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Magma
magma: G := TransitiveGroup(34, 41);
Group action invariants
| Degree $n$: | $34$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $41$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $D_{17}:F_{17}$ | ||
| 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: | (1,25,2,34,15,32,14,23)(3,26,11,30,13,31,5,27)(4,18,7,28,12,22,9,29)(6,19,16,24,10,21,17,33)(8,20), (1,8,17,14,15,9,11,16,3,13,4,7,6,12,10,5)(18,29,31,19,23,33,24,27,26,32,30,25,21,28,20,34) | magma: Generators(G);
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Low degree resolvents
$\card{(G/N)}$ Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_4$ x 2, $C_2^2$ $8$: $C_8$ x 2, $C_4\times C_2$ $16$: $C_{16}$ x 2, $C_8\times C_2$ $32$: 32T32 $272$: $F_{17}$ x 2 $544$: 34T9 x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 17: None
Low degree siblings
34T41 x 7Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
| Label | Cycle Type | Size | Order | Index | Representative |
| 1A | $1^{34}$ | $1$ | $1$ | $0$ | $()$ |
| 2A | $2^{17}$ | $17$ | $2$ | $17$ | $( 1,21)( 2,20)( 3,19)( 4,18)( 5,34)( 6,33)( 7,32)( 8,31)( 9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)$ |
| 2B | $2^{17}$ | $17$ | $2$ | $17$ | $( 1,28)( 2,29)( 3,30)( 4,31)( 5,32)( 6,33)( 7,34)( 8,18)( 9,19)(10,20)(11,21)(12,22)(13,23)(14,24)(15,25)(16,26)(17,27)$ |
| 2C | $2^{16},1^{2}$ | $289$ | $2$ | $16$ | $( 2,17)( 3,16)( 4,15)( 5,14)( 6,13)( 7,12)( 8,11)( 9,10)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)$ |
| 4A1 | $4^{8},1^{2}$ | $289$ | $4$ | $24$ | $( 2,14,17, 5)( 3,10,16, 9)( 4, 6,15,13)( 7,11,12, 8)(19,31,34,22)(20,27,33,26)(21,23,32,30)(24,28,29,25)$ |
| 4A-1 | $4^{8},1^{2}$ | $289$ | $4$ | $24$ | $( 2, 5,17,14)( 3, 9,16,10)( 4,13,15, 6)( 7, 8,12,11)(19,22,34,31)(20,26,33,27)(21,30,32,23)(24,25,29,28)$ |
| 4B1 | $4^{8},2$ | $289$ | $4$ | $25$ | $( 1,29,10,31)( 2,33, 9,27)( 3,20, 8,23)( 4,24, 7,19)( 5,28, 6,32)(11,18,17,25)(12,22,16,21)(13,26,15,34)(14,30)$ |
| 4B-1 | $4^{8},2$ | $289$ | $4$ | $25$ | $( 1,24,12,31)( 2,20,11,18)( 3,33,10,22)( 4,29, 9,26)( 5,25, 8,30)( 6,21, 7,34)(13,27,17,28)(14,23,16,32)(15,19)$ |
| 8A1 | $8^{4},2$ | $289$ | $8$ | $29$ | $( 1,23, 5,21, 6,29, 2,31)( 3,22,14,25, 4,30,10,27)( 7,20,15,33,17,32, 9,19)( 8,28,11,18,16,24,13,34)(12,26)$ |
| 8A-1 | $8^{4},2$ | $289$ | $8$ | $29$ | $( 1,21, 4,32,16,25,13,31)( 2,19, 8,24,15,27, 9,22)( 3,34,12,33,14,29, 5,30)( 6,28, 7,26,11,18,10,20)(17,23)$ |
| 8A3 | $8^{4},1^{2}$ | $289$ | $8$ | $28$ | $( 2,10,14,16,17, 9, 5, 3)( 4,11, 6,12,15, 8,13, 7)(19,27,31,33,34,26,22,20)(21,28,23,29,32,25,30,24)$ |
| 8A-3 | $8^{4},1^{2}$ | $289$ | $8$ | $28$ | $( 2,16, 5,10,17, 3,14, 9)( 4,12,13,11,15, 7, 6, 8)(19,33,22,27,34,20,31,26)(21,29,30,28,32,24,23,25)$ |
| 8B1 | $8^{4},1^{2}$ | $289$ | $8$ | $28$ | $( 2, 9,14, 3,17,10, 5,16)( 4, 8, 6, 7,15,11,13,12)(19,26,31,20,34,27,22,33)(21,25,23,24,32,28,30,29)$ |
| 8B-1 | $8^{4},2$ | $289$ | $8$ | $29$ | $( 1,32, 3,19,11,18, 9,31)( 2,34, 7,27,10,33, 5,23)( 4,21,15,26, 8,29,14,24)( 6,25)(12,20,13,22,17,30,16,28)$ |
| 8B3 | $8^{4},2$ | $289$ | $8$ | $29$ | $( 1,30, 9,34,11,18, 3,31)( 2,22, 5,32,10,26, 7,33)( 4,23,14,28, 8,25,15,20)( 6,24)(12,27,16,29,17,21,13,19)$ |
| 8B-3 | $8^{4},1^{2}$ | $289$ | $8$ | $28$ | $( 2, 3, 5, 9,17,16,14,10)( 4, 7,13, 8,15,12, 6,11)(19,20,22,26,34,33,31,27)(21,24,30,25,32,29,23,28)$ |
| 16A1 | $16^{2},1^{2}$ | $289$ | $16$ | $30$ | $( 2, 7, 3,13, 5, 8, 9,15,17,12,16, 6,14,11,10, 4)(19,24,20,30,22,25,26,32,34,29,33,23,31,28,27,21)$ |
| 16A-1 | $16^{2},1^{2}$ | $289$ | $16$ | $30$ | $( 2, 6, 9, 7,14,15, 3,11,17,13,10,12, 5, 4,16, 8)(19,23,26,24,31,32,20,28,34,30,27,29,22,21,33,25)$ |
| 16A3 | $16^{2},2$ | $289$ | $16$ | $31$ | $( 1,27, 8,19, 5,20,16,22, 4,26,14,34,17,33, 6,31)( 2,21,10,24, 9,30, 7,25, 3,32,12,29,13,23,15,28)(11,18)$ |
| 16A-3 | $16^{2},2$ | $289$ | $16$ | $31$ | $( 1,22, 8,26, 3,28, 9,29,12,21, 5,34,10,32, 4,31)( 2,25,17,19,16,33, 7,23,11,18,13,24,14,27, 6,20)(15,30)$ |
| 16A5 | $16^{2},1^{2}$ | $289$ | $16$ | $30$ | $( 2,11,16,15, 5, 7,10, 6,17, 8, 3, 4,14,12, 9,13)(19,28,33,32,22,24,27,23,34,25,20,21,31,29,26,30)$ |
| 16A-5 | $16^{2},1^{2}$ | $289$ | $16$ | $30$ | $( 2, 4,10,11,14, 6,16,12,17,15, 9, 8, 5,13, 3, 7)(19,21,27,28,31,23,33,29,34,32,26,25,22,30,20,24)$ |
| 16A7 | $16^{2},1^{2}$ | $289$ | $16$ | $30$ | $( 2,12, 3, 6, 5,11, 9, 4,17, 7,16,13,14, 8,10,15)(19,29,20,23,22,28,26,21,34,24,33,30,31,25,27,32)$ |
| 16A-7 | $16^{2},2$ | $289$ | $16$ | $31$ | $( 1,19, 9,25, 5,22, 7,32, 6,27,15,21, 2,24,17,31)( 3,29, 8,20,14,33,11,18, 4,34,16,26,10,30,13,28)(12,23)$ |
| 16B1 | $16^{2},2$ | $289$ | $16$ | $31$ | $( 1,20,10,25, 9,32,11,18, 7,29,15,24,16,34,14,31)( 2,30, 8,22,13,21, 3,23, 6,19,17,27,12,28, 5,26)( 4,33)$ |
| 16B-1 | $16^{2},1^{2}$ | $289$ | $16$ | $30$ | $( 2,13, 9,12,14, 4, 3, 8,17, 6,10, 7, 5,15,16,11)(19,30,26,29,31,21,20,25,34,23,27,24,22,32,33,28)$ |
| 16B3 | $16^{2},1^{2}$ | $289$ | $16$ | $30$ | $( 2, 8,16, 4, 5,12,10,13,17,11, 3,15,14, 7, 9, 6)(19,25,33,21,22,29,27,30,34,28,20,32,31,24,26,23)$ |
| 16B-3 | $16^{2},2$ | $289$ | $16$ | $31$ | $( 1,34, 3,24, 2,29,11,18,15,32,13,25,14,20, 5,31)( 4,19,10,23, 7,21,17,22,12,30, 6,26, 9,28,16,27)( 8,33)$ |
| 16B5 | $16^{2},2$ | $289$ | $16$ | $31$ | $( 1,31)( 2,28,10,21,14,26,16,20,17,34, 9,24, 5,19, 3,25)( 4,22,11,18, 6,33,12,32,15,23, 8,27,13,29, 7,30)$ |
| 16B-5 | $16^{2},1^{2}$ | $289$ | $16$ | $30$ | $( 2,15,10, 8,14,13,16, 7,17, 4, 9,11, 5, 6, 3,12)(19,32,27,25,31,30,33,24,34,21,26,28,22,23,20,29)$ |
| 16B7 | $16^{2},2$ | $289$ | $16$ | $31$ | $( 1,26, 5,33,13,30,12,24,10,29, 6,22,15,25,16,31)( 2,32, 7,28,17,20, 3,21, 9,23, 4,27,11,18, 8,34)(14,19)$ |
| 16B-7 | $16^{2},2$ | $289$ | $16$ | $31$ | $( 1,33,15,29, 4,20, 9,21,16,19, 2,23,13,32, 8,31)( 3,30,11,18,12,25,10,28,14,22, 6,34, 5,27, 7,24)(17,26)$ |
| 17A | $17^{2}$ | $16$ | $17$ | $32$ | $( 1, 4, 7,10,13,16, 2, 5, 8,11,14,17, 3, 6, 9,12,15)(18,32,29,26,23,20,34,31,28,25,22,19,33,30,27,24,21)$ |
| 17B | $17^{2}$ | $16$ | $17$ | $32$ | $( 1,12, 6,17,11, 5,16,10, 4,15, 9, 3,14, 8, 2,13, 7)(18,29,23,34,28,22,33,27,21,32,26,20,31,25,19,30,24)$ |
| 17C | $17^{2}$ | $32$ | $17$ | $32$ | $( 1,16,14,12,10, 8, 6, 4, 2,17,15,13,11, 9, 7, 5, 3)(18,25,32,22,29,19,26,33,23,30,20,27,34,24,31,21,28)$ |
| 17D | $17^{2}$ | $32$ | $17$ | $32$ | $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16,17)(18,22,26,30,34,21,25,29,33,20,24,28,32,19,23,27,31)$ |
| 17E | $17^{2}$ | $32$ | $17$ | $32$ | $( 1,15,12, 9, 6, 3,17,14,11, 8, 5, 2,16,13,10, 7, 4)(18,26,34,25,33,24,32,23,31,22,30,21,29,20,28,19,27)$ |
| 17F | $17^{2}$ | $32$ | $17$ | $32$ | $( 1, 4, 7,10,13,16, 2, 5, 8,11,14,17, 3, 6, 9,12,15)(18,20,22,24,26,28,30,32,34,19,21,23,25,27,29,31,33)$ |
| 17G | $17^{2}$ | $32$ | $17$ | $32$ | $( 1, 7,13, 2, 8,14, 3, 9,15, 4,10,16, 5,11,17, 6,12)(18,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19)$ |
| 17H | $17^{2}$ | $32$ | $17$ | $32$ | $( 1,10, 2,11, 3,12, 4,13, 5,14, 6,15, 7,16, 8,17, 9)(18,31,27,23,19,32,28,24,20,33,29,25,21,34,30,26,22)$ |
| 17I | $17^{2}$ | $32$ | $17$ | $32$ | $( 1,13, 8, 3,15,10, 5,17,12, 7, 2,14, 9, 4,16,11, 6)(18,28,21,31,24,34,27,20,30,23,33,26,19,29,22,32,25)$ |
| 17J | $17,1^{17}$ | $32$ | $17$ | $16$ | $(18,23,28,33,21,26,31,19,24,29,34,22,27,32,20,25,30)$ |
| 34A | $34$ | $272$ | $34$ | $33$ | $( 1,28, 4,25, 7,22,10,19,13,33,16,30, 2,27, 5,24, 8,21,11,18,14,32,17,29, 3,26, 6,23, 9,20,12,34,15,31)$ |
| 34B | $34$ | $272$ | $34$ | $33$ | $( 1,25,12,19, 6,30,17,24,11,18, 5,29,16,23,10,34, 4,28,15,22, 9,33, 3,27,14,21, 8,32, 2,26,13,20, 7,31)$ |
Malle's constant $a(G)$: $1/16$
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.ba | magma: IdentifyGroup(G);
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| Character table: | 44 x 44 character table |
magma: CharacterTable(G);