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Magma
magma: G := TransitiveGroup(34, 33);
Group action invariants
| Degree $n$: | $34$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{17}^2:Q_{32}$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,20,16,22)(2,19,15,23)(3,18,14,24)(4,34,13,25)(5,33,12,26)(6,32,11,27)(7,31,10,28)(8,30,9,29)(17,21), (1,18,9,24)(2,23,8,19)(3,28,7,31)(4,33,6,26)(5,21)(10,29,17,30)(11,34,16,25)(12,22,15,20)(13,27,14,32) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $8$: $D_{4}$ $16$: $D_{8}$ $32$: 32T51 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 17: 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
| Label | 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 $ | $1$ | $1$ | $()$ | |
| $ 17, 17 $ | $32$ | $17$ | $( 1,15,12, 9, 6, 3,17,14,11, 8, 5, 2,16,13,10, 7, 4)(18,33,31,29,27,25,23,21, 19,34,32,30,28,26,24,22,20)$ | |
| $ 17, 17 $ | $32$ | $17$ | $( 1, 9,17, 8,16, 7,15, 6,14, 5,13, 4,12, 3,11, 2,10)(18,29,23,34,28,22,33,27, 21,32,26,20,31,25,19,30,24)$ | |
| $ 17, 17 $ | $32$ | $17$ | $( 1, 8,15, 5,12, 2, 9,16, 6,13, 3,10,17, 7,14, 4,11)(18,34,33,32,31,30,29,28, 27,26,25,24,23,22,21,20,19)$ | |
| $ 17, 17 $ | $32$ | $17$ | $( 1, 5, 9,13,17, 4, 8,12,16, 3, 7,11,15, 2, 6,10,14)(18,32,29,26,23,20,34,31, 28,25,22,19,33,30,27,24,21)$ | |
| $ 17, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $32$ | $17$ | $(18,22,26,30,34,21,25,29,33,20,24,28,32,19,23,27,31)$ | |
| $ 17, 17 $ | $32$ | $17$ | $( 1, 9,17, 8,16, 7,15, 6,14, 5,13, 4,12, 3,11, 2,10)(18,33,31,29,27,25,23,21, 19,34,32,30,28,26,24,22,20)$ | |
| $ 17, 17 $ | $32$ | $17$ | $( 1, 8,15, 5,12, 2, 9,16, 6,13, 3,10,17, 7,14, 4,11)(18,21,24,27,30,33,19,22, 25,28,31,34,20,23,26,29,32)$ | |
| $ 17, 17 $ | $32$ | $17$ | $( 1,13, 8, 3,15,10, 5,17,12, 7, 2,14, 9, 4,16,11, 6)(18,30,25,20,32,27,22,34, 29,24,19,31,26,21,33,28,23)$ | |
| $ 17, 17 $ | $32$ | $17$ | $( 1, 5, 9,13,17, 4, 8,12,16, 3, 7,11,15, 2, 6,10,14)(18,27,19,28,20,29,21,30, 22,31,23,32,24,33,25,34,26)$ | |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ | $289$ | $2$ | $( 2,17)( 3,16)( 4,15)( 5,14)( 6,13)( 7,12)( 8,11)( 9,10)(19,34)(20,33)(21,32) (22,31)(23,30)(24,29)(25,28)(26,27)$ | |
| $ 4, 4, 4, 4, 4, 4, 4, 4, 1, 1 $ | $578$ | $4$ | $( 2,14,17, 5)( 3,10,16, 9)( 4, 6,15,13)( 7,11,12, 8)(19,22,34,31)(20,26,33,27) (21,30,32,23)(24,25,29,28)$ | |
| $ 4, 4, 4, 4, 4, 4, 4, 4, 2 $ | $2312$ | $4$ | $( 1,20,16,22)( 2,19,15,23)( 3,18,14,24)( 4,34,13,25)( 5,33,12,26)( 6,32,11,27) ( 7,31,10,28)( 8,30, 9,29)(17,21)$ | |
| $ 8, 8, 8, 8, 1, 1 $ | $578$ | $8$ | $( 2,10,14,16,17, 9, 5, 3)( 4,11, 6,12,15, 8,13, 7)(19,20,22,26,34,33,31,27) (21,24,30,25,32,29,23,28)$ | |
| $ 8, 8, 8, 8, 1, 1 $ | $578$ | $8$ | $( 2, 9,14, 3,17,10, 5,16)( 4, 8, 6, 7,15,11,13,12)(19,33,22,27,34,20,31,26) (21,29,30,28,32,24,23,25)$ | |
| $ 16, 16, 1, 1 $ | $578$ | $16$ | $( 2, 6, 9, 7,14,15, 3,11,17,13,10,12, 5, 4,16, 8)(19,25,33,21,22,29,27,30,34, 28,20,32,31,24,26,23)$ | |
| $ 16, 16, 1, 1 $ | $578$ | $16$ | $( 2,13, 9,12,14, 4, 3, 8,17, 6,10, 7, 5,15,16,11)(19,28,33,32,22,24,27,23,34, 25,20,21,31,29,26,30)$ | |
| $ 16, 16, 1, 1 $ | $578$ | $16$ | $( 2,15,10, 8,14,13,16, 7,17, 4, 9,11, 5, 6, 3,12)(19,29,20,23,22,28,26,21,34, 24,33,30,31,25,27,32)$ | |
| $ 16, 16, 1, 1 $ | $578$ | $16$ | $( 2, 4,10,11,14, 6,16,12,17,15, 9, 8, 5,13, 3, 7)(19,24,20,30,22,25,26,32,34, 29,33,23,31,28,27,21)$ | |
| $ 4, 4, 4, 4, 4, 4, 4, 4, 2 $ | $2312$ | $4$ | $( 1,20,11,21)( 2,32,10,26)( 3,27, 9,31)( 4,22, 8,19)( 5,34, 7,24)( 6,29) (12,33,17,25)(13,28,16,30)(14,23,15,18)$ |
magma: ConjugacyClasses(G);
Group invariants
| Order: | $9248=2^{5} \cdot 17^{2}$ | 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: | yes | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 9248.t | magma: IdentifyGroup(G);
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| Character table: |
| Size | |
| 2 P | |
| 17 P | |
| Type |
magma: CharacterTable(G);