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Magma
magma: G := TransitiveGroup(33, 40);
Group action invariants
| Degree $n$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $40$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $\PSL(2,32)$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | yes | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,32)(2,19)(3,6)(4,30)(5,11)(7,28)(8,23)(9,21)(10,17)(12,20)(13,24)(14,15)(16,25)(18,31)(22,26)(27,29), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31), (2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(32,33) | magma: Generators(G);
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Low degree resolvents
noneResolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 11: 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
| Cycle Type | Size | Order | Representative |
| $ 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 $ | $992$ | $11$ | $( 1, 3,23, 9, 5,19,10,17,22,14, 8)( 2,16,12,29,18,20,13, 7,30, 4,11) ( 6,25,31,33,32,21,27,15,28,26,24)$ |
| $ 11, 11, 11 $ | $992$ | $11$ | $( 1, 9,10,14, 3, 5,17, 8,23,19,22)( 2,29,13, 4,16,18, 7,11,12,20,30) ( 6,33,27,26,25,32,15,24,31,21,28)$ |
| $ 11, 11, 11 $ | $992$ | $11$ | $( 1,14,17,19, 9, 3, 8,22,10, 5,23)( 2, 4, 7,20,29,16,11,30,13,18,12) ( 6,26,15,21,33,25,24,28,27,32,31)$ |
| $ 11, 11, 11 $ | $992$ | $11$ | $( 1,19, 8, 5,14, 9,22,23,17, 3,10)( 2,20,11,18, 4,29,30,12, 7,16,13) ( 6,21,24,32,26,33,28,31,15,25,27)$ |
| $ 11, 11, 11 $ | $992$ | $11$ | $( 1, 5,22, 3,19,14,23,10, 8, 9,17)( 2,18,30,16,20, 4,12,13,11,29, 7) ( 6,32,28,25,21,26,31,27,24,33,15)$ |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ | $992$ | $3$ | $( 1, 6, 4)( 2,23,31)( 3,25,11)( 5,32,12)( 7,14,26)( 8,24,30)( 9,33,16) (10,27,18)(13,22,28)(15,20,17)(19,21,29)$ |
| $ 33 $ | $992$ | $33$ | $( 1,11,31, 9,12,21,10,20,28,14,30, 6, 3, 2,33, 5,29,27,17,13,26, 8, 4,25,23, 16,32,19,18,15,22, 7,24)$ |
| $ 33 $ | $992$ | $33$ | $( 1,25, 2, 9,32,29,10,15,13,14,24, 4, 3,31,16, 5,21,18,17,28, 7, 8, 6,11,23, 33,12,19,27,20,22,26,30)$ |
| $ 33 $ | $992$ | $33$ | $( 1, 2,32,10,13,24, 3,16,21,17, 7, 6,23,12,27,22,30,25, 9,29,15,14, 4,31, 5, 18,28, 8,11,33,19,20,26)$ |
| $ 33 $ | $992$ | $33$ | $( 1,31,12,10,28,30, 3,33,29,17,26, 4,23,32,18,22,24,11, 9,21,20,14, 6, 2, 5, 27,13, 8,25,16,19,15, 7)$ |
| $ 33 $ | $992$ | $33$ | $( 1,12,28, 3,29,26,23,18,24, 9,20, 6, 5,13,25,19, 7,31,10,30,33,17, 4,32,22, 11,21,14, 2,27, 8,16,15)$ |
| $ 33 $ | $992$ | $33$ | $( 1,32,13, 3,21, 7,23,27,30, 9,15, 4, 5,28,11,19,26, 2,10,24,16,17, 6,12,22, 25,29,14,31,18, 8,33,20)$ |
| $ 33 $ | $992$ | $33$ | $( 1,13,21,23,30,15, 5,11,26,10,16, 6,22,29,31, 8,20,32, 3, 7,27, 9, 4,28,19, 2,24,17,12,25,14,18,33)$ |
| $ 33 $ | $992$ | $33$ | $( 1,28,29,23,24,20, 5,25, 7,10,33, 4,22,21, 2, 8,15,12, 3,26,18, 9, 6,13,19, 31,30,17,32,11,14,27,16)$ |
| $ 33 $ | $992$ | $33$ | $( 1,29,24, 5, 7,33,22, 2,15, 3,18, 6,19,30,32,14,16,28,23,20,25,10, 4,21, 8, 12,26, 9,13,31,17,11,27)$ |
| $ 33 $ | $992$ | $33$ | $( 1,21,30, 5,26,16,22,31,20, 3,27, 4,19,24,12,14,33,13,23,15,11,10, 6,29, 8, 32, 7, 9,28, 2,17,25,18)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,21,23,12,15,28, 9, 7,30,31, 5,11,10,25,33,27,18,22,26,17,32,19, 3, 2, 8, 13,14, 6, 4,16,29)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,18,21,22,23,26,12,17,15,32,28,19, 9, 3, 7, 2,30, 8,31,13, 5,14,11, 6,10, 4,25,16,33,29,27)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,30,18, 8,21,31,22,13,23, 5,26,14,12,11,17, 6,15,10,32, 4,28,25,19,16, 9, 33, 3,29, 7,27, 2)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,15,30,10,18,32, 8, 4,21,28,31,25,22,19,13,16,23, 9, 5,33,26, 3,14,29,12, 7,11,27,17, 2, 6)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,23,15, 9,30, 5,10,33,18,26,32, 3, 8,14, 4,29,21,12,28, 7,31,11,25,27,22, 17,19, 2,13, 6,16)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,13,17,25, 7,21,14,32,33,30,23, 6,19,27,31,12, 4, 3,18, 5,15,16, 2,22,11, 28,29, 8,26,10, 9)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1, 4,13, 3,17,18,25, 5, 7,15,21,16,14, 2,32,22,33,11,30,28,23,29, 6, 8,19, 26,27,10,31, 9,12)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,33, 4,11,13,30, 3,28,17,23,18,29,25, 6, 5, 8, 7,19,15,26,21,27,16,10,14, 31, 2, 9,32,12,22)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1, 7,33,19, 4,15,11,26,13,21,30,27, 3,16,28,10,17,14,23,31,18, 2,29, 9,25, 32, 6,12, 5,22, 8)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,17, 7,14,33,23,19,31, 4,18,15, 2,11,29,26, 9,13,25,21,32,30, 6,27,12, 3, 5,16,22,28, 8,10)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,28, 5,27,32,13,29,15,31,33,17, 8,16,12,30,25,26, 2, 4,23, 7,10,22, 3, 6, 21, 9,11,18,19,14)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,26,28, 2, 5, 4,27,23,32, 7,13,10,29,22,15, 3,31, 6,33,21,17, 9, 8,11,16, 18,12,19,30,14,25)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,31,26, 6,28,33, 2,21, 5,17, 4, 9,27, 8,23,11,32,16, 7,18,13,12,10,19,29, 30,22,14,15,25, 3)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,32,31,16,26, 7, 6,18,28,13,33,12, 2,10,21,19, 5,29,17,30, 4,22, 9,14,27, 15, 8,25,23, 3,11)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1, 5,32,29,31,17,16,30,26, 4, 7,22, 6, 9,18,14,28,27,13,15,33, 8,12,25, 2, 23,10, 3,21,11,19)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1 $ | $1023$ | $2$ | $( 1, 6)( 2, 9)( 3, 5)( 4,23)( 7,14)(10,15)(11,13)(12,24)(16,29)(17,26)(18,31) (19,22)(20,33)(21,30)(25,28)(27,32)$ |
magma: ConjugacyClasses(G);
Group invariants
| Order: | $32736=2^{5} \cdot 3 \cdot 11 \cdot 31$ | magma: Order(G);
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| Cyclic: | no | magma: IsCyclic(G);
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| Abelian: | no | magma: IsAbelian(G);
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| Solvable: | no | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 32736.a | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);