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Properties

Label 33T12
Degree $33$
Order $726$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{11}^2:C_6$

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Show commands: Magma

magma: G := TransitiveGroup(33, 12);
 

Group action invariants

Degree $n$:  $33$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $12$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $C_{11}^2:C_6$
Parity:  $-1$
magma: IsEven(G);
 
Primitive:  no
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $1$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,19,25)(2,12,30)(3,16,24)(4,20,29)(5,13,23)(6,17,28)(7,21,33)(8,14,27)(9,18,32)(10,22,26)(11,15,31), (1,25,18,5,27,12)(2,31,22,4,32,19)(3,26,15)(6,33,16,11,30,14)(7,28,20,10,24,21)(8,23,13,9,29,17)
magma: Generators(G);
 

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$6$:  $C_6$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 11: None

Low degree siblings

33T12 x 3

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

LabelCycle TypeSizeOrderRepresentative
$ 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, 1, 1, 1 $ $1$ $1$ $()$
$ 11, 11, 11 $ $6$ $11$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,21,19,17,15,13,22,20,18,16,14) (23,32,30,28,26,24,33,31,29,27,25)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,19,15,22,18,14,21,17,13,20,16) (23,30,26,33,29,25,32,28,24,31,27)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,15,18,21,13,16,19,22,14,17,20) (23,26,29,32,24,27,30,33,25,28,31)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,18,13,19,14,20,15,21,16,22,17) (23,29,24,30,25,31,26,32,27,33,28)$
$ 11, 11, 11 $ $6$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,13,14,15,16,17,18,19,20,21,22) (23,24,25,26,27,28,29,30,31,32,33)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $11$ $(12,13,14,15,16,17,18,19,20,21,22)(23,30,26,33,29,25,32,28,24,31,27)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,22,21,20,19,18,17,16,15,14,13) (23,28,33,27,32,26,31,25,30,24,29)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,19,15,22,18,14,21,17,13,20,16) (23,25,27,29,31,33,24,26,28,30,32)$
$ 11, 11, 11 $ $6$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,14,16,18,20,22,13,15,17,19,21) (23,31,28,25,33,30,27,24,32,29,26)$
$ 11, 11, 11 $ $6$ $11$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,15,18,21,13,16,19,22,14,17,20) (23,32,30,28,26,24,33,31,29,27,25)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $11$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,17,22,16,21,15,20,14,19,13,18)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,21,19,17,15,13,22,20,18,16,14) (23,27,31,24,28,32,25,29,33,26,30)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(23,29,24,30,25,31,26,32,27,33,28)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $11$ $(12,14,16,18,20,22,13,15,17,19,21)(23,26,29,32,24,27,30,33,25,28,31)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $11$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(23,24,25,26,27,28,29,30,31,32,33)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,21,19,17,15,13,22,20,18,16,14) (23,33,32,31,30,29,28,27,26,25,24)$
$ 11, 11, 11 $ $6$ $11$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,16,20,13,17,21,14,18,22,15,19) (23,28,33,27,32,26,31,25,30,24,29)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,18,13,19,14,20,15,21,16,22,17) (23,30,26,33,29,25,32,28,24,31,27)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,19,15,22,18,14,21,17,13,20,16) (23,32,30,28,26,24,33,31,29,27,25)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,15,18,21,13,16,19,22,14,17,20) (23,30,26,33,29,25,32,28,24,31,27)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $121$ $3$ $( 1,19,25)( 2,12,30)( 3,16,24)( 4,20,29)( 5,13,23)( 6,17,28)( 7,21,33) ( 8,14,27)( 9,18,32)(10,22,26)(11,15,31)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $121$ $3$ $( 1,25,19)( 2,30,12)( 3,24,16)( 4,29,20)( 5,23,13)( 6,28,17)( 7,33,21) ( 8,27,14)( 9,32,18)(10,26,22)(11,31,15)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1 $ $121$ $2$ $( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)(17,18)(23,29) (24,28)(25,27)(30,33)(31,32)$
$ 6, 6, 6, 6, 6, 3 $ $121$ $6$ $( 1,19,24, 6,21,27)( 2,15,29, 5,14,33)( 3,22,23, 4,18,28)( 7,17,32,11,12,30) ( 8,13,26,10,16,25)( 9,20,31)$
$ 6, 6, 6, 6, 6, 3 $ $121$ $6$ $( 1,25,14, 7,28,16)( 2,31,18, 6,33,12)( 3,26,22, 5,27,19)( 4,32,15) ( 8,23,20,11,30,21)( 9,29,13,10,24,17)$

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $726=2 \cdot 3 \cdot 11^{2}$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  726.6
magma: IdentifyGroup(G);
 
Character table:

1A 2A 3A1 3A-1 6A1 6A-1 11A1 11A2 11A3 11A4 11A5 11B1 11B2 11B3 11B4 11B5 11C1 11C2 11C3 11C4 11C5 11D1 11D2 11D3 11D4 11D5
Size 1 121 121 121 121 121 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
2 P 1A 1A 3A-1 3A1 3A1 3A-1 11A1 11B2 11A5 11D4 11A3 11C3 11C2 11B1 11D5 11B4 11C4 11A4 11D1 11B5 11B3 11D3 11C5 11C1 11A2 11D2
3 P 1A 2A 1A 1A 2A 2A 11A4 11B3 11A2 11D5 11A1 11C1 11C3 11B4 11D2 11B5 11C5 11A5 11D4 11B2 11B1 11D1 11C2 11C4 11A3 11D3
11 P 1A 2A 3A-1 3A1 6A-1 6A1 11A3 11B5 11A4 11D1 11A2 11C2 11C5 11B3 11D4 11B1 11C1 11A1 11D3 11B4 11B2 11D2 11C4 11C3 11A5 11D5
Type
726.6.1a 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
726.6.1b 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
726.6.1c1 C 1 1 ζ3−1 ζ3 ζ3 ζ3−1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
726.6.1c2 C 1 1 ζ3 ζ3−1 ζ3−1 ζ3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
726.6.1d1 C 1 −1 ζ3−1 ζ3 −ζ3 −ζ3−1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
726.6.1d2 C 1 −1 ζ3 ζ3−1 −ζ3−1 −ζ3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
726.6.6a1 R 6 0 0 0 0 0 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−4−1−ζ114−ζ115 ζ11−5+2ζ11−3+2ζ113+ζ115 2ζ11−5+ζ11−1+ζ11+2ζ115 ζ11−4+2ζ11−2+2ζ112+ζ114 ζ11−2+2ζ11−1+2ζ11+ζ112 2ζ11−4+ζ11−3+ζ113+2ζ114 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−4−1−ζ114−ζ115 2ζ11−1+2+2ζ11 2ζ11−2+2+2ζ112 2ζ11−3+2+2ζ113 2ζ11−4+2+2ζ114 2ζ11−5+2+2ζ115
726.6.6a2 R 6 0 0 0 0 0 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 ζ11−4+2ζ11−2+2ζ112+ζ114 2ζ11−4+ζ11−3+ζ113+2ζ114 2ζ11−5+ζ11−1+ζ11+2ζ115 ζ11−5+2ζ11−3+2ζ113+ζ115 ζ11−2+2ζ11−1+2ζ11+ζ112 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 2ζ11−3+2+2ζ113 2ζ11−5+2+2ζ115 2ζ11−2+2+2ζ112 2ζ11−1+2+2ζ11 2ζ11−4+2+2ζ114
726.6.6a3 R 6 0 0 0 0 0 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−5−ζ11−2−1−ζ112−ζ115 ζ11−2+2ζ11−1+2ζ11+ζ112 ζ11−4+2ζ11−2+2ζ112+ζ114 ζ11−5+2ζ11−3+2ζ113+ζ115 2ζ11−4+ζ11−3+ζ113+2ζ114 2ζ11−5+ζ11−1+ζ11+2ζ115 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−5−ζ11−2−1−ζ112−ζ115 2ζ11−4+2+2ζ114 2ζ11−3+2+2ζ113 2ζ11−1+2+2ζ11 2ζ11−5+2+2ζ115 2ζ11−2+2+2ζ112
726.6.6a4 R 6 0 0 0 0 0 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−3−ζ11−1−1−ζ11−ζ113 2ζ11−5+ζ11−1+ζ11+2ζ115 ζ11−2+2ζ11−1+2ζ11+ζ112 2ζ11−4+ζ11−3+ζ113+2ζ114 ζ11−4+2ζ11−2+2ζ112+ζ114 ζ11−5+2ζ11−3+2ζ113+ζ115 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−3−ζ11−1−1−ζ11−ζ113 2ζ11−2+2+2ζ112 2ζ11−4+2+2ζ114 2ζ11−5+2+2ζ115 2ζ11−3+2+2ζ113 2ζ11−1+2+2ζ11
726.6.6a5 R 6 0 0 0 0 0 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 2ζ11−4+ζ11−3+ζ113+2ζ114 ζ11−5+2ζ11−3+2ζ113+ζ115 ζ11−2+2ζ11−1+2ζ11+ζ112 2ζ11−5+ζ11−1+ζ11+2ζ115 ζ11−4+2ζ11−2+2ζ112+ζ114 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 2ζ11−5+2+2ζ115 2ζ11−1+2+2ζ11 2ζ11−4+2+2ζ114 2ζ11−2+2+2ζ112 2ζ11−3+2+2ζ113
726.6.6b1 R 6 0 0 0 0 0 2ζ11−4+ζ11−3+ζ113+2ζ114 ζ11−5+2ζ11−3+2ζ113+ζ115 ζ11−2+2ζ11−1+2ζ11+ζ112 2ζ11−5+ζ11−1+ζ11+2ζ115 ζ11−4+2ζ11−2+2ζ112+ζ114 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 2ζ11−2+2+2ζ112 2ζ11−4+2+2ζ114 2ζ11−5+2+2ζ115 2ζ11−3+2+2ζ113 2ζ11−1+2+2ζ11 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−5−ζ11−2−1−ζ112−ζ115
726.6.6b2 R 6 0 0 0 0 0 ζ11−5+2ζ11−3+2ζ113+ζ115 2ζ11−5+ζ11−1+ζ11+2ζ115 ζ11−4+2ζ11−2+2ζ112+ζ114 ζ11−2+2ζ11−1+2ζ11+ζ112 2ζ11−4+ζ11−3+ζ113+2ζ114 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−4−1−ζ114−ζ115 2ζ11−4+2+2ζ114 2ζ11−3+2+2ζ113 2ζ11−1+2+2ζ11 2ζ11−5+2+2ζ115 2ζ11−2+2+2ζ112 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114
726.6.6b3 R 6 0 0 0 0 0 2ζ11−5+ζ11−1+ζ11+2ζ115 ζ11−2+2ζ11−1+2ζ11+ζ112 2ζ11−4+ζ11−3+ζ113+2ζ114 ζ11−4+2ζ11−2+2ζ112+ζ114 ζ11−5+2ζ11−3+2ζ113+ζ115 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−3−ζ11−1−1−ζ11−ζ113 2ζ11−3+2+2ζ113 2ζ11−5+2+2ζ115 2ζ11−2+2+2ζ112 2ζ11−1+2+2ζ11 2ζ11−4+2+2ζ114 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113
726.6.6b4 R 6 0 0 0 0 0 ζ11−4+2ζ11−2+2ζ112+ζ114 2ζ11−4+ζ11−3+ζ113+2ζ114 2ζ11−5+ζ11−1+ζ11+2ζ115 ζ11−5+2ζ11−3+2ζ113+ζ115 ζ11−2+2ζ11−1+2ζ11+ζ112 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 2ζ11−1+2+2ζ11 2ζ11−2+2+2ζ112 2ζ11−3+2+2ζ113 2ζ11−4+2+2ζ114 2ζ11−5+2+2ζ115 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−3−ζ11−1−1−ζ11−ζ113
726.6.6b5 R 6 0 0 0 0 0 ζ11−2+2ζ11−1+2ζ11+ζ112 ζ11−4+2ζ11−2+2ζ112+ζ114 ζ11−5+2ζ11−3+2ζ113+ζ115 2ζ11−4+ζ11−3+ζ113+2ζ114 2ζ11−5+ζ11−1+ζ11+2ζ115 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−5−ζ11−2−1−ζ112−ζ115 2ζ11−5+2+2ζ115 2ζ11−1+2+2ζ11 2ζ11−4+2+2ζ114 2ζ11−2+2+2ζ112 2ζ11−3+2+2ζ113 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−4−1−ζ114−ζ115
726.6.6c1 R 6 0 0 0 0 0 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−4−1−ζ114−ζ115 2ζ11−4+2+2ζ114 2ζ11−3+2+2ζ113 2ζ11−1+2+2ζ11 2ζ11−5+2+2ζ115 2ζ11−2+2+2ζ112 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−4−1−ζ114−ζ115 ζ11−4+2ζ11−2+2ζ112+ζ114 2ζ11−4+ζ11−3+ζ113+2ζ114 2ζ11−5+ζ11−1+ζ11+2ζ115 ζ11−5+2ζ11−3+2ζ113+ζ115 ζ11−2+2ζ11−1+2ζ11+ζ112
726.6.6c2 R 6 0 0 0 0 0 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 2ζ11−1+2+2ζ11 2ζ11−2+2+2ζ112 2ζ11−3+2+2ζ113 2ζ11−4+2+2ζ114 2ζ11−5+2+2ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 2ζ11−5+ζ11−1+ζ11+2ζ115 ζ11−2+2ζ11−1+2ζ11+ζ112 2ζ11−4+ζ11−3+ζ113+2ζ114 ζ11−4+2ζ11−2+2ζ112+ζ114 ζ11−5+2ζ11−3+2ζ113+ζ115
726.6.6c3 R 6 0 0 0 0 0 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−5−ζ11−2−1−ζ112−ζ115 2ζ11−5+2+2ζ115 2ζ11−1+2+2ζ11 2ζ11−4+2+2ζ114 2ζ11−2+2+2ζ112 2ζ11−3+2+2ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−5−ζ11−2−1−ζ112−ζ115 ζ11−5+2ζ11−3+2ζ113+ζ115 2ζ11−5+ζ11−1+ζ11+2ζ115 ζ11−4+2ζ11−2+2ζ112+ζ114 ζ11−2+2ζ11−1+2ζ11+ζ112 2ζ11−4+ζ11−3+ζ113+2ζ114
726.6.6c4 R 6 0 0 0 0 0 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−3−ζ11−1−1−ζ11−ζ113 2ζ11−3+2+2ζ113 2ζ11−5+2+2ζ115 2ζ11−2+2+2ζ112 2ζ11−1+2+2ζ11 2ζ11−4+2+2ζ114 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−3−ζ11−1−1−ζ11−ζ113 2ζ11−4+ζ11−3+ζ113+2ζ114 ζ11−5+2ζ11−3+2ζ113+ζ115 ζ11−2+2ζ11−1+2ζ11+ζ112 2ζ11−5+ζ11−1+ζ11+2ζ115 ζ11−4+2ζ11−2+2ζ112+ζ114
726.6.6c5 R 6 0 0 0 0 0 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 2ζ11−2+2+2ζ112 2ζ11−4+2+2ζ114 2ζ11−5+2+2ζ115 2ζ11−3+2+2ζ113 2ζ11−1+2+2ζ11 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 ζ11−2+2ζ11−1+2ζ11+ζ112 ζ11−4+2ζ11−2+2ζ112+ζ114 ζ11−5+2ζ11−3+2ζ113+ζ115 2ζ11−4+ζ11−3+ζ113+2ζ114 2ζ11−5+ζ11−1+ζ11+2ζ115
726.6.6d1 R 6 0 0 0 0 0 2ζ11−5+2+2ζ115 2ζ11−1+2+2ζ11 2ζ11−4+2+2ζ114 2ζ11−2+2+2ζ112 2ζ11−3+2+2ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−5−ζ11−2−1−ζ112−ζ115 ζ11−2+2ζ11−1+2ζ11+ζ112 ζ11−4+2ζ11−2+2ζ112+ζ114 ζ11−5+2ζ11−3+2ζ113+ζ115 2ζ11−4+ζ11−3+ζ113+2ζ114 2ζ11−5+ζ11−1+ζ11+2ζ115 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−4−1−ζ114−ζ115
726.6.6d2 R 6 0 0 0 0 0 2ζ11−4+2+2ζ114 2ζ11−3+2+2ζ113 2ζ11−1+2+2ζ11 2ζ11−5+2+2ζ115 2ζ11−2+2+2ζ112 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−4−1−ζ114−ζ115 ζ11−5+2ζ11−3+2ζ113+ζ115 2ζ11−5+ζ11−1+ζ11+2ζ115 ζ11−4+2ζ11−2+2ζ112+ζ114 ζ11−2+2ζ11−1+2ζ11+ζ112 2ζ11−4+ζ11−3+ζ113+2ζ114 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114
726.6.6d3 R 6 0 0 0 0 0 2ζ11−3+2+2ζ113 2ζ11−5+2+2ζ115 2ζ11−2+2+2ζ112 2ζ11−1+2+2ζ11 2ζ11−4+2+2ζ114 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−3−ζ11−1−1−ζ11−ζ113 2ζ11−5+ζ11−1+ζ11+2ζ115 ζ11−2+2ζ11−1+2ζ11+ζ112 2ζ11−4+ζ11−3+ζ113+2ζ114 ζ11−4+2ζ11−2+2ζ112+ζ114 ζ11−5+2ζ11−3+2ζ113+ζ115 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113
726.6.6d4 R 6 0 0 0 0 0 2ζ11−2+2+2ζ112 2ζ11−4+2+2ζ114 2ζ11−5+2+2ζ115 2ζ11−3+2+2ζ113 2ζ11−1+2+2ζ11 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 2ζ11−4+ζ11−3+ζ113+2ζ114 ζ11−5+2ζ11−3+2ζ113+ζ115 ζ11−2+2ζ11−1+2ζ11+ζ112 2ζ11−5+ζ11−1+ζ11+2ζ115 ζ11−4+2ζ11−2+2ζ112+ζ114 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−5−ζ11−2−1−ζ112−ζ115
726.6.6d5 R 6 0 0 0 0 0 2ζ11−1+2+2ζ11 2ζ11−2+2+2ζ112 2ζ11−3+2+2ζ113 2ζ11−4+2+2ζ114 2ζ11−5+2+2ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−3−ζ11−1−1−ζ11−ζ113 −ζ11−4−ζ11−1−1−ζ11−ζ114 ζ11−4+2ζ11−2+2ζ112+ζ114 2ζ11−4+ζ11−3+ζ113+2ζ114 2ζ11−5+ζ11−1+ζ11+2ζ115 ζ11−5+2ζ11−3+2ζ113+ζ115 ζ11−2+2ζ11−1+2ζ11+ζ112 −ζ11−5−ζ11−2−1−ζ112−ζ115 −ζ11−4−ζ11−1−1−ζ11−ζ114 −ζ11−5−ζ11−4−1−ζ114−ζ115 −ζ11−3−ζ11−2−1−ζ112−ζ113 −ζ11−3−ζ11−1−1−ζ11−ζ113

magma: CharacterTable(G);