Properties

Label 16T24
16T24 1 3 1->3 10 1->10 2 4 2->4 9 2->9 3->4 5 3->5 6 4->6 7 5->7 14 5->14 8 6->8 13 6->13 7->8 7->10 8->9 12 9->12 11 10->11 11->12 11->14 12->13 16 13->16 15 14->15 15->1 15->16 16->2
Degree 1616
Order 3232
Cyclic no
Abelian no
Solvable yes
Primitive no
pp-group yes
Group: C22:C8C_2^2 : C_8

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Copy content magma:G := TransitiveGroup(16, 24);
 

Group invariants

Abstract group:  C22:C8C_2^2 : C_8
Copy content magma:IdentifyGroup(G);
 
Order:  32=2532=2^{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:  22
Copy content magma:NilpotencyClass(G);
 

Group action invariants

Degree nn:  1616
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number tt:  2424
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  11
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
#Aut(F/K)\card{\Aut(F/K)}:  88
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,3,5,7,10,11,14,15)(2,4,6,8,9,12,13,16)(1,3,5,7,10,11,14,15)(2,4,6,8,9,12,13,16), (1,10)(2,9)(3,4)(5,14)(6,13)(7,8)(11,12)(15,16)(1,10)(2,9)(3,4)(5,14)(6,13)(7,8)(11,12)(15,16)
Copy content magma:Generators(G);
 

Low degree resolvents

#(G/N)\card{(G/N)}Galois groups for stem field(s)
22C2C_2 x 3
44C4C_4 x 2, C22C_2^2
88D4D_{4} x 2, C8C_8 x 2, C4×C2C_4\times C_2
1616C8:C2C_8:C_2, C22:C4C_2^2:C_4, C8×C2C_8\times C_2

Resolvents shown for degrees 47\leq 47

Subfields

Degree 2: C2C_2

Degree 4: C4C_4, D4D_{4} x 2

Degree 8: C8C_8, C8:C2C_8:C_2, C22:C4C_2^2:C_4

Low degree siblings

16T24, 32T10

Siblings are shown with degree 47\leq 47

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

Conjugacy classes

LabelCycle TypeSizeOrderIndexRepresentative
1A 1161^{16} 11 11 00 ()()
2A 282^{8} 11 22 88 (1,9)(2,10)(3,12)(4,11)(5,13)(6,14)(7,16)(8,15)( 1, 9)( 2,10)( 3,12)( 4,11)( 5,13)( 6,14)( 7,16)( 8,15)
2B 282^{8} 11 22 88 (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)
2C 282^{8} 11 22 88 (1,10)(2,9)(3,11)(4,12)(5,14)(6,13)(7,15)(8,16)( 1,10)( 2, 9)( 3,11)( 4,12)( 5,14)( 6,13)( 7,15)( 8,16)
2D 24,182^{4},1^{8} 22 22 44 (3,12)(4,11)(7,16)(8,15)( 3,12)( 4,11)( 7,16)( 8,15)
2E 282^{8} 22 22 88 (1,10)(2,9)(3,4)(5,14)(6,13)(7,8)(11,12)(15,16)( 1,10)( 2, 9)( 3, 4)( 5,14)( 6,13)( 7, 8)(11,12)(15,16)
4A1 444^{4} 11 44 1212 (1,5,10,14)(2,6,9,13)(3,7,11,15)(4,8,12,16)( 1, 5,10,14)( 2, 6, 9,13)( 3, 7,11,15)( 4, 8,12,16)
4A-1 444^{4} 11 44 1212 (1,14,10,5)(2,13,9,6)(3,15,11,7)(4,16,12,8)( 1,14,10, 5)( 2,13, 9, 6)( 3,15,11, 7)( 4,16,12, 8)
4B1 444^{4} 11 44 1212 (1,13,10,6)(2,14,9,5)(3,16,11,8)(4,15,12,7)( 1,13,10, 6)( 2,14, 9, 5)( 3,16,11, 8)( 4,15,12, 7)
4B-1 444^{4} 11 44 1212 (1,6,10,13)(2,5,9,14)(3,8,11,16)(4,7,12,15)( 1, 6,10,13)( 2, 5, 9,14)( 3, 8,11,16)( 4, 7,12,15)
4C1 444^{4} 22 44 1212 (1,5,10,14)(2,6,9,13)(3,16,11,8)(4,15,12,7)( 1, 5,10,14)( 2, 6, 9,13)( 3,16,11, 8)( 4,15,12, 7)
4C-1 444^{4} 22 44 1212 (1,14,10,5)(2,13,9,6)(3,8,11,16)(4,7,12,15)( 1,14,10, 5)( 2,13, 9, 6)( 3, 8,11,16)( 4, 7,12,15)
8A1 828^{2} 22 88 1414 (1,3,5,7,10,11,14,15)(2,4,6,8,9,12,13,16)( 1, 3, 5, 7,10,11,14,15)( 2, 4, 6, 8, 9,12,13,16)
8A-1 828^{2} 22 88 1414 (1,15,14,11,10,7,5,3)(2,16,13,12,9,8,6,4)( 1,15,14,11,10, 7, 5, 3)( 2,16,13,12, 9, 8, 6, 4)
8A3 828^{2} 22 88 1414 (1,7,14,3,10,15,5,11)(2,8,13,4,9,16,6,12)( 1, 7,14, 3,10,15, 5,11)( 2, 8,13, 4, 9,16, 6,12)
8A-3 828^{2} 22 88 1414 (1,11,5,15,10,3,14,7)(2,12,6,16,9,4,13,8)( 1,11, 5,15,10, 3,14, 7)( 2,12, 6,16, 9, 4,13, 8)
8B1 828^{2} 22 88 1414 (1,3,13,16,10,11,6,8)(2,4,14,15,9,12,5,7)( 1, 3,13,16,10,11, 6, 8)( 2, 4,14,15, 9,12, 5, 7)
8B-1 828^{2} 22 88 1414 (1,15,6,4,10,7,13,12)(2,16,5,3,9,8,14,11)( 1,15, 6, 4,10, 7,13,12)( 2,16, 5, 3, 9, 8,14,11)
8B3 828^{2} 22 88 1414 (1,7,6,12,10,15,13,4)(2,8,5,11,9,16,14,3)( 1, 7, 6,12,10,15,13, 4)( 2, 8, 5,11, 9,16,14, 3)
8B-3 828^{2} 22 88 1414 (1,11,13,8,10,3,6,16)(2,12,14,7,9,4,5,15)( 1,11,13, 8,10, 3, 6,16)( 2,12,14, 7, 9, 4, 5,15)

Malle's constant a(G)a(G):     1/41/4

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Character table

1A 2A 2B 2C 2D 2E 4A1 4A-1 4B1 4B-1 4C1 4C-1 8A1 8A-1 8A3 8A-3 8B1 8B-1 8B3 8B-3
Size 1 1 1 1 2 2 1 1 1 1 2 2 2 2 2 2 2 2 2 2
2 P 1A 1A 1A 1A 1A 1A 2C 2C 2C 2C 2C 2C 4A1 4A-1 4A-1 4A1 4B1 4B-1 4B-1 4B1
Type
32.5.1a R 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
32.5.1b R 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
32.5.1c R 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
32.5.1d R 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
32.5.1e1 C 1 1 1 1 1 1 1 1 1 1 1 1 i i i i i i i i
32.5.1e2 C 1 1 1 1 1 1 1 1 1 1 1 1 i i i i i i i i
32.5.1f1 C 1 1 1 1 1 1 1 1 1 1 1 1 i i i i i i i i
32.5.1f2 C 1 1 1 1 1 1 1 1 1 1 1 1 i i i i i i i i
32.5.1g1 C 1 1 1 1 1 1 ζ82 ζ82 ζ82 ζ82 ζ82 ζ82 ζ8 ζ8 ζ83 ζ83 ζ8 ζ83 ζ83 ζ8
32.5.1g2 C 1 1 1 1 1 1 ζ82 ζ82 ζ82 ζ82 ζ82 ζ82 ζ83 ζ83 ζ8 ζ8 ζ83 ζ8 ζ8 ζ83
32.5.1g3 C 1 1 1 1 1 1 ζ82 ζ82 ζ82 ζ82 ζ82 ζ82 ζ8 ζ8 ζ83 ζ83 ζ8 ζ83 ζ83 ζ8
32.5.1g4 C 1 1 1 1 1 1 ζ82 ζ82 ζ82 ζ82 ζ82 ζ82 ζ83 ζ83 ζ8 ζ8 ζ83 ζ8 ζ8 ζ83
32.5.1h1 C 1 1 1 1 1 1 ζ82 ζ82 ζ82 ζ82 ζ82 ζ82 ζ8 ζ8 ζ83 ζ83 ζ8 ζ83 ζ83 ζ8
32.5.1h2 C 1 1 1 1 1 1 ζ82 ζ82 ζ82 ζ82 ζ82 ζ82 ζ83 ζ83 ζ8 ζ8 ζ83 ζ8 ζ8 ζ83
32.5.1h3 C 1 1 1 1 1 1 ζ82 ζ82 ζ82 ζ82 ζ82 ζ82 ζ8 ζ8 ζ83 ζ83 ζ8 ζ83 ζ83 ζ8
32.5.1h4 C 1 1 1 1 1 1 ζ82 ζ82 ζ82 ζ82 ζ82 ζ82 ζ83 ζ83 ζ8 ζ8 ζ83 ζ8 ζ8 ζ83
32.5.2a R 2 2 2 2 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0
32.5.2b R 2 2 2 2 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0
32.5.2c1 C 2 2 2 2 0 0 2i 2i 2i 2i 0 0 0 0 0 0 0 0 0 0
32.5.2c2 C 2 2 2 2 0 0 2i 2i 2i 2i 0 0 0 0 0 0 0 0 0 0

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Regular extensions

Data not computed