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Group invariants
Abstract group: | $C_2^9:C_{17}$ |
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Order: | $8704=2^{9} \cdot 17$ |
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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 $t$: | $29$ |
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Parity: | $-1$ |
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Primitive: | no |
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$\card{\Aut(F/K)}$: | $2$ |
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Generators: | $(1,5,9,13,18,21,25,29,33,3,7,11,15,19,23,28,32)(2,6,10,14,17,22,26,30,34,4,8,12,16,20,24,27,31)$, $(1,32,28,23,19,15,11,8,4,33,29,25,22,17,14,9,5,2,31,27,24,20,16,12,7,3,34,30,26,21,18,13,10,6)$ |
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Low degree resolvents
$\card{(G/N)}$ Galois groups for stem field(s) $2$: $C_2$ $17$: $C_{17}$ $34$: $C_{34}$ $4352$: 34T18 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 17: $C_{17}$
Low degree siblings
34T29 x 14Siblings 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
64 x 64 character table
Regular extensions
Data not computed