Properties

Label 35T32
35T32 1 26 1->26 27 1->27 2 30 2->30 2->30 3 3->26 28 3->28 4 29 4->29 4->29 5 5->27 5->28 6 8 6->8 22 6->22 7 24 7->24 10 8->10 21 8->21 9 25 9->25 10->6 23 10->23 11 13 11->13 20 11->20 12 12->11 18 12->18 14 13->14 16 13->16 15 14->15 17 14->17 15->12 19 15->19 16->1 32 16->32 17->2 33 17->33 18->4 31 18->31 19->5 35 19->35 20->3 34 20->34 21->3 21->6 22->1 22->7 23->4 23->9 24->2 24->10 25->5 25->8 26->22 26->31 27->25 27->32 28->21 28->33 29->23 29->34 30->24 30->35 31->12 31->17 32->13 32->20 33->14 33->16 34->11 34->19 35->15 35->18
Degree $35$
Order $10080$
Cyclic no
Abelian no
Solvable no
Transitivity $1$
Primitive no
$p$-group no
Group: $A_5\times \GL(3,2)$

Related objects

Downloads

Learn more

Show commands: Gap / Magma / Oscar / SageMath

Copy content comment:Define the Galois group
 
Copy content magma:G := TransitiveGroup(35, 32);
 
Copy content sage:G = TransitiveGroup(35, 32)
 
Copy content oscar:G = transitive_group(35, 32)
 
Copy content gap:G := TransitiveGroup(35, 32);
 

Group invariants

Abstract group:  $A_5\times \GL(3,2)$
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:  $10080=2^{5} \cdot 3^{2} \cdot 5 \cdot 7$
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:  no
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:  no
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:  no
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:   not nilpotent
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 $n$:  $35$
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 $t$:  $32$
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);
 
$\card{\Aut(F/K)}$:  $1$
Copy content comment:Order of the centralizer of G in S_n
 
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Copy content sage:SymmetricGroup(35).centralizer(G).order()
 
Copy content oscar:order(centralizer(symmetric_group(35), G)[1])
 
Copy content gap:Order(Centralizer(SymmetricGroup(35), G));
 
Generators:  $(1,26,22)(2,30,24)(3,28,21)(4,29,23)(5,27,25)(6,8,10)(11,20,34)(12,18,31)(13,16,32)(14,17,33)(15,19,35)$, $(1,27,32,20,3,26,31,17,2,30,35,18,4,29,34,19,5,28,33,16)(6,22,7,24,10,23,9,25,8,21)(11,13,14,15,12)$
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)
$60$:  $A_5$
$168$:  $\GL(3,2)$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 5: $A_5$

Degree 7: $\GL(3,2)$

Low degree siblings

35T32, 40T5863, 42T552 x 2

Siblings are shown with degree $\leq 47$

A number field with this Galois group has exactly one arithmetically equivalent field.

Conjugacy classes

LabelCycle TypeSizeOrderIndexRepresentative
1A $1^{35}$ $1$ $1$ $0$ $()$
2A $2^{14},1^{7}$ $15$ $2$ $14$ $( 2, 5)( 3, 4)( 6, 8)( 7,10)(11,14)(12,13)(16,17)(18,20)(21,25)(23,24)(27,29)(28,30)(31,33)(32,34)$
2B $2^{10},1^{15}$ $21$ $2$ $10$ $( 6,34)( 7,31)( 8,32)( 9,35)(10,33)(11,17)(12,18)(13,20)(14,16)(15,19)$
2C $2^{16},1^{3}$ $315$ $2$ $16$ $( 1,32)( 2,33)( 3,31)( 4,35)( 5,34)( 6, 7)( 8, 9)(11,15)(12,14)(16,27)(17,26)(18,30)(19,28)(20,29)(22,24)(23,25)$
3A $3^{7},1^{14}$ $20$ $3$ $14$ $( 3, 5, 4)( 6, 7, 8)(11,14,12)(16,18,17)(23,25,24)(27,28,30)(31,32,34)$
3B $3^{10},1^{5}$ $56$ $3$ $20$ $( 6,23,34)( 7,25,31)( 8,24,32)( 9,22,35)(10,21,33)(11,17,28)(12,18,27)(13,20,29)(14,16,30)(15,19,26)$
3C $3^{11},1^{2}$ $1120$ $3$ $22$ $( 1,19,15)( 2,18,14)( 3,20,12)( 4,17,11)( 5,16,13)( 6,29,31)( 7,30,33)( 8,28,32)( 9,26,35)(10,27,34)(21,25,23)$
4A $4^{5},2^{5},1^{5}$ $42$ $4$ $20$ $( 1,22)( 2,21)( 3,23)( 4,24)( 5,25)( 6,16,34,14)( 7,18,31,12)( 8,17,32,11)( 9,19,35,15)(10,20,33,13)$
4B $4^{5},2^{7},1$ $630$ $4$ $22$ $( 1,24)( 2,23)( 3,21)( 4,22)( 5,25)( 6,20,34,13)( 7,18,31,12)( 8,19,32,15)( 9,17,35,11)(10,16,33,14)(26,28)(29,30)$
5A1 $5^{7}$ $12$ $5$ $28$ $( 1, 2, 5, 3, 4)( 6, 8, 9,10, 7)(11,15,13,12,14)(16,17,19,20,18)(21,25,23,24,22)(26,29,27,30,28)(31,34,32,35,33)$
5A2 $5^{7}$ $12$ $5$ $28$ $( 1, 5, 4, 2, 3)( 6, 9, 7, 8,10)(11,13,14,15,12)(16,19,18,17,20)(21,23,22,25,24)(26,27,28,29,30)(31,32,33,34,35)$
6A $6^{2},3^{3},2^{4},1^{6}$ $420$ $6$ $20$ $( 3, 4, 5)( 6,28, 7,30, 8,27)( 9,26)(10,29)(11,12,14)(16,24,18,23,17,25)(19,22)(20,21)(31,34,32)$
6B $6^{4},3^{2},2^{2},1$ $840$ $6$ $26$ $( 1,15, 9)( 2,12,10, 5,13, 7)( 3,11, 6, 4,14, 8)(16,32,23,17,34,24)(18,33,25,20,31,21)(19,35,22)(27,29)(28,30)$
7A1 $7^{5}$ $24$ $7$ $30$ $( 1,35,26,22,19,15, 9)( 2,33,29,21,20,13,10)( 3,34,30,23,16,14, 6)( 4,32,28,24,17,11, 8)( 5,31,27,25,18,12, 7)$
7A-1 $7^{5}$ $24$ $7$ $30$ $( 1, 9,15,19,22,26,35)( 2,10,13,20,21,29,33)( 3, 6,14,16,23,30,34)( 4, 8,11,17,24,28,32)( 5, 7,12,18,25,27,31)$
10A1 $10^{2},5^{3}$ $252$ $10$ $30$ $( 1, 5, 2, 4, 3)( 6,35, 7,33, 8,34, 9,31,10,32)(11,16,15,18,13,17,14,19,12,20)(21,24,23,22,25)(26,27,29,28,30)$
10A3 $10^{2},5^{3}$ $252$ $10$ $30$ $( 1, 4, 5, 3, 2)( 6,33, 9,32, 7,34,10,35, 8,31)(11,18,14,20,15,17,12,16,13,19)(21,22,24,25,23)(26,28,27,30,29)$
12A $12,6,4^{2},3,2^{2},1^{2}$ $840$ $12$ $26$ $( 1,15)( 2,13)( 3,12, 4,14, 5,11)( 6,25,28,16, 7,24,30,18, 8,23,27,17)( 9,22,26,19)(10,21,29,20)(31,32,34)$
14A1 $14^{2},7$ $360$ $14$ $32$ $( 1,14,22,30,19,34, 9, 3,15,23,26,16,35, 6)( 2,13,21,29,20,33,10)( 4,12,24,27,17,31, 8, 5,11,25,28,18,32, 7)$
14A-1 $14^{2},7$ $360$ $14$ $32$ $( 1, 6,35,16,26,23,15, 3, 9,34,19,30,22,14)( 2,10,33,20,29,21,13)( 4, 7,32,18,28,25,11, 5, 8,31,17,27,24,12)$
15A1 $15^{2},5$ $672$ $15$ $32$ $( 1, 4, 5, 3, 2)( 6,33,22, 8,31,23,10,35,24, 7,34,21, 9,32,25)(11,27,16,13,26,17,12,30,20,15,28,18,14,29,19)$
15A2 $15^{2},5$ $672$ $15$ $32$ $( 1, 5, 2, 4, 3)( 6,22,31,10,24,34, 9,25,33, 8,23,35, 7,21,32)(11,16,26,12,20,28,14,19,27,13,17,30,15,18,29)$
20A1 $20,10,5$ $504$ $20$ $32$ $( 1,24, 5,23, 2,22, 4,25, 3,21)( 6,20,35,11, 7,16,33,15, 8,18,34,13, 9,17,31,14,10,19,32,12)(26,28,27,30,29)$
20A3 $20,10,5$ $504$ $20$ $32$ $( 1,23, 4,21, 5,22, 3,24, 2,25)( 6,11,33,18, 9,14,32,20, 7,15,34,17,10,12,35,16, 8,13,31,19)(26,30,28,29,27)$
21A1 $21,7^{2}$ $480$ $21$ $32$ $( 1,22,19, 9,15,26,35)( 2,24,16,10,11,30,33, 4,23,20, 8,14,29,32, 3,21,17, 6,13,28,34)( 5,25,18, 7,12,27,31)$
21A-1 $21,7^{2}$ $480$ $21$ $32$ $( 1,35,26,15, 9,19,22)( 2,34,28,13, 6,17,21, 3,32,29,14, 8,20,23, 4,33,30,11,10,16,24)( 5,31,27,12, 7,18,25)$
35A1 $35$ $288$ $35$ $34$ $( 1,23,10,28,12,35,16, 2,24, 7,26,14,33,17, 5,22, 6,29,11,31,19, 3,21, 8,27,15,34,20, 4,25, 9,30,13,32,18)$
35A-1 $35$ $288$ $35$ $34$ $( 1,18,32,13,30, 9,25, 4,20,34,15,27, 8,21, 3,19,31,11,29, 6,22, 5,17,33,14,26, 7,24, 2,16,35,12,28,10,23)$
35A2 $35$ $288$ $35$ $34$ $( 1,10,12,16,24,26,33, 5, 6,11,19,21,27,34, 4, 9,13,18,23,28,35, 2, 7,14,17,22,29,31, 3, 8,15,20,25,30,32)$
35A-2 $35$ $288$ $35$ $34$ $( 1,32,30,25,20,15, 8, 3,31,29,22,17,14, 7, 2,35,28,23,18,13, 9, 4,34,27,21,19,11, 6, 5,33,26,24,16,12,10)$

Malle's constant $a(G)$:     $1/10$

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 2B 2C 3A 3B 3C 4A 4B 5A1 5A2 6A 6B 7A1 7A-1 10A1 10A3 12A 14A1 14A-1 15A1 15A2 20A1 20A3 21A1 21A-1 35A1 35A-1 35A2 35A-2
Size 1 15 21 315 20 56 1120 42 630 12 12 420 840 24 24 252 252 840 360 360 672 672 504 504 480 480 288 288 288 288
2 P 1A 1A 1A 1A 3A 3B 3C 2B 2B 5A2 5A1 3A 3B 7A1 7A-1 5A2 5A1 6A 7A1 7A-1 15A2 15A1 10A1 10A3 21A1 21A-1 35A2 35A-2 35A1 35A-1
3 P 1A 2A 2B 2C 1A 1A 1A 4A 4B 5A2 5A1 2B 2A 7A-1 7A1 10A3 10A1 4A 14A-1 14A1 5A1 5A2 20A3 20A1 7A-1 7A1 35A-2 35A2 35A-1 35A1
5 P 1A 2A 2B 2C 3A 3B 3C 4A 4B 1A 1A 6A 6B 7A-1 7A1 2B 2B 12A 14A-1 14A1 3B 3B 4A 4A 21A-1 21A1 7A1 7A-1 7A1 7A-1
7 P 1A 2A 2B 2C 3A 3B 3C 4A 4B 5A2 5A1 6A 6B 1A 1A 10A3 10A1 12A 2A 2A 15A2 15A1 20A3 20A1 3A 3A 5A1 5A1 5A2 5A2
Type
10080.p.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
10080.p.3a1 R 3 −1 3 −1 0 3 0 3 −1 −ζ5−1−ζ5 −ζ5−2−ζ52 0 −1 3 3 −ζ5−1−ζ5 −ζ5−2−ζ52 0 −1 −1 −ζ5−2−ζ52 −ζ5−1−ζ5 −ζ5−2−ζ52 −ζ5−1−ζ5 0 0 −ζ5−2−ζ52 −ζ5−2−ζ52 −ζ5−1−ζ5 −ζ5−1−ζ5
10080.p.3a2 R 3 −1 3 −1 0 3 0 3 −1 −ζ5−2−ζ52 −ζ5−1−ζ5 0 −1 3 3 −ζ5−2−ζ52 −ζ5−1−ζ5 0 −1 −1 −ζ5−1−ζ5 −ζ5−2−ζ52 −ζ5−1−ζ5 −ζ5−2−ζ52 0 0 −ζ5−1−ζ5 −ζ5−1−ζ5 −ζ5−2−ζ52 −ζ5−2−ζ52
10080.p.3b1 C 3 3 −1 −1 3 0 0 1 1 3 3 −1 0 −ζ7−3−1−ζ7−ζ72 ζ7−3+ζ7+ζ72 −1 −1 1 −ζ7−3−1−ζ7−ζ72 ζ7−3+ζ7+ζ72 0 0 1 1 −ζ7−3−1−ζ7−ζ72 ζ7−3+ζ7+ζ72 ζ7−3+ζ7+ζ72 −ζ7−3−1−ζ7−ζ72 ζ7−3+ζ7+ζ72 −ζ7−3−1−ζ7−ζ72
10080.p.3b2 C 3 3 −1 −1 3 0 0 1 1 3 3 −1 0 ζ7−3+ζ7+ζ72 −ζ7−3−1−ζ7−ζ72 −1 −1 1 ζ7−3+ζ7+ζ72 −ζ7−3−1−ζ7−ζ72 0 0 1 1 ζ7−3+ζ7+ζ72 −ζ7−3−1−ζ7−ζ72 −ζ7−3−1−ζ7−ζ72 ζ7−3+ζ7+ζ72 −ζ7−3−1−ζ7−ζ72 ζ7−3+ζ7+ζ72
10080.p.4a R 4 0 4 0 1 4 1 4 0 −1 −1 1 0 4 4 −1 −1 1 0 0 −1 −1 −1 −1 1 1 −1 −1 −1 −1
10080.p.5a R 5 1 5 1 −1 5 −1 5 1 0 0 −1 1 5 5 0 0 −1 1 1 0 0 0 0 −1 −1 0 0 0 0
10080.p.6a R 6 6 2 2 6 0 0 0 0 6 6 2 0 −1 −1 2 2 0 −1 −1 0 0 0 0 −1 −1 −1 −1 −1 −1
10080.p.7a R 7 7 −1 −1 7 1 1 −1 −1 7 7 −1 1 0 0 −1 −1 −1 0 0 1 1 −1 −1 0 0 0 0 0 0
10080.p.8a R 8 8 0 0 8 −1 −1 0 0 8 8 0 −1 1 1 0 0 0 1 1 −1 −1 0 0 1 1 1 1 1 1
10080.p.9a1 C 9 −3 −3 1 0 0 0 3 −1 −3ζ35−7−3ζ357 −3ζ35−14−3ζ3514 0 0 −3ζ35−15−3−3ζ355−3ζ3510 3ζ35−15+3ζ355+3ζ3510 ζ35−7+ζ357 ζ35−14+ζ3514 0 ζ35−15+1+ζ355+ζ3510 −ζ35−15−ζ355−ζ3510 0 0 −ζ35−14−ζ3514 −ζ35−7−ζ357 0 0 ζ35−14−ζ35−13+ζ354−ζ358+ζ359+ζ3511+ζ3514−ζ3515+ζ3516 ζ35−13−ζ354+ζ358−ζ359−ζ3511+ζ3515−ζ3516 −ζ35−14+ζ35−13−ζ35−10−ζ35−5−1−ζ354+ζ358−ζ359−ζ3511−ζ3514−ζ3516 −ζ35−13+ζ35−10+ζ35−5+ζ354−ζ358+ζ359+ζ3511+ζ3516
10080.p.9a2 C 9 −3 −3 1 0 0 0 3 −1 −3ζ35−7−3ζ357 −3ζ35−14−3ζ3514 0 0 3ζ35−15+3ζ355+3ζ3510 −3ζ35−15−3−3ζ355−3ζ3510 ζ35−7+ζ357 ζ35−14+ζ3514 0 −ζ35−15−ζ355−ζ3510 ζ35−15+1+ζ355+ζ3510 0 0 −ζ35−14−ζ3514 −ζ35−7−ζ357 0 0 ζ35−13−ζ354+ζ358−ζ359−ζ3511+ζ3515−ζ3516 ζ35−14−ζ35−13+ζ354−ζ358+ζ359+ζ3511+ζ3514−ζ3515+ζ3516 −ζ35−13+ζ35−10+ζ35−5+ζ354−ζ358+ζ359+ζ3511+ζ3516 −ζ35−14+ζ35−13−ζ35−10−ζ35−5−1−ζ354+ζ358−ζ359−ζ3511−ζ3514−ζ3516
10080.p.9a3 C 9 −3 −3 1 0 0 0 3 −1 −3ζ35−14−3ζ3514 −3ζ35−7−3ζ357 0 0 −3ζ35−15−3−3ζ355−3ζ3510 3ζ35−15+3ζ355+3ζ3510 ζ35−14+ζ3514 ζ35−7+ζ357 0 ζ35−15+1+ζ355+ζ3510 −ζ35−15−ζ355−ζ3510 0 0 −ζ35−7−ζ357 −ζ35−14−ζ3514 0 0 −ζ35−14+ζ35−13−ζ35−10−ζ35−5−1−ζ354+ζ358−ζ359−ζ3511−ζ3514−ζ3516 −ζ35−13+ζ35−10+ζ35−5+ζ354−ζ358+ζ359+ζ3511+ζ3516 ζ35−14−ζ35−13+ζ354−ζ358+ζ359+ζ3511+ζ3514−ζ3515+ζ3516 ζ35−13−ζ354+ζ358−ζ359−ζ3511+ζ3515−ζ3516
10080.p.9a4 C 9 −3 −3 1 0 0 0 3 −1 −3ζ35−14−3ζ3514 −3ζ35−7−3ζ357 0 0 3ζ35−15+3ζ355+3ζ3510 −3ζ35−15−3−3ζ355−3ζ3510 ζ35−14+ζ3514 ζ35−7+ζ357 0 −ζ35−15−ζ355−ζ3510 ζ35−15+1+ζ355+ζ3510 0 0 −ζ35−7−ζ357 −ζ35−14−ζ3514 0 0 −ζ35−13+ζ35−10+ζ35−5+ζ354−ζ358+ζ359+ζ3511+ζ3516 −ζ35−14+ζ35−13−ζ35−10−ζ35−5−1−ζ354+ζ358−ζ359−ζ3511−ζ3514−ζ3516 ζ35−13−ζ354+ζ358−ζ359−ζ3511+ζ3515−ζ3516 ζ35−14−ζ35−13+ζ354−ζ358+ζ359+ζ3511+ζ3514−ζ3515+ζ3516
10080.p.12a1 C 12 0 −4 0 3 0 0 4 0 −3 −3 −1 0 −4ζ7−3−4−4ζ7−4ζ72 4ζ7−3+4ζ7+4ζ72 1 1 1 0 0 0 0 −1 −1 −ζ7−3−1−ζ7−ζ72 ζ7−3+ζ7+ζ72 −ζ7−3−ζ7−ζ72 ζ7−3+1+ζ7+ζ72 −ζ7−3−ζ7−ζ72 ζ7−3+1+ζ7+ζ72
10080.p.12a2 C 12 0 −4 0 3 0 0 4 0 −3 −3 −1 0 4ζ7−3+4ζ7+4ζ72 −4ζ7−3−4−4ζ7−4ζ72 1 1 1 0 0 0 0 −1 −1 ζ7−3+ζ7+ζ72 −ζ7−3−1−ζ7−ζ72 ζ7−3+1+ζ7+ζ72 −ζ7−3−ζ7−ζ72 ζ7−3+1+ζ7+ζ72 −ζ7−3−ζ7−ζ72
10080.p.15a1 C 15 3 −5 −1 −3 0 0 5 1 0 0 1 0 −5ζ7−3−5−5ζ7−5ζ72 5ζ7−3+5ζ7+5ζ72 0 0 −1 −ζ7−3−1−ζ7−ζ72 ζ7−3+ζ7+ζ72 0 0 0 0 ζ7−3+1+ζ7+ζ72 −ζ7−3−ζ7−ζ72 0 0 0 0
10080.p.15a2 C 15 3 −5 −1 −3 0 0 5 1 0 0 1 0 5ζ7−3+5ζ7+5ζ72 −5ζ7−3−5−5ζ7−5ζ72 0 0 −1 ζ7−3+ζ7+ζ72 −ζ7−3−1−ζ7−ζ72 0 0 0 0 −ζ7−3−ζ7−ζ72 ζ7−3+1+ζ7+ζ72 0 0 0 0
10080.p.18a1 R 18 −6 6 −2 0 0 0 0 0 −6ζ5−1−6ζ5 −6ζ5−2−6ζ52 0 0 −3 −3 −2ζ5−1−2ζ5 −2ζ5−2−2ζ52 0 1 1 0 0 0 0 0 0 ζ5−2+ζ52 ζ5−2+ζ52 ζ5−1+ζ5 ζ5−1+ζ5
10080.p.18a2 R 18 −6 6 −2 0 0 0 0 0 −6ζ5−2−6ζ52 −6ζ5−1−6ζ5 0 0 −3 −3 −2ζ5−2−2ζ52 −2ζ5−1−2ζ5 0 1 1 0 0 0 0 0 0 ζ5−1+ζ5 ζ5−1+ζ5 ζ5−2+ζ52 ζ5−2+ζ52
10080.p.21a1 R 21 −7 −3 1 0 3 0 −3 1 −7ζ5−1−7ζ5 −7ζ5−2−7ζ52 0 −1 0 0 ζ5−1+ζ5 ζ5−2+ζ52 0 0 0 −ζ5−2−ζ52 −ζ5−1−ζ5 ζ5−2+ζ52 ζ5−1+ζ5 0 0 0 0 0 0
10080.p.21a2 R 21 −7 −3 1 0 3 0 −3 1 −7ζ5−2−7ζ52 −7ζ5−1−7ζ5 0 −1 0 0 ζ5−2+ζ52 ζ5−1+ζ5 0 0 0 −ζ5−1−ζ5 −ζ5−2−ζ52 ζ5−1+ζ5 ζ5−2+ζ52 0 0 0 0 0 0
10080.p.24a R 24 0 8 0 6 0 0 0 0 −6 −6 2 0 −4 −4 −2 −2 0 0 0 0 0 0 0 −1 −1 1 1 1 1
10080.p.24b1 R 24 −8 0 0 0 −3 0 0 0 −8ζ5−1−8ζ5 −8ζ5−2−8ζ52 0 1 3 3 0 0 0 −1 −1 ζ5−2+ζ52 ζ5−1+ζ5 0 0 0 0 −ζ5−2−ζ52 −ζ5−2−ζ52 −ζ5−1−ζ5 −ζ5−1−ζ5
10080.p.24b2 R 24 −8 0 0 0 −3 0 0 0 −8ζ5−2−8ζ52 −8ζ5−1−8ζ5 0 1 3 3 0 0 0 −1 −1 ζ5−1+ζ5 ζ5−2+ζ52 0 0 0 0 −ζ5−1−ζ5 −ζ5−1−ζ5 −ζ5−2−ζ52 −ζ5−2−ζ52
10080.p.28a R 28 0 −4 0 7 4 1 −4 0 −7 −7 −1 0 0 0 1 1 −1 0 0 −1 −1 1 1 0 0 0 0 0 0
10080.p.30a R 30 6 10 2 −6 0 0 0 0 0 0 −2 0 −5 −5 0 0 0 −1 −1 0 0 0 0 1 1 0 0 0 0
10080.p.32a R 32 0 0 0 8 −4 −1 0 0 −8 −8 0 0 4 4 0 0 0 0 0 1 1 0 0 1 1 −1 −1 −1 −1
10080.p.35a R 35 7 −5 −1 −7 5 −1 −5 −1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
10080.p.40a R 40 8 0 0 −8 −5 1 0 0 0 0 0 −1 5 5 0 0 0 1 1 0 0 0 0 −1 −1 0 0 0 0

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