Properties

Label 18T472
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 $t$ :  $472$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (3,5)(4,6)(7,11,10)(8,12,9)(13,14)(15,17)(16,18), (1,5)(2,6)(7,12,10,8,11,9)(13,14)(15,17)(16,18), (1,9,13)(2,10,14)(3,12,15,5,8,18)(4,11,16,6,7,17)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
3:  $C_3$
4:  $C_2^2$
6:  $C_6$ x 3
12:  $A_4$ x 5, $C_6\times C_2$
24:  $A_4\times C_2$ x 15
48:  $C_2^2 \times A_4$ x 5, $C_2^4:C_3$
96:  12T56 x 3
192:  12T90
648:  $S_3 \wr C_3 $
1296:  18T283
2592:  18T399

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: $C_3$

Degree 6: $A_4\times C_2$

Degree 9: $S_3 \wr C_3 $

Low degree siblings

18T472 x 23

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 88 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.