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Properties

Label 21T49
Degree $21$
Order $9261$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_7^3:C_9:C_3$

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Show commands: Magma

magma: G := TransitiveGroup(21, 49);
 

Group invariants

Abstract group:  $C_7^3:C_9:C_3$
magma: IdentifyGroup(G);
 
Order:  $9261=3^{3} \cdot 7^{3}$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
magma: NilpotencyClass(G);
 

Group action invariants

Degree $n$:  $21$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $49$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $1$
magma: IsEven(G);
 
Primitive:  no
magma: IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $1$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,11,17)(2,12,15,3,13,20,5,8,16)(4,14,18,7,10,19,6,9,21)$, $(1,7,3)(2,4,5)(8,11,14,10,13,9,12)(15,16,18)(17,20,19)$
magma: Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$3$:  $C_3$ x 4
$9$:  $C_3^2$
$27$:  $C_9:C_3$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 7: 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 $1^{21}$ $1$ $1$ $0$ $()$
3A1 $3^{4},1^{9}$ $147$ $3$ $8$ $( 1, 6, 2)( 4, 5, 7)(15,17,18)(16,21,20)$
3A-1 $3^{4},1^{9}$ $147$ $3$ $8$ $( 1, 2, 6)( 4, 7, 5)(15,18,17)(16,20,21)$
3B1 $3^{6},1^{3}$ $343$ $3$ $12$ $( 1, 2, 6)( 4, 7, 5)( 8,11, 9)(10,12,13)(15,21,17)(16,18,19)$
3B-1 $3^{6},1^{3}$ $343$ $3$ $12$ $( 1, 6, 2)( 4, 5, 7)( 8, 9,11)(10,13,12)(15,17,21)(16,19,18)$
7A1 $7,1^{14}$ $9$ $7$ $6$ $( 8,12, 9,13,10,14,11)$
7A-1 $7,1^{14}$ $9$ $7$ $6$ $( 8,11,14,10,13, 9,12)$
7B1 $7^{3}$ $27$ $7$ $18$ $( 1, 4, 7, 3, 6, 2, 5)( 8,12, 9,13,10,14,11)(15,18,21,17,20,16,19)$
7B-1 $7^{3}$ $27$ $7$ $18$ $( 1, 3, 5, 7, 2, 4, 6)( 8,13,11, 9,14,12,10)(15,17,19,21,16,18,20)$
7C1 $7^{2},1^{7}$ $27$ $7$ $12$ $( 8,12, 9,13,10,14,11)(15,18,21,17,20,16,19)$
7C-1 $7^{2},1^{7}$ $27$ $7$ $12$ $( 8,13,11, 9,14,12,10)(15,17,19,21,16,18,20)$
7D1 $7^{3}$ $27$ $7$ $18$ $( 1, 4, 7, 3, 6, 2, 5)( 8,14,13,12,11,10, 9)(15,18,21,17,20,16,19)$
7D-1 $7^{3}$ $27$ $7$ $18$ $( 1, 4, 7, 3, 6, 2, 5)( 8, 9,10,11,12,13,14)(15,21,20,19,18,17,16)$
7E1 $7^{3}$ $27$ $7$ $18$ $( 1, 5, 2, 6, 3, 7, 4)( 8,12, 9,13,10,14,11)(15,18,21,17,20,16,19)$
7E-1 $7^{3}$ $27$ $7$ $18$ $( 1, 7, 6, 5, 4, 3, 2)( 8,13,11, 9,14,12,10)(15,17,19,21,16,18,20)$
7F1 $7^{3}$ $27$ $7$ $18$ $( 1, 4, 7, 3, 6, 2, 5)( 8, 9,10,11,12,13,14)(15,18,21,17,20,16,19)$
7F-1 $7^{3}$ $27$ $7$ $18$ $( 1, 4, 7, 3, 6, 2, 5)( 8,11,14,10,13, 9,12)(15,18,21,17,20,16,19)$
7G1 $7^{2},1^{7}$ $27$ $7$ $12$ $( 1, 6, 4, 2, 7, 5, 3)( 8,10,12,14, 9,11,13)$
7G-1 $7^{2},1^{7}$ $27$ $7$ $12$ $( 1, 5, 2, 6, 3, 7, 4)( 8,14,13,12,11,10, 9)$
9A1 $9^{2},3$ $1029$ $9$ $18$ $( 1,17,10, 2,15,12, 6,21,13)( 3,20,14)( 4,18, 9, 7,19, 8, 5,16,11)$
9A-1 $9^{2},3$ $1029$ $9$ $18$ $( 1,13,21, 6,12,15, 2,10,17)( 3,14,20)( 4,11,16, 5, 8,19, 7, 9,18)$
9B1 $9^{2},3$ $1029$ $9$ $18$ $( 1,14,16, 5, 9,15, 6,13,20)( 2,11,21, 7,10,18, 3, 8,19)( 4,12,17)$
9B-1 $9^{2},3$ $1029$ $9$ $18$ $( 1,20,13, 6,15, 9, 5,16,14)( 2,19, 8, 3,18,10, 7,21,11)( 4,17,12)$
9C1 $9^{2},3$ $1029$ $9$ $18$ $( 1,13,21, 2, 8,19, 4,12,15)( 3,10,17, 6, 9,18, 5,14,20)( 7,11,16)$
9C-1 $9^{2},3$ $1029$ $9$ $18$ $( 1,15,12, 4,19, 8, 2,21,13)( 3,20,14, 5,18, 9, 6,17,10)( 7,16,11)$
21A1 $7,3^{4},1^{2}$ $441$ $21$ $14$ $( 1, 6, 2)( 4, 5, 7)( 8,14,13,12,11,10, 9)(15,17,18)(16,21,20)$
21A-1 $7,3^{4},1^{2}$ $441$ $21$ $14$ $( 1, 2, 6)( 4, 7, 5)( 8, 9,10,11,12,13,14)(15,18,17)(16,20,21)$
21A2 $7,3^{4},1^{2}$ $441$ $21$ $14$ $( 1, 2, 6)( 4, 7, 5)( 8,13,11, 9,14,12,10)(15,18,17)(16,20,21)$
21A-2 $7,3^{4},1^{2}$ $441$ $21$ $14$ $( 1, 6, 2)( 4, 5, 7)( 8,10,12,14, 9,11,13)(15,17,18)(16,21,20)$

Malle's constant $a(G)$:     $1/6$

magma: ConjugacyClasses(G);
 

Character table

1A 3A1 3A-1 3B1 3B-1 7A1 7A-1 7B1 7B-1 7C1 7C-1 7D1 7D-1 7E1 7E-1 7F1 7F-1 7G1 7G-1 9A1 9A-1 9B1 9B-1 9C1 9C-1 21A1 21A-1 21A2 21A-2
Size 1 147 147 343 343 9 9 27 27 27 27 27 27 27 27 27 27 27 27 1029 1029 1029 1029 1029 1029 441 441 441 441
3 P 1A 3A-1 3A1 3B-1 3B1 7A1 7A-1 7B1 7B-1 7C1 7C-1 7D1 7D-1 7E1 7E-1 7F1 7F-1 7G1 7G-1 9A-1 9A1 9B-1 9B1 9C-1 9C1 21A2 21A-2 21A1 21A-1
7 P 1A 1A 1A 1A 1A 7A-1 7A1 7B-1 7B1 7C-1 7C1 7D-1 7D1 7E-1 7E1 7F-1 7F1 7G-1 7G1 3B1 3B-1 3B-1 3B1 3B-1 3B1 7A1 7A-1 7A1 7A-1
Type
9261.f.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
9261.f.1b1 C 1 ζ3−1 ζ3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ζ3−1 ζ3 1 1 ζ3 ζ3−1 ζ3−1 ζ3 ζ3 ζ3−1
9261.f.1b2 C 1 ζ3 ζ3−1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ζ3 ζ3−1 1 1 ζ3−1 ζ3 ζ3 ζ3−1 ζ3−1 ζ3
9261.f.1c1 C 1 ζ3−1 ζ3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ζ3 1 ζ3 ζ3−1 ζ3−1 1 ζ3−1 ζ3 ζ3 ζ3−1
9261.f.1c2 C 1 ζ3 ζ3−1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ζ3−1 1 ζ3−1 ζ3 ζ3 1 ζ3 ζ3−1 ζ3−1 ζ3
9261.f.1d1 C 1 ζ3−1 ζ3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ζ3−1 ζ3−1 ζ3 1 ζ3 ζ3−1 ζ3 ζ3 ζ3−1
9261.f.1d2 C 1 ζ3 ζ3−1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ζ3 ζ3 ζ3−1 1 ζ3−1 ζ3 ζ3−1 ζ3−1 ζ3
9261.f.1e1 C 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ζ3−1 ζ3−1 ζ3 ζ3−1 ζ3 ζ3 1 1 1 1
9261.f.1e2 C 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ζ3 ζ3 ζ3−1 ζ3 ζ3−1 ζ3−1 1 1 1 1
9261.f.3a1 C 3 0 0 3ζ3−1 3ζ3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0
9261.f.3a2 C 3 0 0 3ζ3 3ζ3−1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0
9261.f.9a1 C 9 3 3 0 0 −ζ7−3+5−ζ7−ζ72 ζ7−3+6+ζ7+ζ72 2ζ7−3+3+2ζ7+2ζ72 ζ7−3−1+ζ7+ζ72 3ζ7−3+3ζ7+3ζ72 ζ7−3−1+ζ7+ζ72 −ζ7−3−2−ζ7−ζ72 −ζ7−3−2−ζ7−ζ72 2 −3ζ7−3−3−3ζ7−3ζ72 −2ζ7−3+1−2ζ7−2ζ72 ζ7−3−1+ζ7+ζ72 −ζ7−3−2−ζ7−ζ72 2 0 0 0 0 0 0 ζ7−3+ζ7+ζ72 −ζ7−3−1−ζ7−ζ72 ζ7−3+ζ7+ζ72 −ζ7−3−1−ζ7−ζ72
9261.f.9a2 C 9 3 3 0 0 ζ7−3+6+ζ7+ζ72 −ζ7−3+5−ζ7−ζ72 −2ζ7−3+1−2ζ7−2ζ72 −ζ7−3−2−ζ7−ζ72 −3ζ7−3−3−3ζ7−3ζ72 −ζ7−3−2−ζ7−ζ72 ζ7−3−1+ζ7+ζ72 ζ7−3−1+ζ7+ζ72 2 3ζ7−3+3ζ7+3ζ72 2ζ7−3+3+2ζ7+2ζ72 −ζ7−3−2−ζ7−ζ72 ζ7−3−1+ζ7+ζ72 2 0 0 0 0 0 0 −ζ7−3−1−ζ7−ζ72 ζ7−3+ζ7+ζ72 −ζ7−3−1−ζ7−ζ72 ζ7−3+ζ7+ζ72
9261.f.9b1 C 9 3ζ21−7 3ζ217 0 0 −ζ21−10+6−ζ21−ζ214−ζ218+ζ219 ζ21−10+5+ζ21+ζ214+ζ218−ζ219 2ζ21−10+1+2ζ21+2ζ214+2ζ218−2ζ219 ζ21−10−2+ζ21+ζ214+ζ218−ζ219 3ζ21−10−3+3ζ21+3ζ214+3ζ218−3ζ219 ζ21−10−2+ζ21+ζ214+ζ218−ζ219 −ζ21−10−1−ζ21−ζ214−ζ218+ζ219 −ζ21−10−1−ζ21−ζ214−ζ218+ζ219 2 −3ζ21−10−3ζ21−3ζ214−3ζ218+3ζ219 −2ζ21−10+3−2ζ21−2ζ214−2ζ218+2ζ219 ζ21−10−2+ζ21+ζ214+ζ218−ζ219 −ζ21−10−1−ζ21−ζ214−ζ218+ζ219 2 0 0 0 0 0 0 −ζ21−10+1−ζ212+ζ217−ζ218 ζ21−ζ212+ζ214−ζ219 −ζ21+ζ212−ζ214−ζ217+ζ219 ζ21−10+ζ212+ζ218
9261.f.9b2 C 9 3ζ217 3ζ21−7 0 0 ζ21−10+5+ζ21+ζ214+ζ218−ζ219 −ζ21−10+6−ζ21−ζ214−ζ218+ζ219 −2ζ21−10+3−2ζ21−2ζ214−2ζ218+2ζ219 −ζ21−10−1−ζ21−ζ214−ζ218+ζ219 −3ζ21−10−3ζ21−3ζ214−3ζ218+3ζ219 −ζ21−10−1−ζ21−ζ214−ζ218+ζ219 ζ21−10−2+ζ21+ζ214+ζ218−ζ219 ζ21−10−2+ζ21+ζ214+ζ218−ζ219 2 3ζ21−10−3+3ζ21+3ζ214+3ζ218−3ζ219 2ζ21−10+1+2ζ21+2ζ214+2ζ218−2ζ219 −ζ21−10−1−ζ21−ζ214−ζ218+ζ219 ζ21−10−2+ζ21+ζ214+ζ218−ζ219 2 0 0 0 0 0 0 ζ21−ζ212+ζ214−ζ219 −ζ21−10+1−ζ212+ζ217−ζ218 ζ21−10+ζ212+ζ218 −ζ21+ζ212−ζ214−ζ217+ζ219
9261.f.9b3 C 9 3ζ21−7 3ζ217 0 0 ζ21−10+5+ζ21+ζ214+ζ218−ζ219 −ζ21−10+6−ζ21−ζ214−ζ218+ζ219 −2ζ21−10+3−2ζ21−2ζ214−2ζ218+2ζ219 −ζ21−10−1−ζ21−ζ214−ζ218+ζ219 −3ζ21−10−3ζ21−3ζ214−3ζ218+3ζ219 −ζ21−10−1−ζ21−ζ214−ζ218+ζ219 ζ21−10−2+ζ21+ζ214+ζ218−ζ219 ζ21−10−2+ζ21+ζ214+ζ218−ζ219 2 3ζ21−10−3+3ζ21+3ζ214+3ζ218−3ζ219 2ζ21−10+1+2ζ21+2ζ214+2ζ218−2ζ219 −ζ21−10−1−ζ21−ζ214−ζ218+ζ219 ζ21−10−2+ζ21+ζ214+ζ218−ζ219 2 0 0 0 0 0 0 ζ21−10+ζ212+ζ218 −ζ21+ζ212−ζ214−ζ217+ζ219 ζ21−ζ212+ζ214−ζ219 −ζ21−10+1−ζ212+ζ217−ζ218
9261.f.9b4 C 9 3ζ217 3ζ21−7 0 0 −ζ21−10+6−ζ21−ζ214−ζ218+ζ219 ζ21−10+5+ζ21+ζ214+ζ218−ζ219 2ζ21−10+1+2ζ21+2ζ214+2ζ218−2ζ219 ζ21−10−2+ζ21+ζ214+ζ218−ζ219 3ζ21−10−3+3ζ21+3ζ214+3ζ218−3ζ219 ζ21−10−2+ζ21+ζ214+ζ218−ζ219 −ζ21−10−1−ζ21−ζ214−ζ218+ζ219 −ζ21−10−1−ζ21−ζ214−ζ218+ζ219 2 −3ζ21−10−3ζ21−3ζ214−3ζ218+3ζ219 −2ζ21−10+3−2ζ21−2ζ214−2ζ218+2ζ219 ζ21−10−2+ζ21+ζ214+ζ218−ζ219 −ζ21−10−1−ζ21−ζ214−ζ218+ζ219 2 0 0 0 0 0 0 −ζ21+ζ212−ζ214−ζ217+ζ219 ζ21−10+ζ212+ζ218 −ζ21−10+1−ζ212+ζ217−ζ218 ζ21−ζ212+ζ214−ζ219
9261.f.27a1 C 27 0 0 0 0 −9ζ7−3−9−9ζ7−9ζ72 9ζ7−3+9ζ7+9ζ72 −3ζ7−3−6−3ζ7−3ζ72 2ζ7−3+2ζ7+2ζ72 −ζ7−3+2−ζ7−ζ72 2ζ7−3+2ζ7+2ζ72 −2ζ7−3−2−2ζ7−2ζ72 −2ζ7−3−2−2ζ7−2ζ72 6 ζ7−3+3+ζ7+ζ72 3ζ7−3−3+3ζ7+3ζ72 2ζ7−3+2ζ7+2ζ72 −2ζ7−3−2−2ζ7−2ζ72 6 0 0 0 0 0 0 0 0 0 0
9261.f.27a2 C 27 0 0 0 0 9ζ7−3+9ζ7+9ζ72 −9ζ7−3−9−9ζ7−9ζ72 3ζ7−3−3+3ζ7+3ζ72 −2ζ7−3−2−2ζ7−2ζ72 ζ7−3+3+ζ7+ζ72 −2ζ7−3−2−2ζ7−2ζ72 2ζ7−3+2ζ7+2ζ72 2ζ7−3+2ζ7+2ζ72 6 −ζ7−3+2−ζ7−ζ72 −3ζ7−3−6−3ζ7−3ζ72 −2ζ7−3−2−2ζ7−2ζ72 2ζ7−3+2ζ7+2ζ72 6 0 0 0 0 0 0 0 0 0 0
9261.f.27b1 C 27 0 0 0 0 −3ζ7−3−6−3ζ7−3ζ72 3ζ7−3−3+3ζ7+3ζ72 −ζ7−3+2−ζ7−ζ72 3ζ7−3−3+3ζ7+3ζ72 2ζ7−3+2ζ7+2ζ72 −4ζ7−3−3−4ζ7−4ζ72 4ζ7−3+8+4ζ7+4ζ72 −3ζ7−3−6−3ζ7−3ζ72 −1 −2ζ7−3−2−2ζ7−2ζ72 ζ7−3+3+ζ7+ζ72 −4ζ7−3+4−4ζ7−4ζ72 4ζ7−3+1+4ζ7+4ζ72 −1 0 0 0 0 0 0 0 0 0 0
9261.f.27b2 C 27 0 0 0 0 3ζ7−3−3+3ζ7+3ζ72 −3ζ7−3−6−3ζ7−3ζ72 ζ7−3+3+ζ7+ζ72 −3ζ7−3−6−3ζ7−3ζ72 −2ζ7−3−2−2ζ7−2ζ72 4ζ7−3+1+4ζ7+4ζ72 −4ζ7−3+4−4ζ7−4ζ72 3ζ7−3−3+3ζ7+3ζ72 −1 2ζ7−3+2ζ7+2ζ72 −ζ7−3+2−ζ7−ζ72 4ζ7−3+8+4ζ7+4ζ72 −4ζ7−3−3−4ζ7−4ζ72 −1 0 0 0 0 0 0 0 0 0 0
9261.f.27c1 C 27 0 0 0 0 −3ζ7−3−6−3ζ7−3ζ72 3ζ7−3−3+3ζ7+3ζ72 −ζ7−3+2−ζ7−ζ72 −4ζ7−3−3−4ζ7−4ζ72 2ζ7−3+2ζ7+2ζ72 −4ζ7−3+4−4ζ7−4ζ72 −3ζ7−3−6−3ζ7−3ζ72 4ζ7−3+1+4ζ7+4ζ72 −1 −2ζ7−3−2−2ζ7−2ζ72 ζ7−3+3+ζ7+ζ72 3ζ7−3−3+3ζ7+3ζ72 4ζ7−3+8+4ζ7+4ζ72 −1 0 0 0 0 0 0 0 0 0 0
9261.f.27c2 C 27 0 0 0 0 3ζ7−3−3+3ζ7+3ζ72 −3ζ7−3−6−3ζ7−3ζ72 ζ7−3+3+ζ7+ζ72 4ζ7−3+1+4ζ7+4ζ72 −2ζ7−3−2−2ζ7−2ζ72 4ζ7−3+8+4ζ7+4ζ72 3ζ7−3−3+3ζ7+3ζ72 −4ζ7−3−3−4ζ7−4ζ72 −1 2ζ7−3+2ζ7+2ζ72 −ζ7−3+2−ζ7−ζ72 −3ζ7−3−6−3ζ7−3ζ72 −4ζ7−3+4−4ζ7−4ζ72 −1 0 0 0 0 0 0 0 0 0 0
9261.f.27d1 C 27 0 0 0 0 −3ζ7−3−6−3ζ7−3ζ72 3ζ7−3−3+3ζ7+3ζ72 −ζ7−3+2−ζ7−ζ72 −4ζ7−3+4−4ζ7−4ζ72 2ζ7−3+2ζ7+2ζ72 3ζ7−3−3+3ζ7+3ζ72 4ζ7−3+1+4ζ7+4ζ72 4ζ7−3+8+4ζ7+4ζ72 −1 −2ζ7−3−2−2ζ7−2ζ72 ζ7−3+3+ζ7+ζ72 −4ζ7−3−3−4ζ7−4ζ72 −3ζ7−3−6−3ζ7−3ζ72 −1 0 0 0 0 0 0 0 0 0 0
9261.f.27d2 C 27 0 0 0 0 3ζ7−3−3+3ζ7+3ζ72 −3ζ7−3−6−3ζ7−3ζ72 ζ7−3+3+ζ7+ζ72 4ζ7−3+8+4ζ7+4ζ72 −2ζ7−3−2−2ζ7−2ζ72 −3ζ7−3−6−3ζ7−3ζ72 −4ζ7−3−3−4ζ7−4ζ72 −4ζ7−3+4−4ζ7−4ζ72 −1 2ζ7−3+2ζ7+2ζ72 −ζ7−3+2−ζ7−ζ72 4ζ7−3+1+4ζ7+4ζ72 3ζ7−3−3+3ζ7+3ζ72 −1 0 0 0 0 0 0 0 0 0 0
9261.f.27e1 C 27 0 0 0 0 −6ζ7−3+3−6ζ7−6ζ72 6ζ7−3+9+6ζ7+6ζ72 5ζ7−3−2+5ζ7+5ζ72 −ζ7−3+2−ζ7−ζ72 −3ζ7−3−6−3ζ7−3ζ72 −ζ7−3+2−ζ7−ζ72 ζ7−3+3+ζ7+ζ72 ζ7−3+3+ζ7+ζ72 −1 3ζ7−3−3+3ζ7+3ζ72 −5ζ7−3−7−5ζ7−5ζ72 −ζ7−3+2−ζ7−ζ72 ζ7−3+3+ζ7+ζ72 −1 0 0 0 0 0 0 0 0 0 0
9261.f.27e2 C 27 0 0 0 0 6ζ7−3+9+6ζ7+6ζ72 −6ζ7−3+3−6ζ7−6ζ72 −5ζ7−3−7−5ζ7−5ζ72 ζ7−3+3+ζ7+ζ72 3ζ7−3−3+3ζ7+3ζ72 ζ7−3+3+ζ7+ζ72 −ζ7−3+2−ζ7−ζ72 −ζ7−3+2−ζ7−ζ72 −1 −3ζ7−3−6−3ζ7−3ζ72 5ζ7−3−2+5ζ7+5ζ72 ζ7−3+3+ζ7+ζ72 −ζ7−3+2−ζ7−ζ72 −1 0 0 0 0 0 0 0 0 0 0
9261.f.27f1 C 27 0 0 0 0 6 6 −1 −1 6 −1 −1 −1 −7ζ7−3−8−7ζ7−7ζ72 6 −1 −1 −1 7ζ7−3−1+7ζ7+7ζ72 0 0 0 0 0 0 0 0 0 0
9261.f.27f2 C 27 0 0 0 0 6 6 −1 −1 6 −1 −1 −1 7ζ7−3−1+7ζ7+7ζ72 6 −1 −1 −1 −7ζ7−3−8−7ζ7−7ζ72 0 0 0 0 0 0 0 0 0 0

magma: CharacterTable(G);
 

Regular extensions

Data not computed