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Group invariants
Abstract group: | $D_{17}^2$ |
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Order: | $1156=2^{2} \cdot 17^{2}$ |
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Cyclic: | no |
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Abelian: | no |
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Solvable: | yes |
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Nilpotency class: | not nilpotent |
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Group action invariants
Degree $n$: | $34$ |
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Transitive number $t$: | $11$ |
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Parity: | $-1$ |
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Primitive: | no |
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$\card{\Aut(F/K)}$: | $1$ |
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Generators: | $(1,4)(2,3)(5,17)(6,16)(7,15)(8,14)(9,13)(10,12)(18,23)(19,22)(20,21)(24,34)(25,33)(26,32)(27,31)(28,30)$, $(1,32,6,21,11,27,16,33,4,22,9,28,14,34,2,23,7,29,12,18,17,24,5,30,10,19,15,25,3,31,8,20,13,26)$ |
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Low degree resolvents
$\card{(G/N)}$ Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $34$: $D_{17}$ x 2 $68$: $D_{34}$ x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 17: None
Low degree siblings
34T11 x 7Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
Conjugacy classes not computed
Character table
100 x 100 character table
Regular extensions
Data not computed