Properties

 Label 37T10 Order $$6881876545613172523157989790790451200000000$$ n $$37$$ Cyclic No Abelian No Solvable No Primitive Yes $p$-group No Group: $A_{37}$

Group action invariants

 Degree $n$ : $37$ Transitive number $t$ : $10$ Group : $A_{37}$ Parity: $1$ Primitive: Yes Nilpotency class: $-1$ (not nilpotent) Generators: (3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37), (1,2,3) $|\Aut(F/K)|$: $1$

Low degree resolvents

None

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - 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 10,871 conjugacy classes of elements. Data not shown.

Group invariants

 Order: $6881876545613172523157989790790451200000000=2^{33} \cdot 3^{17} \cdot 5^{8} \cdot 7^{5} \cdot 11^{3} \cdot 13^{2} \cdot 17^{2} \cdot 19 \cdot 23 \cdot 29 \cdot 31 \cdot 37$ Cyclic: No Abelian: No Solvable: No GAP id: Data not available
 Character table: Data not available.