# Properties

 Label 12T295 Order $$95040$$ n $$12$$ Cyclic No Abelian No Solvable No Primitive Yes $p$-group No Group: $M_{12}$

# Related objects

## Group action invariants

 Degree $n$ : $12$ Transitive number $t$ : $295$ Group : $M_{12}$ CHM label : $M(12)$ Parity: $1$ Primitive: Yes Nilpotency class: $-1$ (not nilpotent) Generators: (1,9,5,12,11,8,2,4)(6,10), (1,11,2,3,4)(5,8,12,6,7) $|\Aut(F/K)|$: $1$

## Low degree resolvents

None

Resolvents shown for degrees $\leq 47$

Degree 2: None

Degree 3: None

Degree 4: None

Degree 6: None

## Low degree siblings

12T295

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 $1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $1$ $1$ $()$ $11, 1$ $8640$ $11$ $( 1,12, 2, 8, 9, 7, 3, 4, 5,10, 6)$ $11, 1$ $8640$ $11$ $( 1, 6,10, 5, 4, 3, 7, 9, 8, 2,12)$ $2, 2, 2, 2, 1, 1, 1, 1$ $495$ $2$ $( 1, 8)( 2,11)( 3, 6)( 4,10)$ $4, 4, 2, 2$ $2970$ $4$ $( 1,10, 8, 4)( 2, 3,11, 6)( 5,12)( 7, 9)$ $4, 4, 1, 1, 1, 1$ $2970$ $4$ $( 1, 4, 8,10)( 5, 7,12, 9)$ $3, 3, 3, 1, 1, 1$ $1760$ $3$ $( 1,10, 2)( 4,11, 8)( 5, 7,12)$ $8, 2, 1, 1$ $11880$ $8$ $( 1,11, 4, 6, 8, 2,10, 3)( 5,12)$ $2, 2, 2, 2, 2, 2$ $396$ $2$ $( 1, 5)( 2, 3)( 4, 7)( 6,11)( 8,12)( 9,10)$ $3, 3, 3, 3$ $2640$ $3$ $( 1, 8, 2)( 3, 5,12)( 4,10, 6)( 7, 9,11)$ $5, 5, 1, 1$ $9504$ $5$ $( 1, 4, 6, 3,11)( 2,10, 7, 8, 5)$ $10, 2$ $9504$ $10$ $( 1,10, 4, 7, 6, 8, 3, 5,11, 2)( 9,12)$ $8, 4$ $11880$ $8$ $( 1, 4,11, 2, 7, 8, 3, 5)( 6, 9,10,12)$ $6, 3, 2, 1$ $15840$ $6$ $( 1, 6, 2, 7, 5, 9)( 3, 8)( 4,12,11)$ $6, 6$ $7920$ $6$ $( 1, 5,10, 9, 6, 7)( 2, 4, 3, 8,11,12)$

## Group invariants

 Order: $95040=2^{6} \cdot 3^{3} \cdot 5 \cdot 11$ Cyclic: No Abelian: No Solvable: No GAP id: Data not available
 Character table:  2 6 . . 6 1 1 5 3 1 4 1 5 3 2 2 3 3 . . 1 3 1 . . . 1 . . . 2 1 5 1 . . . . . . . 1 1 1 . . . . 11 1 1 1 . . . . . . . . . . . . 1a 11a 11b 2a 3a 6a 4a 8a 5a 2b 10a 4b 8b 3b 6b 2P 1a 11b 11a 1a 3a 3a 2a 4a 5a 1a 5a 2a 4b 3b 3b 3P 1a 11a 11b 2a 1a 2a 4a 8a 5a 2b 10a 4b 8b 1a 2b 5P 1a 11a 11b 2a 3a 6a 4a 8a 1a 2b 2b 4b 8b 3b 6b 7P 1a 11b 11a 2a 3a 6a 4a 8a 5a 2b 10a 4b 8b 3b 6b 11P 1a 1a 1a 2a 3a 6a 4a 8a 5a 2b 10a 4b 8b 3b 6b X.1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X.2 11 . . 3 2 . -1 -1 1 -1 -1 3 1 -1 -1 X.3 11 . . 3 2 . 3 1 1 -1 -1 -1 -1 -1 -1 X.4 16 A /A . -2 . . . 1 4 -1 . . 1 1 X.5 16 /A A . -2 . . . 1 4 -1 . . 1 1 X.6 45 1 1 -3 . . 1 -1 . 5 . 1 -1 3 -1 X.7 54 -1 -1 6 . . 2 . -1 6 1 2 . . . X.8 55 . . 7 1 1 -1 -1 . -5 . -1 -1 1 1 X.9 55 . . -1 1 -1 -1 1 . -5 . 3 -1 1 1 X.10 55 . . -1 1 -1 3 -1 . -5 . -1 1 1 1 X.11 66 . . 2 3 -1 -2 . 1 6 1 -2 . . . X.12 99 . . 3 . . -1 1 -1 -1 -1 -1 1 3 -1 X.13 120 -1 -1 -8 3 1 . . . . . . . . . X.14 144 1 1 . . . . . -1 4 -1 . . -3 1 X.15 176 . . . -4 . . . 1 -4 1 . . -1 -1 A = E(11)^2+E(11)^6+E(11)^7+E(11)^8+E(11)^10 = (-1-Sqrt(-11))/2 = -1-b11