Properties

Label 18T485
Order \(5184\)
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 $t$ :  $485$
Parity:  $-1$
Primitive:  No
Generators:  (1,4)(2,3)(7,15,9,14,12,18,8,16,10,13,11,17), (1,15,12,5,14,8,4,18,10,2,16,11,6,13,7,3,17,9)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $V_4$
6:  $S_3$
12:  $D_{6}$
24:  $S_4$ x 3
48:  $S_4\times C_2$ x 3
96:  $V_4^2:S_3$
192:  12T100
648:  $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$
1296:  18T301
2592:  18T402

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: $S_3$

Degree 6: $S_4\times C_2$

Degree 9: $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$

Low degree siblings

18T485 x 3

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 58 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $5184=2^{6} \cdot 3^{4}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.