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Magma
magma: G := TransitiveGroup(28, 120);
Group action invariants
Degree $n$: | $28$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $120$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $\PSL(2,13)$ | ||
Parity: | $1$ | magma: IsEven(G);
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Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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$\card{\Aut(F/K)}$: | $2$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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Generators: | (1,26,11,15,17,13,10)(2,25,12,16,18,14,9)(3,7,5,28,20,22,23)(4,8,6,27,19,21,24), (1,14,9,17,28,3,20)(2,13,10,18,27,4,19)(5,7,26,15,23,22,11)(6,8,25,16,24,21,12) | magma: Generators(G);
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Low degree resolvents
noneResolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 7: None
Degree 14: $\PSL(2,13)$
Low degree siblings
14T30, 42T176Siblings are shown 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 $ | $1$ | $1$ | $()$ |
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ | $91$ | $2$ | $( 1,26)( 2,25)( 3,27)( 4,28)( 5,18)( 6,17)( 7,19)( 8,20)( 9,10)(11,12)(13,21) (14,22)(15,24)(16,23)$ |
$ 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1 $ | $182$ | $3$ | $( 1,13,24)( 2,14,23)( 3,18,20)( 4,17,19)( 5, 8,27)( 6, 7,28)(15,26,21) (16,25,22)$ |
$ 6, 6, 6, 6, 2, 2 $ | $182$ | $6$ | $( 1,15,13,26,24,21)( 2,16,14,25,23,22)( 3, 8,18,27,20, 5)( 4, 7,17,28,19, 6) ( 9,10)(11,12)$ |
$ 7, 7, 7, 7 $ | $156$ | $7$ | $( 1, 4,23,21,11,18,14)( 2, 3,24,22,12,17,13)( 5,25,28, 8,15,10,19) ( 6,26,27, 7,16, 9,20)$ |
$ 7, 7, 7, 7 $ | $156$ | $7$ | $( 1,11, 4,18,23,14,21)( 2,12, 3,17,24,13,22)( 5,15,25,10,28,19, 8) ( 6,16,26, 9,27,20, 7)$ |
$ 7, 7, 7, 7 $ | $156$ | $7$ | $( 1,23,11,14, 4,21,18)( 2,24,12,13, 3,22,17)( 5,28,15,19,25, 8,10) ( 6,27,16,20,26, 7, 9)$ |
$ 13, 13, 1, 1 $ | $84$ | $13$ | $( 1,26,28, 7,14,19,17,15,24,12, 5, 3,10)( 2,25,27, 8,13,20,18,16,23,11, 6, 4, 9)$ |
$ 13, 13, 1, 1 $ | $84$ | $13$ | $( 1,24, 7, 3,17,26,12,14,10,15,28, 5,19)( 2,23, 8, 4,18,25,11,13, 9,16,27, 6, 20)$ |
magma: ConjugacyClasses(G);
Group invariants
Order: | $1092=2^{2} \cdot 3 \cdot 7 \cdot 13$ | 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: | 1092.25 | magma: IdentifyGroup(G);
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Character table: |
2 2 2 1 1 . . . . . 3 1 1 1 1 . . . . . 7 1 . . . 1 1 1 . . 13 1 . . . . . . 1 1 1a 2a 3a 6a 7a 7b 7c 13a 13b 2P 1a 1a 3a 3a 7c 7a 7b 13b 13a 3P 1a 2a 1a 2a 7b 7c 7a 13a 13b 5P 1a 2a 3a 6a 7c 7a 7b 13b 13a 7P 1a 2a 3a 6a 1a 1a 1a 13b 13a 11P 1a 2a 3a 6a 7b 7c 7a 13b 13a 13P 1a 2a 3a 6a 7a 7b 7c 1a 1a X.1 1 1 1 1 1 1 1 1 1 X.2 7 -1 1 -1 . . . D *D X.3 7 -1 1 -1 . . . *D D X.4 12 . . . A B C -1 -1 X.5 12 . . . B C A -1 -1 X.6 12 . . . C A B -1 -1 X.7 13 1 1 1 -1 -1 -1 . . X.8 14 2 -1 -1 . . . 1 1 X.9 14 -2 -1 1 . . . 1 1 A = -E(7)^3-E(7)^4 B = -E(7)^2-E(7)^5 C = -E(7)-E(7)^6 D = -E(13)-E(13)^3-E(13)^4-E(13)^9-E(13)^10-E(13)^12 = (1-Sqrt(13))/2 = -b13 |
magma: CharacterTable(G);