 30A-1 30A7 30A-7 30A11 30A-11 30A13 30A-13
Size 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
2 P 1A 1A 3A-1 3A1 5A2 5A-2 5A-1 5A1 3A1 3A-1 5A1 5A-1 5A-2 5A2 15A2 15A-2 15A4 15A-4 15A-7 15A7 15A-1 15A1 15A1 15A-1 15A7 15A-7 15A-4 15A4 15A-2 15A2
3 P 1A 2A 1A 1A 5A-2 5A2 5A1 5A-1 2A 2A 10A3 10A-3 10A-1 10A1 5A1 5A-1 5A2 5A-2 5A-1 5A1 5A2 5A-2 10A1 10A-1 10A-3 10A3 10A1 10A-1 10A3 10A-3
5 P 1A 2A 3A-1 3A1 1A 1A 1A 1A 6A-1 6A1 2A 2A 2A 2A 3A1 3A-1 3A-1 3A1 3A1 3A-1 3A1 3A-1 6A1 6A-1 6A1 6A-1 6A-1 6A1 6A1 6A-1
Type
30.4.1a 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
30.4.1b 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
30.4.1c1 C 1 1 ζ3−1 ζ3 1 1 1 1 ζ3 ζ3−1 1 1 1 1 ζ3 ζ3−1 ζ3−1 ζ3 ζ3 ζ3−1 ζ3 ζ3−1 ζ3−1 ζ3 ζ3−1 ζ3 ζ3 ζ3−1 ζ3−1 ζ3
30.4.1c2 C 1 1 ζ3 ζ3−1 1 1 1 1 ζ3−1 ζ3 1 1 1 1 ζ3−1 ζ3 ζ3 ζ3−1 ζ3−1 ζ3 ζ3−1 ζ3 ζ3 ζ3−1 ζ3 ζ3−1 ζ3−1 ζ3 ζ3 ζ3−1
30.4.1d1 C 1 −1 ζ3−1 ζ3 1 1 1 1 −ζ3 −ζ3−1 −1 −1 −1 −1 ζ3 ζ3−1 ζ3−1 ζ3 ζ3 ζ3−1 ζ3 ζ3−1 −ζ3−1 −ζ3 −ζ3−1 −ζ3 −ζ3 −ζ3−1 −ζ3−1 −ζ3
30.4.1d2 C 1 −1 ζ3 ζ3−1 1 1 1 1 −ζ3−1 −ζ3 −1 −1 −1 −1 ζ3−1 ζ3 ζ3 ζ3−1 ζ3−1 ζ3 ζ3−1 ζ3 −ζ3 −ζ3−1 −ζ3 −ζ3−1 −ζ3−1 −ζ3 −ζ3 −ζ3−1
30.4.1e1 C 1 1 1 1 ζ5−2 ζ52 ζ5 ζ5−1 1 1 ζ5−1 ζ5 ζ52 ζ5−2 ζ5 ζ5−1 ζ52 ζ5−2 ζ5−1 ζ5 ζ52 ζ5−2 ζ5−2 ζ52 ζ5 ζ5−1 ζ5−2 ζ52 ζ5−1 ζ5
30.4.1e2 C 1 1 1 1 ζ52 ζ5−2 ζ5−1 ζ5 1 1 ζ5 ζ5−1 ζ5−2 ζ52 ζ5−1 ζ5 ζ5−2 ζ52 ζ5 ζ5−1 ζ5−2 ζ52 ζ52 ζ5−2 ζ5−1 ζ5 ζ52 ζ5−2 ζ5 ζ5−1
30.4.1e3 C 1 1 1 1 ζ5−1 ζ5 ζ5−2 ζ52 1 1 ζ52 ζ5−2 ζ5 ζ5−1 ζ5−2 ζ52 ζ5 ζ5−1 ζ52 ζ5−2 ζ5 ζ5−1 ζ5−1 ζ5 ζ5−2 ζ52 ζ5−1 ζ5 ζ52 ζ5−2
30.4.1e4 C 1 1 1 1 ζ5 ζ5−1 ζ52 ζ5−2 1 1 ζ5−2 ζ52 ζ5−1 ζ5 ζ52 ζ5−2 ζ5−1 ζ5 ζ5−2 ζ52 ζ5−1 ζ5 ζ5 ζ5−1 ζ52 ζ5−2 ζ5 ζ5−1 ζ5−2 ζ52
30.4.1f1 C 1 −1 1 1 ζ5−2 ζ52 ζ5 ζ5−1 −1 −1 −ζ5−1 −ζ5 −ζ52 −ζ5−2 ζ5 ζ5−1 ζ52 ζ5−2 ζ5−1 ζ5 ζ52 ζ5−2 −ζ5−2 −ζ52 −ζ5 −ζ5−1 −ζ5−2 −ζ52 −ζ5−1 −ζ5
30.4.1f2 C 1 −1 1 1 ζ52 ζ5−2 ζ5−1 ζ5 −1 −1 −ζ5 −ζ5−1 −ζ5−2 −ζ52 ζ5−1 ζ5 ζ5−2 ζ52 ζ5 ζ5−1 ζ5−2 ζ52 −ζ52 −ζ5−2 −ζ5−1 −ζ5 −ζ52 −ζ5−2 −ζ5 −ζ5−1
30.4.1f3 C 1 −1 1 1 ζ5−1 ζ5 ζ5−2 ζ52 −1 −1 −ζ52 −ζ5−2 −ζ5 −ζ5−1 ζ5−2 ζ52 ζ5 ζ5−1 ζ52 ζ5−2 ζ5 ζ5−1 −ζ5−1 −ζ5 −ζ5−2 −ζ52 −ζ5−1 −ζ5 −ζ52 −ζ5−2
30.4.1f4 C 1 −1 1 1 ζ5 ζ5−1 ζ52 ζ5−2 −1 −1 −ζ5−2 −ζ52 −ζ5−1 −ζ5 ζ52 ζ5−2 ζ5−1 ζ5 ζ5−2 ζ52 ζ5−1 ζ5 −ζ5 −ζ5−1 −ζ52 −ζ5−2 −ζ5 −ζ5−1 −ζ5−2 −ζ52
30.4.1g1 C 1 1 ζ15−5 ζ155 ζ15−6 ζ156 ζ153 ζ15−3 ζ155 ζ15−5 ζ15−3 ζ153 ζ156 ζ15−6 ζ15−7 ζ157 ζ15 ζ15−1 ζ152 ζ15−2 ζ15−4 ζ154 ζ154 ζ15−4 ζ15−2 ζ152 ζ15−1 ζ15 ζ157 ζ15−7
30.4.1g2 C 1 1 ζ155 ζ15−5 ζ156 ζ15−6 ζ15−3 ζ153 ζ15−5 ζ155 ζ153 ζ15−3 ζ15−6 ζ156 ζ157 ζ15−7 ζ15−1 ζ15 ζ15−2 ζ152 ζ154 ζ15−4 ζ15−4 ζ154 ζ152 ζ15−2 ζ15 ζ15−1 ζ15−7 ζ157
30.4.1g3 C 1 1 ζ15−5 ζ155 ζ156 ζ15−6 ζ15−3 ζ153 ζ155 ζ15−5 ζ153 ζ15−3 ζ15−6 ζ156 ζ152 ζ15−2 ζ154 ζ15−4 ζ15−7 ζ157 ζ15−1 ζ15 ζ15 ζ15−1 ζ157 ζ15−7 ζ15−4 ζ154 ζ15−2 ζ152
30.4.1g4 C 1 1 ζ155 ζ15−5 ζ15−6 ζ156 ζ153 ζ15−3 ζ15−5 ζ155 ζ15−3 ζ153 ζ156 ζ15−6 ζ15−2 ζ152 ζ15−4 ζ154 ζ157 ζ15−7 ζ15 ζ15−1 ζ15−1 ζ15 ζ15−7 ζ157 ζ154 ζ15−4 ζ152 ζ15−2
30.4.1g5 C 1 1 ζ15−5 ζ155 ζ15−3 ζ153 ζ15−6 ζ156 ζ155 ζ15−5 ζ156 ζ15−6 ζ153 ζ15−3 ζ15−1 ζ15 ζ15−2 ζ152 ζ15−4 ζ154 ζ15−7 ζ157 ζ157 ζ15−7 ζ154 ζ15−4 ζ152 ζ15−2 ζ15 ζ15−1
30.4.1g6 C 1 1 ζ155 ζ15−5 ζ153 ζ15−3 ζ156 ζ15−6 ζ15−5 ζ155 ζ15−6 ζ156 ζ15−3 ζ153 ζ15 ζ15−1 ζ152 ζ15−2 ζ154 ζ15−4 ζ157 ζ15−7 ζ15−7 ζ157 ζ15−4 ζ154 ζ15−2 ζ152 ζ15−1 ζ15
30.4.1g7 C 1 1 ζ15−5 ζ155 ζ153 ζ15−3 ζ156 ζ15−6 ζ155 ζ15−5 ζ15−6 ζ156 ζ15−3 ζ153 ζ15−4 ζ154 ζ157 ζ15−7 ζ15−1 ζ15 ζ152 ζ15−2 ζ15−2 ζ152 ζ15 ζ15−1 ζ15−7 ζ157 ζ154 ζ15−4
30.4.1g8 C 1 1 ζ155 ζ15−5 ζ15−3 ζ153 ζ15−6 ζ156 ζ15−5 ζ155 ζ156 ζ15−6 ζ153 ζ15−3 ζ154 ζ15−4 ζ15−7 ζ157 ζ15 ζ15−1 ζ15−2 ζ152 ζ152 ζ15−2 ζ15−1 ζ15 ζ157 ζ15−7 ζ15−4 ζ154
30.4.1h1 C 1 −1 ζ15−5 ζ155 ζ15−6 ζ156 ζ153 ζ15−3 −ζ155 −ζ15−5 −ζ15−3 −ζ153 −ζ156 −ζ15−6 ζ15−7 ζ157 ζ15 ζ15−1 ζ152 ζ15−2 ζ15−4 ζ154 −ζ154 −ζ15−4 −ζ15−2 −ζ152 −ζ15−1 −ζ15 −ζ157 −ζ15−7
30.4.1h2 C 1 −1 ζ155 ζ15−5 ζ156 ζ15−6 ζ15−3 ζ153 −ζ15−5 −ζ155 −ζ153 −ζ15−3 −ζ15−6 −ζ156 ζ157 ζ15−7 ζ15−1 ζ15 ζ15−2 ζ152 ζ154 ζ15−4 −ζ15−4 −ζ154 −ζ152 −ζ15−2 −ζ15 −ζ15−1 −ζ15−7 −ζ157
30.4.1h3 C 1 −1 ζ15−5 ζ155 ζ156 ζ15−6 ζ15−3 ζ153 −ζ155 −ζ15−5 −ζ153 −ζ15−3 −ζ15−6 −ζ156 ζ152 ζ15−2 ζ154 ζ15−4 ζ15−7 ζ157 ζ15−1 ζ15 −ζ15 −ζ15−1 −ζ157 −ζ15−7 −ζ15−4 −ζ154 −ζ15−2 −ζ152
30.4.1h4 C 1 −1 ζ155 ζ15−5 ζ15−6 ζ156 ζ153 ζ15−3 −ζ15−5 −ζ155 −ζ15−3 −ζ153 −ζ156 −ζ15−6 ζ15−2 ζ152 ζ15−4 ζ154 ζ157 ζ15−7 ζ15 ζ15−1 −ζ15−1 −ζ15 −ζ15−7 −ζ157 −ζ154 −ζ15−4 −ζ152 −ζ15−2
30.4.1h5 C 1 −1 ζ15−5 ζ155 ζ15−3 ζ153 ζ15−6 ζ156 −ζ155 −ζ15−5 −ζ156 −ζ15−6 −ζ153 −ζ15−3 ζ15−1 ζ15 ζ15−2 ζ152 ζ15−4 ζ154 ζ15−7 ζ157 −ζ157 −ζ15−7 −ζ154 −ζ15−4 −ζ152 −ζ15−2 −ζ15 −ζ15−1
30.4.1h6 C 1 −1 ζ155 ζ15−5 ζ153 ζ15−3 ζ156 ζ15−6 −ζ15−5 −ζ155 −ζ15−6 −ζ156 −ζ15−3 −ζ153 ζ15 ζ15−1 ζ152 ζ15−2 ζ154 ζ15−4 ζ157 ζ15−7 −ζ15−7 −ζ157 −ζ15−4 −ζ154 −ζ15−2 −ζ152 −ζ15−1 −ζ15
30.4.1h7 C 1 −1 ζ15−5 ζ155 ζ153 ζ15−3 ζ156 ζ15−6 −ζ155 −ζ15−5 −ζ15−6 −ζ156 −ζ15−3 −ζ153 ζ15−4 ζ154 ζ157 ζ15−7 ζ15−1 ζ15 ζ152 ζ15−2 −ζ15−2 −ζ152 −ζ15 −ζ15−1 −ζ15−7 −ζ157 −ζ154 −ζ15−4
30.4.1h8 C 1 −1 ζ155 ζ15−5 ζ15−3 ζ153 ζ15−6 ζ156 −ζ15−5 −ζ155 −ζ156 −ζ15−6 −ζ153 −ζ15−3 ζ154 ζ15−4 ζ15−7 ζ157 ζ15 ζ15−1 ζ15−2 ζ152 −ζ152 −ζ15−2 −ζ15−1 −ζ15 −ζ157 −ζ15−7 −ζ15−4 −ζ154

Copy content comment:Character table
 
Copy content magma:CharacterTable(G);
 
Copy content sage:G.character_table()
 
Copy content oscar:character_table(G)
 
Copy content gap:CharacterTable(G);
 

Regular extensions

Data not computed