Properties

Label 27T2392
Degree $27$
Order $1.089\times 10^{28}$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $S_{27}$

Related objects

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Group action invariants

Degree $n$:  $27$
Transitive number $t$:  $2392$
Group:  $S_{27}$
Parity:  $-1$
Primitive:  yes
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,2), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 9: 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

There are 3,010 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $10888869450418352160768000000=2^{23} \cdot 3^{13} \cdot 5^{6} \cdot 7^{3} \cdot 11^{2} \cdot 13^{2} \cdot 17 \cdot 19 \cdot 23$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.