Properties

 Label 10T41 Degree $10$ Order $14400$ Cyclic no Abelian no Solvable no Primitive no $p$-group no Group: $(A_5^2 : C_2):C_2$

Related objects

Show commands: Magma

magma: G := TransitiveGroup(10, 41);

Group action invariants

 Degree $n$: $10$ magma: t, n := TransitiveGroupIdentification(G); n; Transitive number $t$: $41$ magma: t, n := TransitiveGroupIdentification(G); t; Group: $(A_5^2 : C_2):C_2$ CHM label: $[1/2.S(5)^{2}]2=[A(5):2]2$ Parity: $-1$ magma: IsEven(G); Primitive: no magma: IsPrimitive(G); Nilpotency class: $-1$ (not nilpotent) magma: NilpotencyClass(G); $\card{\Aut(F/K)}$: $1$ magma: Order(Centralizer(SymmetricGroup(n), G)); Generators: (2,10)(5,7), (2,4,6,8,10), (1,6)(2,7)(3,8)(4,9)(5,10) magma: Generators(G);

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 5: None

Low degree siblings

12T279, 20T456, 20T459, 24T12117, 25T101, 30T819, 36T9862, 40T10506, 40T10507, 40T10508

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

 Cycle Type Size Order Representative $1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $1$ $1$ $()$ $2, 2, 1, 1, 1, 1, 1, 1$ $100$ $2$ $(1,3)(6,8)$ $2, 2, 2, 2, 1, 1$ $225$ $2$ $( 1, 3)( 2,10)( 5, 7)( 6, 8)$ $3, 3, 1, 1, 1, 1$ $400$ $3$ $( 1, 3, 5)( 6, 8,10)$ $3, 3, 2, 2$ $400$ $6$ $( 1, 3, 5)( 2, 4)( 6, 8,10)( 7, 9)$ $4, 4, 1, 1$ $900$ $4$ $( 1, 3, 5, 7)( 2, 6, 8,10)$ $5, 5$ $288$ $5$ $( 1, 3, 5, 7, 9)( 2, 4, 6, 8,10)$ $5, 5$ $288$ $5$ $( 1, 3, 5, 7, 9)( 2, 6, 8,10, 4)$ $2, 2, 1, 1, 1, 1, 1, 1$ $30$ $2$ $( 2,10)( 6, 8)$ $3, 1, 1, 1, 1, 1, 1, 1$ $40$ $3$ $( 6, 8,10)$ $5, 1, 1, 1, 1, 1$ $48$ $5$ $( 2, 4, 6, 8,10)$ $3, 2, 2, 1, 1, 1$ $400$ $6$ $( 1, 3)( 2, 4)( 6, 8,10)$ $4, 2, 1, 1, 1, 1$ $600$ $4$ $( 1, 3)( 2, 6, 8,10)$ $3, 2, 2, 1, 1, 1$ $600$ $6$ $( 1, 3)( 5, 7)( 6, 8,10)$ $5, 2, 2, 1$ $720$ $10$ $( 1, 3)( 2, 4, 6, 8,10)( 5, 7)$ $5, 3, 1, 1$ $960$ $15$ $( 1, 3, 5)( 2, 4, 6, 8,10)$ $4, 3, 2, 1$ $1200$ $12$ $( 1, 3, 5)( 2, 6, 8,10)( 7, 9)$ $2, 2, 2, 2, 2$ $60$ $2$ $( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10)$ $4, 4, 2$ $900$ $4$ $( 1, 8, 3, 6)( 2, 7,10, 5)( 4, 9)$ $6, 2, 2$ $1200$ $6$ $( 1, 8, 3,10, 5, 6)( 2, 7)( 4, 9)$ $10$ $1440$ $10$ $( 1, 8, 3,10, 5, 2, 7, 4, 9, 6)$ $2, 2, 2, 2, 2$ $60$ $2$ $( 1, 8)( 2, 7)( 3, 6)( 4, 9)( 5,10)$ $6, 2, 2$ $1200$ $6$ $( 1, 8)( 2, 7, 4, 9,10, 5)( 3, 6)$ $4, 4, 2$ $900$ $4$ $( 1, 6, 3, 8)( 2, 7,10, 5)( 4, 9)$ $10$ $1440$ $10$ $( 1,10, 5, 2, 7, 6, 3, 4, 9, 8)$

magma: ConjugacyClasses(G);

Group invariants

 Order: $14400=2^{6} \cdot 3^{2} \cdot 5^{2}$ magma: Order(G); Cyclic: no magma: IsCyclic(G); Abelian: no magma: IsAbelian(G); Solvable: no magma: IsSolvable(G); Label: 14400.c magma: IdentifyGroup(G);
 Character table: not available.

magma: CharacterTable(G);