↑

Properties

Label 18T802
Degree $18$
Order $129024$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $C_2^8:\SL(2,8)$

Related objects

Downloads

Learn more

Show commands: Magma

magma: G := TransitiveGroup(18, 802);
 

Group action invariants

Degree $n$:  $18$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $802$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $C_2^8:\SL(2,8)$
Parity:  $1$
magma: IsEven(G);
 
Primitive:  no
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $2$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,10,16,13,6,3,17,2,9,15,14,5,4,18)(7,8), (1,14,2,13)(3,7,4,8)(5,9)(6,10)(11,18)(12,17)
magma: Generators(G);
 

Low degree resolvents

|G/N|Galois groups for stem field(s)
$504$:  $\PSL(2,8)$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: None

Degree 6: None

Degree 9: $\PSL(2,8)$

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

LabelCycle TypeSizeOrderRepresentative
$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1$ $1$ $()$
$ 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $126$ $2$ $( 7, 8)( 9,10)(11,12)(17,18)$
$ 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $84$ $2$ $( 1, 2)( 3, 4)( 5, 6)( 9,10)(11,12)(15,16)$
$ 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $36$ $2$ $(13,14)(17,18)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ $9$ $2$ $( 1, 2)( 3, 4)( 5, 6)( 9,10)(11,12)(13,14)(15,16)(17,18)$
$ 7, 7, 1, 1, 1, 1 $ $4608$ $7$ $( 5, 7,11, 9,14,17,16)( 6, 8,12,10,13,18,15)$
$ 14, 2, 1, 1 $ $4608$ $14$ $( 3, 4)( 5, 7,12,10,13,17,16, 6, 8,11, 9,14,18,15)$
$ 14, 2, 1, 1 $ $4608$ $14$ $( 1, 2)( 5, 7,11,10,13,17,15, 6, 8,12, 9,14,18,16)$
$ 7, 7, 2, 2 $ $4608$ $14$ $( 1, 2)( 3, 4)( 5, 7,12, 9,14,17,15)( 6, 8,11,10,13,18,16)$
$ 7, 7, 1, 1, 1, 1 $ $4608$ $7$ $( 5, 9,16,11,17, 7,14)( 6,10,15,12,18, 8,13)$
$ 14, 2, 1, 1 $ $4608$ $14$ $( 3, 4)( 5, 9,16,12,17, 7,14, 6,10,15,11,18, 8,13)$
$ 14, 2, 1, 1 $ $4608$ $14$ $( 1, 2)( 5,10,16,11,18, 8,13, 6, 9,15,12,17, 7,14)$
$ 7, 7, 2, 2 $ $4608$ $14$ $( 1, 2)( 3, 4)( 5,10,16,12,18, 8,13)( 6, 9,15,11,17, 7,14)$
$ 7, 7, 1, 1, 1, 1 $ $4608$ $7$ $( 5,11,14,16, 7, 9,17)( 6,12,13,15, 8,10,18)$
$ 14, 2, 1, 1 $ $4608$ $14$ $( 3, 4)( 5,12,13,15, 8,10,17, 6,11,14,16, 7, 9,18)$
$ 14, 2, 1, 1 $ $4608$ $14$ $( 1, 2)( 5,11,14,15, 8, 9,18, 6,12,13,16, 7,10,17)$
$ 7, 7, 2, 2 $ $4608$ $14$ $( 1, 2)( 3, 4)( 5,12,13,16, 7,10,18)( 6,11,14,15, 8, 9,17)$
$ 4, 4, 2, 2, 2, 2, 1, 1 $ $2016$ $4$ $( 3, 5)( 4, 6)( 7,18, 8,17)( 9,12)(10,11)(13,15,14,16)$
$ 4, 4, 2, 2, 2, 2, 1, 1 $ $2016$ $4$ $( 3, 6)( 4, 5)( 7,17)( 8,18)( 9,11,10,12)(13,15,14,16)$
$ 4, 2, 2, 2, 2, 2, 2, 2 $ $4032$ $4$ $( 1, 2)( 3, 5)( 4, 6)( 7,17)( 8,18)( 9,12,10,11)(13,16)(14,15)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ $1008$ $2$ $( 3, 5)( 4, 6)( 7,17)( 8,18)( 9,12)(10,11)(13,15)(14,16)$
$ 4, 4, 2, 2, 2, 2, 1, 1 $ $2016$ $4$ $( 3, 6)( 4, 5)( 7,18, 8,17)( 9,11,10,12)(13,15)(14,16)$
$ 4, 4, 4, 2, 2, 2 $ $4032$ $4$ $( 1, 2)( 3, 5)( 4, 6)( 7,18, 8,17)( 9,12,10,11)(13,16,14,15)$
$ 4, 4, 4, 4, 1, 1 $ $1008$ $4$ $( 3, 6, 4, 5)( 7,18, 8,17)( 9,12,10,11)(13,16,14,15)$
$ 6, 6, 3, 3 $ $10752$ $6$ $( 1, 3, 6, 2, 4, 5)( 7,11,14)( 8,12,13)( 9,17,16,10,18,15)$
$ 3, 3, 3, 3, 3, 3 $ $3584$ $3$ $( 1, 3, 6)( 2, 4, 5)( 7,11,14)( 8,12,13)( 9,18,16)(10,17,15)$
$ 9, 9 $ $14336$ $9$ $( 1, 3, 6, 8,15,18,13,12, 9)( 2, 4, 5, 7,16,17,14,11,10)$
$ 9, 9 $ $14336$ $9$ $( 1, 3, 6,12,18, 9, 7,14,16)( 2, 4, 5,11,17,10, 8,13,15)$
$ 9, 9 $ $14336$ $9$ $( 1, 3, 6,13, 9,16,11, 7,17)( 2, 4, 5,14,10,15,12, 8,18)$

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $129024=2^{11} \cdot 3^{2} \cdot 7$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  no
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  129024.a
magma: IdentifyGroup(G);
 
Character table:

Size
2 P
3 P
7 P
Type

magma: CharacterTable(G);