Properties

Label 40T14344
Degree 4040
Order 2592025920
Cyclic no
Abelian no
Solvable no
Primitive yes
pp-group no
Group: PSp(4,3)\PSp(4,3)

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Copy content magma:G := TransitiveGroup(40, 14344);
 

Group invariants

Abstract group:  PSp(4,3)\PSp(4,3)
Copy content magma:IdentifyGroup(G);
 
Order:  25920=2634525920=2^{6} \cdot 3^{4} \cdot 5
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  no
Copy content magma:IsSolvable(G);
 
Nilpotency class:   not nilpotent
Copy content magma:NilpotencyClass(G);
 

Group action invariants

Degree nn:  4040
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number tt:  1434414344
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  11
Copy content magma:IsEven(G);
 
Primitive:  yes
Copy content magma:IsPrimitive(G);
 
#Aut(F/K)\card{\Aut(F/K)}:  11
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,3,8,16,7)(2,6,13,19,17)(4,9,5,10,20)(11,23,36,26,35)(12,21,31,25,18)(14,27,29,22,34)(15,28,30,38,32)(24,37,40,39,33)(1,3,8,16,7)(2,6,13,19,17)(4,9,5,10,20)(11,23,36,26,35)(12,21,31,25,18)(14,27,29,22,34)(15,28,30,38,32)(24,37,40,39,33), (1,2,5,10,19)(3,4,7,15,28)(6,12,21,13,25)(8,16,29,38,14)(9,18,31,20,27)(11,22,33,37,34)(17,30,23,35,32)(24,26,39,40,36)(1,2,5,10,19)(3,4,7,15,28)(6,12,21,13,25)(8,16,29,38,14)(9,18,31,20,27)(11,22,33,37,34)(17,30,23,35,32)(24,26,39,40,36)
Copy content magma:Generators(G);
 

Low degree resolvents

none

Resolvents shown for degrees 47\leq 47

Subfields

Degree 2: None

Degree 4: None

Degree 5: None

Degree 8: None

Degree 10: None

Degree 20: None

Low degree siblings

27T993, 36T12781, 40T14345, 45T666

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 1401^{40} 11 11 00 ()()
2A 216,182^{16},1^{8} 4545 22 1616 (1,13)(3,32)(4,31)(5,21)(7,14)(8,19)(10,38)(11,24)(12,25)(15,20)(16,34)(26,30)(28,35)(29,37)(33,39)(36,40)( 1,13)( 3,32)( 4,31)( 5,21)( 7,14)( 8,19)(10,38)(11,24)(12,25)(15,20)(16,34)(26,30)(28,35)(29,37)(33,39)(36,40)
2B 2202^{20} 270270 22 2020 (1,4)(2,7)(3,12)(5,19)(6,14)(8,29)(9,24)(10,40)(11,22)(13,15)(16,31)(17,30)(18,33)(20,34)(21,35)(23,39)(25,38)(26,27)(28,37)(32,36)( 1, 4)( 2, 7)( 3,12)( 5,19)( 6,14)( 8,29)( 9,24)(10,40)(11,22)(13,15)(16,31)(17,30)(18,33)(20,34)(21,35)(23,39)(25,38)(26,27)(28,37)(32,36)
3A1 39,1133^{9},1^{13} 4040 33 1818 (1,12,19)(2,20,38)(3,6,31)(4,9,21)(5,17,32)(10,29,27)(14,30,24)(15,22,37)(16,36,35)( 1,12,19)( 2,20,38)( 3, 6,31)( 4, 9,21)( 5,17,32)(10,29,27)(14,30,24)(15,22,37)(16,36,35)
3A-1 39,1133^{9},1^{13} 4040 33 1818 (1,19,12)(2,38,20)(3,31,6)(4,21,9)(5,32,17)(10,27,29)(14,24,30)(15,37,22)(16,35,36)( 1,19,12)( 2,38,20)( 3,31, 6)( 4,21, 9)( 5,32,17)(10,27,29)(14,24,30)(15,37,22)(16,35,36)
3B 312,143^{12},1^{4} 240240 33 2424 (1,21,40)(3,30,28)(4,24,22)(5,39,32)(6,25,37)(7,9,29)(8,18,11)(10,15,33)(12,23,14)(13,20,35)(19,31,27)(26,36,38)( 1,21,40)( 3,30,28)( 4,24,22)( 5,39,32)( 6,25,37)( 7, 9,29)( 8,18,11)(10,15,33)(12,23,14)(13,20,35)(19,31,27)(26,36,38)
3C 312,143^{12},1^{4} 480480 33 2424 (1,38,25)(2,27,22)(3,21,33)(5,39,32)(6,23,9)(7,20,30)(8,34,11)(10,12,13)(14,15,26)(16,24,19)(28,36,29)(35,40,37)( 1,38,25)( 2,27,22)( 3,21,33)( 5,39,32)( 6,23, 9)( 7,20,30)( 8,34,11)(10,12,13)(14,15,26)(16,24,19)(28,36,29)(35,40,37)
4A 48,22,144^{8},2^{2},1^{4} 540540 44 2626 (2,15,9,5)(3,35,29,14)(4,32,38,37)(6,16,27,30)(7,40,28,11)(8,25)(10,24,31,36)(13,33)(17,20,22,21)(18,34,23,26)( 2,15, 9, 5)( 3,35,29,14)( 4,32,38,37)( 6,16,27,30)( 7,40,28,11)( 8,25)(10,24,31,36)(13,33)(17,20,22,21)(18,34,23,26)
4B 4104^{10} 32403240 44 3030 (1,25,4,38)(2,18,7,33)(3,30,12,17)(5,8,19,29)(6,39,14,23)(9,31,24,16)(10,27,40,26)(11,15,22,13)(20,36,34,32)(21,28,35,37)( 1,25, 4,38)( 2,18, 7,33)( 3,30,12,17)( 5, 8,19,29)( 6,39,14,23)( 9,31,24,16)(10,27,40,26)(11,15,22,13)(20,36,34,32)(21,28,35,37)
5A 585^{8} 51845184 55 3232 (1,30,26,14,32)(2,36,27,31,39)(3,38,5,21,19)(4,11,37,33,9)(6,20,13,7,34)(8,16,22,15,10)(12,28,17,40,23)(18,25,29,24,35)( 1,30,26,14,32)( 2,36,27,31,39)( 3,38, 5,21,19)( 4,11,37,33, 9)( 6,20,13, 7,34)( 8,16,22,15,10)(12,28,17,40,23)(18,25,29,24,35)
6A1 64,3,24,156^{4},3,2^{4},1^{5} 360360 66 2626 (1,19,12)(2,4,20,9,38,21)(3,10,6,29,31,27)(5,37,17,15,32,22)(7,28)(11,40)(14,36,30,35,24,16)(18,23)(26,34)( 1,19,12)( 2, 4,20, 9,38,21)( 3,10, 6,29,31,27)( 5,37,17,15,32,22)( 7,28)(11,40)(14,36,30,35,24,16)(18,23)(26,34)
6A-1 64,3,24,156^{4},3,2^{4},1^{5} 360360 66 2626 (1,12,19)(2,21,38,9,20,4)(3,27,31,29,6,10)(5,22,32,15,17,37)(7,28)(11,40)(14,16,24,35,30,36)(18,23)(26,34)( 1,12,19)( 2,21,38, 9,20, 4)( 3,27,31,29, 6,10)( 5,22,32,15,17,37)( 7,28)(11,40)(14,16,24,35,30,36)(18,23)(26,34)
6B1 65,32,2,126^{5},3^{2},2,1^{2} 720720 66 3030 (1,12,3,6,10,29)(2,32,5,16,36,38)(4,25,9,18,21,28)(7,14,11,30,33,24)(8,15,40,22,23,37)(17,20,35)(19,27,31)(26,39)( 1,12, 3, 6,10,29)( 2,32, 5,16,36,38)( 4,25, 9,18,21,28)( 7,14,11,30,33,24)( 8,15,40,22,23,37)(17,20,35)(19,27,31)(26,39)
6B-1 65,32,2,126^{5},3^{2},2,1^{2} 720720 66 3030 (1,29,10,6,3,12)(2,38,36,16,5,32)(4,28,21,18,9,25)(7,24,33,30,11,14)(8,37,23,22,40,15)(17,35,20)(19,31,27)(26,39)( 1,29,10, 6, 3,12)( 2,38,36,16, 5,32)( 4,28,21,18, 9,25)( 7,24,33,30,11,14)( 8,37,23,22,40,15)(17,35,20)(19,31,27)(26,39)
6C 65,32,2,126^{5},3^{2},2,1^{2} 14401440 66 3030 (1,12,38,13,25,10)(2,22,27)(3,39,21,32,33,5)(4,31)(6,9,23)(7,26,20,14,30,15)(8,24,34,19,11,16)(28,37,36,35,29,40)( 1,12,38,13,25,10)( 2,22,27)( 3,39,21,32,33, 5)( 4,31)( 6, 9,23)( 7,26,20,14,30,15)( 8,24,34,19,11,16)(28,37,36,35,29,40)
6D 66,226^{6},2^{2} 21602160 66 3232 (1,6,21,25,40,37)(2,16)(3,23,30,14,28,12)(4,36,24,38,22,26)(5,19,39,31,32,27)(7,10,9,15,29,33)(8,13,18,20,11,35)(17,34)( 1, 6,21,25,40,37)( 2,16)( 3,23,30,14,28,12)( 4,36,24,38,22,26)( 5,19,39,31,32,27)( 7,10, 9,15,29,33)( 8,13,18,20,11,35)(17,34)
9A1 93,34,19^{3},3^{4},1 28802880 99 3232 (1,14,17,12,30,32,19,24,5)(2,31,9,20,3,21,38,6,4)(7,18,25)(8,33,11)(10,22,36,29,37,35,27,15,16)(13,26,34)(23,40,28)( 1,14,17,12,30,32,19,24, 5)( 2,31, 9,20, 3,21,38, 6, 4)( 7,18,25)( 8,33,11)(10,22,36,29,37,35,27,15,16)(13,26,34)(23,40,28)
9A-1 93,34,19^{3},3^{4},1 28802880 99 3232 (1,5,24,19,32,30,12,17,14)(2,4,6,38,21,3,20,9,31)(7,25,18)(8,11,33)(10,16,15,27,35,37,29,36,22)(13,34,26)(23,28,40)( 1, 5,24,19,32,30,12,17,14)( 2, 4, 6,38,21, 3,20, 9,31)( 7,25,18)( 8,11,33)(10,16,15,27,35,37,29,36,22)(13,34,26)(23,28,40)
12A1 122,42,3,22,112^{2},4^{2},3,2^{2},1 21602160 1212 3232 (1,12,19)(2,17,4,15,20,32,9,22,38,5,21,37)(3,30,10,35,6,24,29,16,31,14,27,36)(7,11,28,40)(8,25)(13,33)(18,26,23,34)( 1,12,19)( 2,17, 4,15,20,32, 9,22,38, 5,21,37)( 3,30,10,35, 6,24,29,16,31,14,27,36)( 7,11,28,40)( 8,25)(13,33)(18,26,23,34)
12A-1 122,42,3,22,112^{2},4^{2},3,2^{2},1 21602160 1212 3232 (1,19,12)(2,37,21,5,38,22,9,32,20,15,4,17)(3,36,27,14,31,16,29,24,6,35,10,30)(7,40,28,11)(8,25)(13,33)(18,34,23,26)( 1,19,12)( 2,37,21, 5,38,22, 9,32,20,15, 4,17)( 3,36,27,14,31,16,29,24, 6,35,10,30)( 7,40,28,11)( 8,25)(13,33)(18,34,23,26)

Malle's constant a(G)a(G):     1/161/16

Copy content magma:ConjugacyClasses(G);
 

Character table

1A 2A 2B 3A1 3A-1 3B 3C 4A 4B 5A 6A1 6A-1 6B1 6B-1 6C 6D 9A1 9A-1 12A1 12A-1
Size 1 45 270 40 40 240 480 540 3240 5184 360 360 720 720 1440 2160 2880 2880 2160 2160
2 P 1A 1A 1A 3A-1 3A1 3B 3C 2A 2B 5A 3A1 3A-1 3B 3B 3C 3B 9A-1 9A1 6A1 6A-1
3 P 1A 2A 2B 1A 1A 1A 1A 4A 4B 5A 2A 2A 2A 2A 2A 2B 3A1 3A-1 4A 4A
5 P 1A 2A 2B 3A-1 3A1 3B 3C 4A 4B 1A 6A-1 6A1 6B-1 6B1 6C 6D 9A-1 9A1 12A-1 12A1
Type
25920.a.1a R 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
25920.a.5a1 C 5 3 1 13ζ3 2+3ζ3 1 2 1 1 0 2ζ3 1+ζ3 1+2ζ3 12ζ3 0 1 ζ31 ζ3 ζ31 ζ3
25920.a.5a2 C 5 3 1 2+3ζ3 13ζ3 1 2 1 1 0 1+ζ3 2ζ3 12ζ3 1+2ζ3 0 1 ζ3 ζ31 ζ3 ζ31
25920.a.6a R 6 2 2 3 3 3 0 2 0 1 1 1 1 1 2 1 0 0 1 1
25920.a.10a1 C 10 2 2 53ζ3 2+3ζ3 1 1 2 0 0 2+3ζ3 13ζ3 1 1 1 1 ζ3 ζ31 ζ31 ζ3
25920.a.10a2 C 10 2 2 2+3ζ3 53ζ3 1 1 2 0 0 13ζ3 2+3ζ3 1 1 1 1 ζ31 ζ3 ζ3 ζ31
25920.a.15a R 15 7 3 3 3 0 3 1 1 0 1 1 2 2 1 0 0 0 1 1
25920.a.15b R 15 1 1 6 6 3 0 3 1 0 2 2 1 1 2 1 0 0 0 0
25920.a.20a R 20 4 4 2 2 5 1 0 0 0 2 2 1 1 1 1 1 1 0 0
25920.a.24a R 24 8 0 6 6 0 3 0 0 1 2 2 2 2 1 0 0 0 0 0
25920.a.30a R 30 10 2 3 3 3 3 2 0 0 1 1 1 1 1 1 0 0 1 1
25920.a.30b1 C 30 6 2 69ζ3 3+9ζ3 3 0 2 0 0 1+ζ3 2ζ3 12ζ3 1+2ζ3 0 1 0 0 ζ3 ζ31
25920.a.30b2 C 30 6 2 3+9ζ3 69ζ3 3 0 2 0 0 2ζ3 1+ζ3 1+2ζ3 12ζ3 0 1 0 0 ζ31 ζ3
25920.a.40a1 C 40 8 0 86ζ3 2+6ζ3 2 1 0 0 0 2ζ31 2ζ3 2ζ31 2ζ3 1 0 ζ31 ζ3 0 0
25920.a.40a2 C 40 8 0 2+6ζ3 86ζ3 2 1 0 0 0 2ζ3 2ζ31 2ζ3 2ζ31 1 0 ζ3 ζ31 0 0
25920.a.45a1 C 45 3 3 9ζ3 9ζ31 0 0 1 1 0 3ζ31 3ζ3 0 0 0 0 0 0 ζ3 ζ31
25920.a.45a2 C 45 3 3 9ζ31 9ζ3 0 0 1 1 0 3ζ3 3ζ31 0 0 0 0 0 0 ζ31 ζ3
25920.a.60a R 60 4 4 6 6 3 3 0 0 0 2 2 1 1 1 1 0 0 0 0
25920.a.64a R 64 0 0 8 8 4 2 0 0 1 0 0 0 0 0 0 1 1 0 0
25920.a.81a R 81 9 3 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0

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Regular extensions

Data not computed