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Group invariants
| Abstract group: | $C_{19}^2:(C_9\times D_9)$ |
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| Order: | $58482=2 \cdot 3^{4} \cdot 19^{2}$ |
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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 $n$: | $38$ |
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| Transitive number $t$: | $42$ |
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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: | $(1,30,14,29,16,23,9,25,5,37,19,33,8,28,18,36,2,27)(3,24,7,31,12,35,4,21,13,32,10,22,11,38,17,20,15,26)(6,34)$, $(1,27,11,23,4,22,7,36,3,30,2,38,16,21,10,31,18,24)(5,33,12,34,9,20,13,26,14,37,19,35,6,25,17,32,15,29)(8,28)$ |
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Low degree resolvents
$\card{(G/N)}$ Galois groups for stem field(s) $2$: $C_2$ $3$: $C_3$ $6$: $S_3$, $C_6$ $9$: $C_9$ $18$: $S_3\times C_3$, $D_{9}$, $C_{18}$ $54$: $C_9\times S_3$, 18T19 $162$: 18T74 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 19: 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
Conjugacy classes not computed
Character table
77 x 77 character table
Regular extensions
Data not computed