Properties

Label 18T284
Order \(1296\)
n \(18\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $18$
Transitive number $t$ :  $284$
Parity:  $-1$
Primitive:  No
Generators:  (1,13,10,2,14,9)(3,15,11,4,16,12)(5,18,7,6,17,8), (1,12,4,8,6,9,2,11,3,7,5,10)(13,15,17)(14,16,18)
$|\Aut(F/K)|$:  $6$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
3:  $C_3$
4:  $V_4$
6:  $S_3$, $C_6$ x 3
12:  $D_{6}$, $C_6\times C_2$
18:  $S_3\times C_3$
24:  $S_4$
36:  $C_6\times S_3$
48:  $S_4\times C_2$
54:  $C_3^2 : C_6$
72:  12T45
108:  18T41
144:  18T61
162:  $C_3 \wr S_3 $
216:  18T97
324:  18T119
432:  18T149
648:  18T203

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: $S_3$

Degree 6: $S_4\times C_2$

Degree 9: $C_3 \wr S_3 $

Low degree siblings

18T284 x 5

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 98 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $1296=2^{4} \cdot 3^{4}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [1296, 1827]
Character table: Data not available.