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Group invariants
| Abstract group: | $D_{19}^2:(S_3\times C_9)$ |
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| Order: | $77976=2^{3} \cdot 3^{3} \cdot 19^{2}$ |
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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 $t$: | $44$ |
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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: | $(1,29,19,24,14,37,8,26,16,28,18,38,9,31,2,34,5,30)(3,20,10,36,7,21,11,22,12,27,17,33,4,25,15,23,13,32)(6,35)$, $(1,27,15,34,12,23,14,24,19,36,3,28)(2,37,8,21,4,38,13,33,7,30,11,32)(5,29,6,20,18,26,10,22,9,31,16,25)(17,35)$ |
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Low degree resolvents
$\card{(G/N)}$ Galois groups for stem field(s) $2$: $C_2$ x 3 $3$: $C_3$ $4$: $C_2^2$ $6$: $S_3$, $C_6$ x 3 $8$: $D_{4}$ $9$: $C_9$ $12$: $D_{6}$, $C_6\times C_2$ $18$: $S_3\times C_3$, $C_{18}$ x 3 $24$: $(C_6\times C_2):C_2$, $D_4 \times C_3$ $36$: $C_6\times S_3$, 36T2 $54$: $C_9\times S_3$ $72$: 12T42, 36T15 $108$: 36T63 $216$: 36T181 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
90 x 90 character table
Regular extensions
Data not computed