# Properties

 Label 22T51 Order $$40874803200$$ n $$22$$ Cyclic No Abelian No Solvable No Primitive No $p$-group No

# Related objects

## Group action invariants

Degree $n$ :  $22$
Transitive number $t$ :  $51$
CHM label :  $t22n51$
Parity:  $1$
Primitive:  No
Generators:  (1,17,11,3,13,5,16)(2,18,12,4,14,6,15)(7,19,22,10)(8,20,21,9), (1,14,5,21,11,7,10)(2,13,6,22,12,8,9)(3,19)(4,20)(15,16)(17,18)
$|\Aut(F/K)|$:  $2$
Low degree resolvents:
 2: $C_2$ 39916800: $S_{11}$

## Subfields

Degree 2: None

Degree 11: $S_{11}$

## Low degree siblings

22T50, 44T1749
A number field with this Galois group has no arithmetically equivalent fields.

## Conjugacy Classes

 Cycle Type Size Order Representative $1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $1$ $1$ $()$ $2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $55$ $2$ $(19,20)(21,22)$ $2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $330$ $2$ $( 7, 8)( 9,10)(19,20)(21,22)$ $2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $462$ $2$ $( 3, 4)( 7, 8)( 9,10)(11,12)(19,20)(21,22)$ $2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $165$ $2$ $( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(15,16)(19,20)(21,22)$ $2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1$ $11$ $2$ $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(19,20)(21,22)$ $2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $13860$ $2$ $( 1, 2)( 5, 7)( 6, 8)(11,12)(17,18)(21,22)$ $2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $9240$ $2$ $( 1, 2)( 5, 7)( 6, 8)( 9,10)(11,12)(17,18)(19,20)(21,22)$ $4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $9240$ $4$ $( 1, 2)( 5, 8, 6, 7)(11,12)(17,18)$ $4, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1$ $13860$ $4$ $( 1, 2)( 5, 8, 6, 7)(11,12)(17,18)(19,20)(21,22)$ $2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1$ $990$ $2$ $( 1, 2)( 3, 4)( 5, 7)( 6, 8)( 9,10)(11,12)(13,14)(17,18)(19,20)(21,22)$ $4, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1$ $3960$ $4$ $( 1, 2)( 3, 4)( 5, 8, 6, 7)(11,12)(13,14)(17,18)(19,20)(21,22)$ $4, 2, 2, 2, 2, 2, 2, 2, 2, 2$ $110$ $4$ $( 1, 2)( 3, 4)( 5, 8, 6, 7)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)$ $2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $3960$ $2$ $( 1, 2)( 5, 7)( 6, 8)(17,18)$ $4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $990$ $4$ $( 5, 8, 6, 7)(17,18)$ $2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $110$ $2$ $( 5, 7)( 6, 8)$ $6, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $73920$ $6$ $( 3, 9,12, 4,10,11)(13,14)(15,16)(19,20)$ $3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1$ $92400$ $6$ $( 3,10,11)( 4, 9,12)(13,14)(15,16)(19,20)(21,22)$ $3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $36960$ $6$ $( 3,10,11)( 4, 9,12)(13,14)(15,16)$ $6, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $73920$ $6$ $( 3, 9,12, 4,10,11)( 7, 8)(13,14)(15,16)(19,20)(21,22)$ $6, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $10560$ $6$ $( 3,10,12, 4, 9,11)(15,16)$ $3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1$ $36960$ $6$ $( 3,10,11)( 4, 9,12)( 5, 6)( 7, 8)(13,14)(15,16)(19,20)(21,22)$ $3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $1320$ $3$ $( 3, 9,11)( 4,10,12)$ $6, 2, 2, 2, 2, 2, 2, 2, 1, 1$ $10560$ $6$ $( 1, 2)( 3, 9,12, 4,10,11)( 5, 6)( 7, 8)(13,14)(15,16)(19,20)(21,22)$ $3, 3, 2, 2, 2, 2, 2, 2, 2, 2$ $1320$ $6$ $( 1, 2)( 3,10,11)( 4, 9,12)( 5, 6)( 7, 8)(13,14)(15,16)(17,18)(19,20)(21,22)$ $10, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $3548160$ $10$ $( 1,14,19,15,21, 2,13,20,16,22)( 3, 4)( 7, 8)(11,12)$ $5, 5, 2, 2, 2, 2, 1, 1, 1, 1$ $2661120$ $10$ $( 1,14,19,15,22)( 2,13,20,16,21)( 3, 4)( 7, 8)( 9,10)(11,12)$ $5, 5, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1$ $2661120$ $10$ $( 1,14,19,15,22)( 2,13,20,16,21)( 3, 4)(11,12)$ $10, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $1064448$ $10$ $( 1,14,19,15,21, 2,13,20,16,22)( 7, 8)$ $5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $177408$ $5$ $( 1,14,19,15,22)( 2,13,20,16,21)$ $10, 2, 2, 2, 2, 2, 1, 1$ $1064448$ $10$ $( 1,14,19,15,21, 2,13,20,16,22)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)$ $5, 5, 2, 2, 2, 2, 2, 2$ $177408$ $10$ $( 1,14,19,15,22)( 2,13,20,16,21)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(17,18)$ $3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1$ $1108800$ $6$ $( 3,11,10)( 4,12, 9)( 5, 8)( 6, 7)(13,14)(19,20)$ $6, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $1478400$ $6$ $( 3,11, 9, 4,12,10)( 5, 8)( 6, 7)(13,14)(19,20)(21,22)$ $6, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $443520$ $6$ $( 3,11, 9, 4,12,10)( 5, 8)( 6, 7)(13,14)$ $4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $1478400$ $12$ $( 3,11,10)( 4,12, 9)( 5, 7, 6, 8)(13,14)(19,20)(21,22)$ $4, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $443520$ $12$ $( 3,11,10)( 4,12, 9)( 5, 7, 6, 8)(13,14)$ $6, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1$ $1108800$ $12$ $( 3,11, 9, 4,12,10)( 5, 7, 6, 8)(13,14)(19,20)$ $3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $73920$ $6$ $( 3,12,10)( 4,11, 9)( 5, 8)( 6, 7)$ $6, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $73920$ $12$ $( 3,12, 9, 4,11,10)( 5, 7, 6, 8)$ $3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1$ $1108800$ $6$ $( 3,11,10)( 4,12, 9)( 5, 8)( 6, 7)(13,14)(15,16)(19,20)(21,22)$ $6, 4, 2, 2, 2, 2, 1, 1, 1, 1$ $1108800$ $12$ $( 3,11, 9, 4,12,10)( 5, 7, 6, 8)(13,14)(15,16)(19,20)(21,22)$ $6, 2, 2, 2, 2, 2, 2, 2, 1, 1$ $443520$ $6$ $( 1, 2)( 3,11, 9, 4,12,10)( 5, 8)( 6, 7)(13,14)(15,16)(19,20)(21,22)$ $4, 3, 3, 2, 2, 2, 2, 2, 1, 1$ $443520$ $12$ $( 1, 2)( 3,11,10)( 4,12, 9)( 5, 7, 6, 8)(13,14)(15,16)(19,20)(21,22)$ $3, 3, 2, 2, 2, 2, 2, 2, 2, 2$ $73920$ $6$ $( 1, 2)( 3,11,10)( 4,12, 9)( 5, 8)( 6, 7)(13,14)(15,16)(17,18)(19,20)(21,22)$ $6, 4, 2, 2, 2, 2, 2, 2$ $73920$ $12$ $( 1, 2)( 3,11, 9, 4,12,10)( 5, 7, 6, 8)(13,14)(15,16)(17,18)(19,20)(21,22)$ $5, 5, 4, 2, 1, 1, 1, 1, 1, 1$ $21288960$ $20$ $( 1,15,13,21,19)( 2,16,14,22,20)( 5, 7, 6, 8)(17,18)$ $10, 4, 2, 2, 1, 1, 1, 1$ $31933440$ $20$ $( 1,15,13,22,20, 2,16,14,21,19)( 5, 7, 6, 8)( 9,10)(17,18)$ $10, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $21288960$ $10$ $( 1,15,13,22,20, 2,16,14,21,19)( 5, 8)( 6, 7)(17,18)$ $5, 5, 2, 2, 2, 2, 1, 1, 1, 1$ $31933440$ $10$ $( 1,15,13,21,19)( 2,16,14,22,20)( 5, 8)( 6, 7)( 9,10)(17,18)$ $5, 5, 4, 2, 2, 2, 1, 1$ $21288960$ $20$ $( 1,15,13,21,19)( 2,16,14,22,20)( 3, 4)( 5, 7, 6, 8)(11,12)(17,18)$ $10, 4, 2, 2, 2, 2$ $5322240$ $20$ $( 1,15,13,22,20, 2,16,14,21,19)( 3, 4)( 5, 7, 6, 8)( 9,10)(11,12)(17,18)$ $10, 2, 2, 2, 2, 2, 1, 1$ $21288960$ $10$ $( 1,15,13,22,20, 2,16,14,21,19)( 3, 4)( 5, 8)( 6, 7)(11,12)(17,18)$ $5, 5, 2, 2, 2, 2, 2, 2$ $5322240$ $10$ $( 1,15,13,21,19)( 2,16,14,22,20)( 3, 4)( 5, 8)( 6, 7)( 9,10)(11,12)(17,18)$ $10, 4, 1, 1, 1, 1, 1, 1, 1, 1$ $5322240$ $20$ $( 1,15,13,22,20, 2,16,14,21,19)( 5, 7, 6, 8)$ $5, 5, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1$ $5322240$ $10$ $( 1,15,13,21,19)( 2,16,14,22,20)( 5, 8)( 6, 7)$ $10, 6, 1, 1, 1, 1, 1, 1$ $28385280$ $30$ $( 1,19,22,13,16, 2,20,21,14,15)( 3,12, 9, 4,11,10)$ $5, 5, 3, 3, 1, 1, 1, 1, 1, 1$ $28385280$ $15$ $( 1,19,21,14,15)( 2,20,22,13,16)( 3,12,10)( 4,11, 9)$ $6, 5, 5, 2, 1, 1, 1, 1$ $85155840$ $30$ $( 1,19,21,14,15)( 2,20,22,13,16)( 3,12, 9, 4,11,10)( 7, 8)$ $10, 3, 3, 2, 1, 1, 1, 1$ $85155840$ $30$ $( 1,19,22,13,16, 2,20,21,14,15)( 3,12,10)( 4,11, 9)( 7, 8)$ $10, 6, 2, 2, 1, 1$ $85155840$ $30$ $( 1,19,22,13,16, 2,20,21,14,15)( 3,12, 9, 4,11,10)( 5, 6)( 7, 8)$ $5, 5, 3, 3, 2, 2, 1, 1$ $85155840$ $30$ $( 1,19,21,14,15)( 2,20,22,13,16)( 3,12,10)( 4,11, 9)( 5, 6)( 7, 8)$ $6, 5, 5, 2, 2, 2$ $28385280$ $30$ $( 1,19,21,14,15)( 2,20,22,13,16)( 3,12, 9, 4,11,10)( 5, 6)( 7, 8)(17,18)$ $10, 3, 3, 2, 2, 2$ $28385280$ $30$ $( 1,19,22,13,16, 2,20,21,14,15)( 3,12,10)( 4,11, 9)( 5, 6)( 7, 8)(17,18)$ $10, 6, 2, 2, 1, 1$ $170311680$ $30$ $( 1,13,20,16,22, 2,14,19,15,21)( 3, 9,11, 4,10,12)( 5, 7)( 6, 8)$ $5, 5, 3, 3, 2, 2, 1, 1$ $170311680$ $30$ $( 1,13,20,16,21)( 2,14,19,15,22)( 3,10,12)( 4, 9,11)( 5, 7)( 6, 8)$ $6, 5, 5, 4, 1, 1$ $170311680$ $60$ $( 1,13,20,16,21)( 2,14,19,15,22)( 3, 9,11, 4,10,12)( 5, 8, 6, 7)$ $10, 4, 3, 3, 1, 1$ $170311680$ $60$ $( 1,13,20,16,22, 2,14,19,15,21)( 3,10,12)( 4, 9,11)( 5, 8, 6, 7)$ $6, 5, 5, 2, 2, 2$ $170311680$ $30$ $( 1,13,20,16,21)( 2,14,19,15,22)( 3, 9,11, 4,10,12)( 5, 7)( 6, 8)(17,18)$ $10, 3, 3, 2, 2, 2$ $170311680$ $30$ $( 1,13,20,16,22, 2,14,19,15,21)( 3,10,12)( 4, 9,11)( 5, 7)( 6, 8)(17,18)$ $10, 6, 4, 2$ $170311680$ $60$ $( 1,13,20,16,22, 2,14,19,15,21)( 3, 9,11, 4,10,12)( 5, 8, 6, 7)(17,18)$ $5, 5, 4, 3, 3, 2$ $170311680$ $60$ $( 1,13,20,16,21)( 2,14,19,15,22)( 3,10,12)( 4, 9,11)( 5, 8, 6, 7)(17,18)$ $4, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1$ $166320$ $4$ $( 1,17, 2,18)( 5, 6)( 7, 8)( 9,10)(11,12)(13,15)(14,16)(19,20)$ $4, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1$ $277200$ $4$ $( 1,17, 2,18)( 5, 6)( 7, 8)(11,12)(13,15)(14,16)$ $4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $138600$ $4$ $( 1,17, 2,18)( 5, 6)( 7, 8)( 9,10)(13,15,14,16)(19,20)$ $4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $83160$ $4$ $( 1,17, 2,18)( 5, 6)( 7, 8)(13,15,14,16)$ $4, 4, 2, 2, 2, 2, 2, 2, 1, 1$ $27720$ $4$ $( 1,17, 2,18)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,15,14,16)(19,20)$ $4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $55440$ $4$ $( 1,17, 2,18)(11,12)(13,15)(14,16)$ $4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $3960$ $4$ $( 1,17, 2,18)(13,15,14,16)$ $4, 2, 2, 2, 2, 2, 2, 2, 2, 2$ $7920$ $4$ $( 1,17, 2,18)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,16)(14,15)(19,20)(21,22)$ $2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1$ $27720$ $2$ $( 1,17)( 2,18)( 5, 6)( 7, 8)( 9,10)(11,12)(13,15)(14,16)(19,20)(21,22)$ $2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $138600$ $2$ $( 1,17)( 2,18)( 5, 6)( 7, 8)( 9,10)(11,12)(13,15)(14,16)$ $2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $83160$ $2$ $( 1,17)( 2,18)( 5, 6)(11,12)(13,15)(14,16)$ $2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $3960$ $2$ $( 1,17)( 2,18)(13,16)(14,15)$ $8, 4, 4, 2, 1, 1, 1, 1$ $19958400$ $8$ $( 1,15,18,14, 2,16,17,13)( 5, 7, 6, 8)( 9,10)(19,21,20,22)$ $8, 4, 2, 2, 1, 1, 1, 1, 1, 1$ $13305600$ $8$ $( 1,15,18,14, 2,16,17,13)( 5, 7, 6, 8)(19,22)(20,21)$ $8, 2, 2, 2, 2, 2, 1, 1, 1, 1$ $19958400$ $8$ $( 1,15,18,14, 2,16,17,13)( 5, 8)( 6, 7)( 9,10)(19,22)(20,21)$ $8, 4, 4, 2, 2, 2$ $6652800$ $8$ $( 1,15,18,14, 2,16,17,13)( 3, 4)( 5, 7, 6, 8)( 9,10)(11,12)(19,21,20,22)$ $8, 4, 2, 2, 2, 2, 1, 1$ $39916800$ $8$ $( 1,15,18,14, 2,16,17,13)( 3, 4)( 5, 7, 6, 8)(11,12)(19,22)(20,21)$ $8, 2, 2, 2, 2, 2, 2, 2$ $6652800$ $8$ $( 1,15,18,14, 2,16,17,13)( 3, 4)( 5, 8)( 6, 7)( 9,10)(11,12)(19,22)(20,21)$ $4, 4, 4, 4, 2, 2, 1, 1$ $19958400$ $4$ $( 1,15,18,13)( 2,16,17,14)( 5, 7, 6, 8)( 9,10)(11,12)(19,21,20,22)$ $4, 4, 4, 2, 2, 2, 1, 1, 1, 1$ $39916800$ $4$ $( 1,15,18,13)( 2,16,17,14)( 5, 7, 6, 8)(11,12)(19,22)(20,21)$ $4, 4, 2, 2, 2, 2, 2, 2, 1, 1$ $19958400$ $4$ $( 1,15,18,13)( 2,16,17,14)( 5, 8)( 6, 7)( 9,10)(11,12)(19,22)(20,21)$ $4, 4, 4, 4, 1, 1, 1, 1, 1, 1$ $6652800$ $4$ $( 1,16,17,13)( 2,15,18,14)( 5, 7, 6, 8)(19,21,20,22)$ $4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $6652800$ $4$ $( 1,16,17,13)( 2,15,18,14)( 5, 8)( 6, 7)(19,22)(20,21)$ $4, 4, 4, 2, 2, 2, 2, 2$ $13305600$ $4$ $( 1,16,17,13)( 2,15,18,14)( 3, 4)( 5, 7, 6, 8)( 9,10)(11,12)(19,22)(20,21)$ $4, 4, 2, 2, 2, 2, 2, 2, 1, 1$ $4989600$ $4$ $( 1,18, 2,17)( 3, 4)( 5, 7, 6, 8)( 9,10)(13,15)(14,16)(19,21)(20,22)$ $4, 4, 4, 2, 2, 2, 1, 1, 1, 1$ $3326400$ $4$ $( 1,18, 2,17)( 3, 4)( 5, 7, 6, 8)(13,15)(14,16)(19,22,20,21)$ $4, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1$ $3326400$ $4$ $( 1,18, 2,17)( 3, 4)( 5, 8)( 6, 7)(13,15)(14,16)(19,21)(20,22)$ $4, 4, 4, 2, 2, 2, 2, 2$ $1108800$ $4$ $( 1,18, 2,17)( 3, 4)( 5, 7, 6, 8)( 9,10)(11,12)(13,15,14,16)(19,21)(20,22)$ $4, 4, 4, 4, 2, 2, 1, 1$ $831600$ $4$ $( 1,18, 2,17)( 3, 4)( 5, 7, 6, 8)(11,12)(13,15,14,16)(19,22,20,21)$ $4, 4, 4, 4, 1, 1, 1, 1, 1, 1$ $277200$ $4$ $( 1,18, 2,17)( 5, 7, 6, 8)(13,15,14,16)(19,22,20,21)$ $4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $1663200$ $4$ $( 1,18, 2,17)( 5, 8)( 6, 7)(13,15,14,16)(19,21)(20,22)$ $4, 2, 2, 2, 2, 2, 2, 2, 2, 2$ $1108800$ $4$ $( 1,18, 2,17)( 3, 4)( 5, 8)( 6, 7)( 9,10)(11,12)(13,16)(14,15)(19,21)(20,22)$ $2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1$ $831600$ $2$ $( 1,18)( 2,17)( 3, 4)( 5, 8)( 6, 7)( 9,10)(13,15)(14,16)(19,21)(20,22)$ $2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $277200$ $2$ $( 1,18)( 2,17)( 5, 8)( 6, 7)(13,16)(14,15)(19,21)(20,22)$ $8, 4, 4, 2, 1, 1, 1, 1$ $79833600$ $8$ $( 1,15,18,14)( 2,16,17,13)( 3, 4)( 5,22, 7,19, 6,21, 8,20)$ $4, 4, 4, 4, 2, 2, 1, 1$ $39916800$ $4$ $( 1,15,18,14)( 2,16,17,13)( 3, 4)( 5,21, 8,20)( 6,22, 7,19)( 9,10)$ $8, 8, 2, 2, 1, 1$ $39916800$ $8$ $( 1,15,18,13, 2,16,17,14)( 3, 4)( 5,22, 7,19, 6,21, 8,20)(11,12)$ $8, 4, 4, 2, 2, 2$ $26611200$ $8$ $( 1,15,18,13, 2,16,17,14)( 3, 4)( 5,21, 8,20)( 6,22, 7,19)( 9,10)(11,12)$ $8, 8, 1, 1, 1, 1, 1, 1$ $13305600$ $8$ $( 1,15,18,13, 2,16,17,14)( 5,22, 7,19, 6,21, 8,20)$ $4, 4, 4, 4, 1, 1, 1, 1, 1, 1$ $13305600$ $4$ $( 1,16,17,14)( 2,15,18,13)( 5,21, 8,20)( 6,22, 7,19)$ $6, 4, 2, 2, 2, 2, 2, 2$ $8870400$ $12$ $( 1,17)( 2,18)( 3,10,11, 4, 9,12)( 5, 8, 6, 7)(13,16)(14,15)(19,22)(20,21)$ $4, 4, 3, 3, 2, 2, 2, 2$ $13305600$ $12$ $( 1,17)( 2,18)( 3, 9,12)( 4,10,11)( 5, 8, 6, 7)(13,16)(14,15)(19,21,20,22)$ $3, 3, 2, 2, 2, 2, 2, 2, 2, 2$ $2217600$ $6$ $( 1,17)( 2,18)( 3, 9,12)( 4,10,11)( 5, 7)( 6, 8)(13,16)(14,15)(19,22)(20,21)$ $6, 4, 4, 4, 2, 2$ $8870400$ $12$ $( 1,17)( 2,18)( 3, 9,11, 4,10,12)( 5, 8, 6, 7)(13,16,14,15)(19,21,20,22)$ $4, 4, 4, 4, 3, 3$ $2217600$ $12$ $( 1,17, 2,18)( 3,10,12)( 4, 9,11)( 5, 8, 6, 7)(13,16,14,15)(19,21,20,22)$ $8, 6, 4, 4$ $212889600$ $24$ $( 1,13,18,16, 2,14,17,15)( 3,11,10, 4,12, 9)( 5,20, 8,21)( 6,19, 7,22)$ $8, 8, 3, 3$ $106444800$ $24$ $( 1,13,18,16, 2,14,17,15)( 3,11, 9)( 4,12,10)( 5,20, 8,22, 6,19, 7,21)$ $4, 4, 4, 4, 3, 3$ $106444800$ $12$ $( 1,14,17,15)( 2,13,18,16)( 3,12, 9)( 4,11,10)( 5,20, 8,21)( 6,19, 7,22)$ $16, 2, 1, 1, 1, 1$ $319334400$ $16$ $( 1, 5,21,13,18, 7,19,15, 2, 6,22,14,17, 8,20,16)( 9,10)$ $8, 8, 1, 1, 1, 1, 1, 1$ $106444800$ $8$ $( 1, 5,22,14,17, 8,20,16)( 2, 6,21,13,18, 7,19,15)$ $16, 2, 2, 2$ $106444800$ $16$ $( 1, 5,21,13,18, 7,19,15, 2, 6,22,14,17, 8,20,16)( 3, 4)( 9,10)(11,12)$ $8, 8, 2, 2, 1, 1$ $319334400$ $8$ $( 1, 5,22,14,17, 8,20,16)( 2, 6,21,13,18, 7,19,15)( 3, 4)(11,12)$ $16, 6$ $851558400$ $48$ $( 1,13,20, 5,17,15,21, 7, 2,14,19, 6,18,16,22, 8)( 3, 9,12, 4,10,11)$ $8, 8, 3, 3$ $851558400$ $24$ $( 1,13,20, 5,17,15,22, 8)( 2,14,19, 6,18,16,21, 7)( 3,10,11)( 4, 9,12)$ $6, 6, 2, 2, 1, 1, 1, 1, 1, 1$ $2956800$ $6$ $( 1, 5,13, 2, 6,14)( 3, 4)( 7,16,17, 8,15,18)( 9,10)$ $6, 6, 2, 2, 2, 2, 1, 1$ $1478400$ $6$ $( 1, 5,13, 2, 6,14)( 3, 4)( 7,16,17, 8,15,18)( 9,10)(19,20)(21,22)$ $6, 3, 3, 2, 2, 2, 1, 1, 1, 1$ $5913600$ $6$ $( 1, 5,13, 2, 6,14)( 3, 4)( 7,16,17)( 8,15,18)( 9,10)(21,22)$ $6, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1$ $2956800$ $6$ $( 1, 5,13, 2, 6,14)( 3, 4)( 7,16,17)( 8,15,18)$ $6, 3, 3, 2, 2, 2, 2, 2$ $591360$ $6$ $( 1, 5,14)( 2, 6,13)( 3, 4)( 7,16,17, 8,15,18)( 9,10)(11,12)(19,20)(21,22)$ $3, 3, 3, 3, 2, 2, 2, 2, 1, 1$ $1478400$ $6$ $( 1, 5,14)( 2, 6,13)( 3, 4)( 7,16,17)( 8,15,18)( 9,10)(11,12)(21,22)$ $3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1$ $2956800$ $6$ $( 1, 5,14)( 2, 6,13)( 3, 4)( 7,16,17)( 8,15,18)(11,12)$ $3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $295680$ $3$ $( 1, 5,14)( 2, 6,13)( 7,16,17)( 8,15,18)$ $6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $295680$ $6$ $( 1, 6,13, 2, 5,14)( 7,16,17, 8,15,18)$ $6, 6, 2, 2, 2, 2, 1, 1$ $106444800$ $6$ $( 1,16, 6,17,14, 8)( 2,15, 5,18,13, 7)( 3,10)( 4, 9)(19,20)(21,22)$ $6, 6, 2, 2, 1, 1, 1, 1, 1, 1$ $35481600$ $6$ $( 1,16, 6,17,14, 8)( 2,15, 5,18,13, 7)( 3,10)( 4, 9)$ $6, 6, 4, 2, 1, 1, 1, 1$ $106444800$ $12$ $( 1,16, 6,17,14, 8)( 2,15, 5,18,13, 7)( 3, 9, 4,10)(19,20)$ $12, 2, 2, 2, 1, 1, 1, 1$ $106444800$ $12$ $( 1,16, 6,17,14, 7, 2,15, 5,18,13, 8)( 3,10)( 4, 9)(19,20)$ $12, 4, 2, 2, 1, 1$ $106444800$ $12$ $( 1,16, 6,17,14, 7, 2,15, 5,18,13, 8)( 3, 9, 4,10)(19,20)(21,22)$ $12, 4, 1, 1, 1, 1, 1, 1$ $35481600$ $12$ $( 1,16, 6,17,14, 7, 2,15, 5,18,13, 8)( 3, 9, 4,10)$ $6, 6, 4, 2, 2, 2$ $35481600$ $12$ $( 1,16, 6,17,14, 8)( 2,15, 5,18,13, 7)( 3,10, 4, 9)(11,12)(19,20)(21,22)$ $12, 2, 2, 2, 2, 2$ $35481600$ $12$ $( 1,16, 6,17,14, 7, 2,15, 5,18,13, 8)( 3, 9)( 4,10)(11,12)(19,20)(21,22)$ $8, 4, 4, 4, 1, 1$ $13305600$ $8$ $( 1,20, 2,19)( 5, 9,21,16, 6,10,22,15)( 7,12, 8,11)(13,18,14,17)$ $4, 4, 4, 4, 2, 2, 1, 1$ $39916800$ $4$ $( 1,19)( 2,20)( 5, 9,22,15)( 6,10,21,16)( 7,12, 8,11)(13,18,14,17)$ $8, 4, 2, 2, 2, 2, 1, 1$ $39916800$ $8$ $( 1,19)( 2,20)( 5, 9,21,16, 6,10,22,15)( 7,12)( 8,11)(13,18,14,17)$ $8, 4, 4, 2, 2, 2$ $39916800$ $8$ $( 1,20, 2,19)( 3, 4)( 5, 9,21,16, 6,10,22,15)( 7,11)( 8,12)(13,18,14,17)$ $4, 4, 4, 2, 2, 2, 2, 2$ $39916800$ $4$ $( 1,19)( 2,20)( 3, 4)( 5, 9,22,15)( 6,10,21,16)( 7,11)( 8,12)(13,18,14,17)$ $4, 4, 4, 4, 4, 2$ $13305600$ $4$ $( 1,20, 2,19)( 3, 4)( 5, 9,22,15)( 6,10,21,16)( 7,11, 8,12)(13,18,14,17)$ $4, 4, 2, 2, 2, 2, 2, 2, 1, 1$ $13305600$ $4$ $( 1,19)( 2,20)( 5, 9,22,15)( 6,10,21,16)( 7,11)( 8,12)(13,18)(14,17)$ $8, 2, 2, 2, 2, 2, 2, 2$ $13305600$ $8$ $( 1,19)( 2,20)( 3, 4)( 5, 9,21,16, 6,10,22,15)( 7,12)( 8,11)(13,18)(14,17)$ $4, 4, 3, 3, 3, 3, 1, 1$ $17740800$ $12$ $( 1,12,18)( 2,11,17)( 5,21, 6,22)( 7,13,20)( 8,14,19)( 9,15,10,16)$ $6, 4, 3, 3, 2, 2, 1, 1$ $70963200$ $12$ $( 1,12,18)( 2,11,17)( 5,22)( 6,21)( 7,13,19, 8,14,20)( 9,15,10,16)$ $3, 3, 3, 3, 2, 2, 2, 2, 1, 1$ $17740800$ $6$ $( 1,12,18)( 2,11,17)( 5,22)( 6,21)( 7,13,20)( 8,14,19)( 9,15)(10,16)$ $6, 4, 4, 3, 3, 2$ $35481600$ $12$ $( 1,11,17, 2,12,18)( 3, 4)( 5,21, 6,22)( 7,13,20)( 8,14,19)( 9,15,10,16)$ $6, 6, 4, 2, 2, 2$ $35481600$ $12$ $( 1,11,17, 2,12,18)( 3, 4)( 5,22)( 6,21)( 7,13,19, 8,14,20)( 9,15,10,16)$ $6, 3, 3, 2, 2, 2, 2, 2$ $35481600$ $6$ $( 1,11,17, 2,12,18)( 3, 4)( 5,22)( 6,21)( 7,13,20)( 8,14,19)( 9,15)(10,16)$ $6, 6, 4, 4, 1, 1$ $17740800$ $12$ $( 1,11,17, 2,12,18)( 5,21, 6,22)( 7,14,19, 8,13,20)( 9,15,10,16)$ $6, 6, 2, 2, 2, 2, 1, 1$ $17740800$ $6$ $( 1,11,17, 2,12,18)( 5,22)( 6,21)( 7,14,19, 8,13,20)( 9,15)(10,16)$ $4, 3, 3, 3, 3, 2, 2, 2$ $35481600$ $12$ $( 1,12,18)( 2,11,17)( 3, 4)( 5,22)( 6,21)( 7,14,20)( 8,13,19)( 9,15,10,16)$ $12, 8, 1, 1$ $425779200$ $24$ $( 1,13,12,20,18, 8, 2,14,11,19,17, 7)( 5,15,22, 9, 6,16,21,10)$ $6, 6, 4, 4, 1, 1$ $425779200$ $12$ $( 1,13,12,19,17, 7)( 2,14,11,20,18, 8)( 5,15,21,10)( 6,16,22, 9)$ $8, 6, 6, 2$ $425779200$ $24$ $( 1,13,11,19,17, 7)( 2,14,12,20,18, 8)( 3, 4)( 5,15,22, 9, 6,16,21,10)$ $12, 4, 4, 2$ $425779200$ $12$ $( 1,13,11,20,18, 8, 2,14,12,19,17, 7)( 3, 4)( 5,15,21,10)( 6,16,22, 9)$ $4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $554400$ $4$ $( 1, 2)( 3,12,17,10)( 4,11,18, 9)( 7, 8)(13,14)(19,20)$ $8, 2, 2, 2, 2, 2, 1, 1, 1, 1$ $332640$ $8$ $( 1, 2)( 3,12,17, 9, 4,11,18,10)( 7, 8)(13,14)(19,20)(21,22)$ $8, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1$ $554400$ $8$ $( 1, 2)( 3,12,17, 9, 4,11,18,10)( 7, 8)(13,14)$ $4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $332640$ $4$ $( 1, 2)( 3,12,17,10)( 4,11,18, 9)(13,14)$ $8, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $110880$ $8$ $( 1, 2)( 3,11,18, 9, 4,12,17,10)$ $4, 4, 2, 2, 2, 2, 2, 2, 1, 1$ $110880$ $4$ $( 1, 2)( 3,12,17,10)( 4,11,18, 9)( 5, 6)( 7, 8)(13,14)(19,20)(21,22)$ $8, 2, 2, 2, 2, 2, 2, 2$ $15840$ $8$ $( 1, 2)( 3,12,17, 9, 4,11,18,10)( 5, 6)( 7, 8)(13,14)(15,16)(19,20)(21,22)$ $4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $15840$ $4$ $( 3,11,18,10)( 4,12,17, 9)$ $10, 4, 2, 2, 2, 2$ $63866880$ $20$ $( 1,16,13,22,19, 2,15,14,21,20)( 3,17, 4,18)( 5, 6)( 7, 8)( 9,12)(10,11)$ $5, 5, 4, 4, 2, 2$ $31933440$ $20$ $( 1,16,13,21,20)( 2,15,14,22,19)( 3,17, 4,18)( 5, 6)( 7, 8)( 9,12,10,11)$ $5, 5, 4, 2, 2, 2, 1, 1$ $127733760$ $20$ $( 1,16,13,21,20)( 2,15,14,22,19)( 3,17, 4,18)( 5, 6)( 9,12)(10,11)$ $10, 4, 4, 2, 1, 1$ $63866880$ $20$ $( 1,16,13,22,19, 2,15,14,21,20)( 3,17, 4,18)( 5, 6)( 9,12,10,11)$ $5, 5, 2, 2, 2, 2, 2, 2$ $31933440$ $10$ $( 1,16,13,21,20)( 2,15,14,22,19)( 3,17)( 4,18)( 5, 6)( 7, 8)( 9,11)(10,12)$ $10, 2, 2, 2, 2, 2, 1, 1$ $63866880$ $10$ $( 1,16,13,22,19, 2,15,14,21,20)( 3,17)( 4,18)( 5, 6)( 9,11)(10,12)$ $10, 4, 2, 2, 1, 1, 1, 1$ $63866880$ $20$ $( 1,16,13,22,19, 2,15,14,21,20)( 3,17, 4,18)( 9,12)(10,11)$ $5, 5, 4, 4, 1, 1, 1, 1$ $31933440$ $20$ $( 1,16,13,21,20)( 2,15,14,22,19)( 3,17, 4,18)( 9,12,10,11)$ $5, 5, 2, 2, 2, 2, 1, 1, 1, 1$ $31933440$ $10$ $( 1,16,13,21,20)( 2,15,14,22,19)( 3,17)( 4,18)( 9,11)(10,12)$ $5, 5, 4, 4, 2, 2$ $127733760$ $20$ $( 1,21,16,20,13)( 2,22,15,19,14)( 3,11,17,10)( 4,12,18, 9)( 5, 6)( 7, 8)$ $10, 8, 2, 2$ $127733760$ $40$ $( 1,22,15,19,14, 2,21,16,20,13)( 3,11,17, 9, 4,12,18,10)( 5, 6)( 7, 8)$ $10, 4, 4, 2, 1, 1$ $255467520$ $20$ $( 1,22,15,19,14, 2,21,16,20,13)( 3,11,17,10)( 4,12,18, 9)( 5, 6)$ $8, 5, 5, 2, 1, 1$ $255467520$ $40$ $( 1,21,16,20,13)( 2,22,15,19,14)( 3,11,17, 9, 4,12,18,10)( 5, 6)$ $5, 5, 4, 4, 1, 1, 1, 1$ $127733760$ $20$ $( 1,21,16,20,13)( 2,22,15,19,14)( 3,11,17,10)( 4,12,18, 9)$ $10, 8, 1, 1, 1, 1$ $127733760$ $40$ $( 1,22,15,19,14, 2,21,16,20,13)( 3,11,17, 9, 4,12,18,10)$ $3, 3, 3, 3, 2, 2, 2, 2, 1, 1$ $17740800$ $6$ $( 1, 2)( 3,21)( 4,22)( 7,16,18)( 8,15,17)( 9,12,19)(10,11,20)(13,14)$ $6, 4, 3, 3, 2, 2, 1, 1$ $35481600$ $12$ $( 1, 2)( 3,22, 4,21)( 7,16,18)( 8,15,17)( 9,12,20,10,11,19)(13,14)$ $6, 6, 2, 2, 2, 2, 1, 1$ $17740800$ $6$ $( 1, 2)( 3,21)( 4,22)( 7,16,18, 8,15,17)( 9,12,20,10,11,19)(13,14)$ $6, 3, 3, 2, 2, 2, 1, 1, 1, 1$ $35481600$ $6$ $( 1, 2)( 3,21)( 4,22)( 7,16,18)( 8,15,17)( 9,11,20,10,12,19)$ $4, 3, 3, 3, 3, 2, 1, 1, 1, 1$ $17740800$ $12$ $( 1, 2)( 3,22, 4,21)( 7,16,18)( 8,15,17)( 9,11,19)(10,12,20)$ $6, 6, 4, 2, 1, 1, 1, 1$ $17740800$ $12$ $( 1, 2)( 3,22, 4,21)( 7,16,18, 8,15,17)( 9,11,20,10,12,19)$ $4, 3, 3, 3, 3, 2, 2, 2$ $5913600$ $12$ $( 1, 2)( 3,22, 4,21)( 5, 6)( 7,16,18)( 8,15,17)( 9,12,19)(10,11,20)(13,14)$ $6, 3, 3, 2, 2, 2, 2, 2$ $11827200$ $6$ $( 1, 2)( 3,21)( 4,22)( 5, 6)( 7,16,18)( 8,15,17)( 9,12,20,10,11,19)(13,14)$ $6, 6, 4, 2, 2, 2$ $5913600$ $12$ $( 1, 2)( 3,22, 4,21)( 5, 6)( 7,16,18, 8,15,17)( 9,12,20,10,11,19)(13,14)$ $6, 4, 3, 3, 1, 1, 1, 1, 1, 1$ $11827200$ $12$ $( 3,22, 4,21)( 7,16,18)( 8,15,17)( 9,11,20,10,12,19)$ $3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1$ $5913600$ $6$ $( 3,21)( 4,22)( 7,16,18)( 8,15,17)( 9,11,19)(10,12,20)$ $6, 6, 2, 2, 1, 1, 1, 1, 1, 1$ $5913600$ $6$ $( 3,21)( 4,22)( 7,16,18, 8,15,17)( 9,11,20,10,12,19)$ $6, 6, 6, 2, 1, 1$ $15769600$ $6$ $( 1, 5,13, 2, 6,14)( 3, 4)( 7,15,18, 8,16,17)(11,21,19,12,22,20)$ $6, 6, 3, 3, 2, 2$ $23654400$ $6$ $( 1, 5,13, 2, 6,14)( 3, 4)( 7,15,18, 8,16,17)( 9,10)(11,22,20)(12,21,19)$ $6, 3, 3, 3, 3, 2, 1, 1$ $47308800$ $6$ $( 1, 5,13, 2, 6,14)( 3, 4)( 7,15,18)( 8,16,17)(11,22,20)(12,21,19)$ $6, 6, 3, 3, 1, 1, 1, 1$ $23654400$ $6$ $( 1, 5,13, 2, 6,14)( 7,15,18, 8,16,17)(11,21,19)(12,22,20)$ $3, 3, 3, 3, 3, 3, 2, 2$ $7884800$ $6$ $( 1, 5,14)( 2, 6,13)( 3, 4)( 7,15,18)( 8,16,17)( 9,10)(11,21,19)(12,22,20)$ $3, 3, 3, 3, 3, 3, 1, 1, 1, 1$ $7884800$ $3$ $( 1, 5,14)( 2, 6,13)( 7,15,18)( 8,16,17)(11,22,20)(12,21,19)$ $12, 6, 2, 2$ $283852800$ $12$ $( 1,16, 5,18,13, 7, 2,15, 6,17,14, 8)( 3,10)( 4, 9)(11,20,21,12,19,22)$ $12, 4, 3, 3$ $283852800$ $12$ $( 1,16, 5,18,13, 7, 2,15, 6,17,14, 8)( 3, 9, 4,10)(11,20,22)(12,19,21)$ $6, 6, 3, 3, 2, 2$ $283852800$ $6$ $( 1,16, 5,18,13, 8)( 2,15, 6,17,14, 7)( 3,10)( 4, 9)(11,20,22)(12,19,21)$ $6, 6, 6, 4$ $283852800$ $12$ $( 1,16, 5,18,13, 8)( 2,15, 6,17,14, 7)( 3, 9, 4,10)(11,20,21,12,19,22)$ $4, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1$ $1663200$ $4$ $( 1,18, 2,17)( 5, 8)( 6, 7)( 9,10)(13,15)(14,16)(19,20)(21,22)$ $4, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1$ $831600$ $4$ $( 1,18, 2,17)( 5, 8)( 6, 7)( 9,10)(13,15)(14,16)$ $4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $1663200$ $4$ $( 1,18, 2,17)( 5, 7, 6, 8)( 9,10)(13,15)(14,16)(19,20)$ $4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $166320$ $4$ $( 1,18, 2,17)( 5, 7, 6, 8)(13,15)(14,16)$ $4, 2, 2, 2, 2, 2, 2, 2, 2, 2$ $166320$ $4$ $( 1,18, 2,17)( 3, 4)( 5, 8)( 6, 7)( 9,10)(11,12)(13,15)(14,16)(19,20)(21,22)$ $4, 4, 2, 2, 2, 2, 2, 2, 1, 1$ $831600$ $4$ $( 1,18, 2,17)( 3, 4)( 5, 7, 6, 8)( 9,10)(11,12)(13,15)(14,16)(19,20)$ $4, 4, 4, 2, 2, 2, 1, 1, 1, 1$ $554400$ $4$ $( 1,18, 2,17)( 5, 7, 6, 8)( 9,10)(11,12)(13,15,14,16)(19,20)$ $4, 4, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1$ $277200$ $4$ $( 1,18, 2,17)( 5, 7, 6, 8)(11,12)(13,15,14,16)$ $4, 4, 4, 2, 2, 2, 2, 2$ $55440$ $4$ $( 1,18, 2,17)( 3, 4)( 5, 7, 6, 8)( 9,10)(11,12)(13,16,14,15)(19,20)(21,22)$ $2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $554400$ $2$ $( 1,18)( 2,17)( 5, 8)( 6, 7)( 9,10)(13,15)(14,16)(19,20)$ $2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $55440$ $2$ $( 1,18)( 2,17)( 5, 8)( 6, 7)(13,15)(14,16)$ $2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1$ $277200$ $2$ $( 1,18)( 2,17)( 3, 4)( 5, 8)( 6, 7)( 9,10)(11,12)(13,15)(14,16)(19,20)$ $12, 3, 3, 2, 1, 1$ $283852800$ $12$ $( 1, 7,14,17, 5,15, 2, 8,13,18, 6,16)( 3, 4)(11,22,19)(12,21,20)$ $12, 6, 2, 2$ $141926400$ $12$ $( 1, 7,14,17, 5,15, 2, 8,13,18, 6,16)( 3, 4)( 9,10)(11,21,20,12,22,19)$ $6, 6, 6, 2, 1, 1$ $283852800$ $6$ $( 1, 8,13,18, 6,16)( 2, 7,14,17, 5,15)( 3, 4)(11,21,20,12,22,19)$ $6, 6, 3, 3, 2, 2$ $141926400$ $6$ $( 1, 8,13,18, 6,16)( 2, 7,14,17, 5,15)( 3, 4)( 9,10)(11,22,19)(12,21,20)$ $12, 6, 1, 1, 1, 1$ $141926400$ $12$ $( 1, 7,14,17, 5,15, 2, 8,13,18, 6,16)(11,22,19,12,21,20)$ $6, 6, 3, 3, 1, 1, 1, 1$ $141926400$ $6$ $( 1, 8,13,18, 6,16)( 2, 7,14,17, 5,15)(11,21,20)(12,22,19)$ $8, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1$ $3326400$ $8$ $( 1, 7,20,16, 2, 8,19,15)( 9,10)(17,21)(18,22)$ $4, 4, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1$ $3326400$ $4$ $( 1, 7,19,15)( 2, 8,20,16)( 9,10)(17,22,18,21)$ $8, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $665280$ $8$ $( 1, 7,20,16, 2, 8,19,15)(17,22,18,21)$ $4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $665280$ $4$ $( 1, 7,19,15)( 2, 8,20,16)(17,21)(18,22)$ $8, 2, 2, 2, 2, 2, 1, 1, 1, 1$ $6652800$ $8$ $( 1, 7,20,16, 2, 8,19,15)( 3, 4)( 9,10)(11,12)(17,21)(18,22)$ $4, 4, 4, 2, 2, 2, 1, 1, 1, 1$ $6652800$ $4$ $( 1, 7,19,15)( 2, 8,20,16)( 3, 4)( 9,10)(11,12)(17,22,18,21)$ $8, 4, 2, 2, 1, 1, 1, 1, 1, 1$ $6652800$ $8$ $( 1, 7,20,16, 2, 8,19,15)( 3, 4)(11,12)(17,22,18,21)$ $4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $6652800$ $4$ $( 1, 7,19,15)( 2, 8,20,16)( 3, 4)(11,12)(17,21)(18,22)$ $8, 4, 2, 2, 2, 2, 1, 1$ $3326400$ $8$ $( 1, 7,20,16, 2, 8,19,15)( 3, 4)( 5, 6)( 9,10)(11,12)(17,22,18,21)$ $4, 4, 2, 2, 2, 2, 2, 2, 1, 1$ $3326400$ $4$ $( 1, 7,19,15)( 2, 8,20,16)( 3, 4)( 5, 6)( 9,10)(11,12)(17,21)(18,22)$ $8, 2, 2, 2, 2, 2, 2, 2$ $665280$ $8$ $( 1, 7,20,16, 2, 8,19,15)( 3, 4)( 5, 6)( 9,10)(11,12)(13,14)(17,21)(18,22)$ $4, 4, 4, 2, 2, 2, 2, 2$ $665280$ $4$ $( 1, 7,19,15)( 2, 8,20,16)( 3, 4)( 5, 6)( 9,10)(11,12)(13,14)(17,22,18,21)$ $4, 4, 3, 3, 2, 2, 1, 1, 1, 1$ $6652800$ $12$ $( 1,19, 2,20)( 3,12, 9)( 4,11,10)( 7,15, 8,16)(17,18)(21,22)$ $4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $8870400$ $12$ $( 1,20)( 2,19)( 3,12, 9)( 4,11,10)( 7,15, 8,16)(17,18)$ $6, 4, 4, 2, 1, 1, 1, 1, 1, 1$ $4435200$ $12$ $( 1,19, 2,20)( 3,12,10, 4,11, 9)( 7,15, 8,16)(17,18)$ $6, 4, 2, 2, 2, 2, 1, 1, 1, 1$ $13305600$ $12$ $( 1,20)( 2,19)( 3,12,10, 4,11, 9)( 7,15, 8,16)(17,18)(21,22)$ $3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1$ $6652800$ $6$ $( 1,20)( 2,19)( 3,12, 9)( 4,11,10)( 7,15)( 8,16)(17,18)(21,22)$ $6, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $4435200$ $6$ $( 1,20)( 2,19)( 3,12,10, 4,11, 9)( 7,15)( 8,16)(17,18)$ $6, 4, 4, 2, 2, 2, 1, 1$ $4435200$ $12$ $( 1,19, 2,20)( 3,11,10, 4,12, 9)( 7,15, 8,16)(13,14)(17,18)(21,22)$ $4, 3, 3, 2, 2, 2, 2, 2, 1, 1$ $8870400$ $12$ $( 1,20)( 2,19)( 3,11, 9)( 4,12,10)( 7,15, 8,16)(13,14)(17,18)(21,22)$ $6, 2, 2, 2, 2, 2, 2, 2, 1, 1$ $4435200$ $6$ $( 1,20)( 2,19)( 3,11,10, 4,12, 9)( 7,15)( 8,16)(13,14)(17,18)(21,22)$ $6, 4, 2, 2, 2, 2, 2, 2$ $2217600$ $12$ $( 1,20)( 2,19)( 3,11,10, 4,12, 9)( 5, 6)( 7,15, 8,16)(13,14)(17,18)(21,22)$ $4, 4, 3, 3, 2, 2, 2, 2$ $1108800$ $12$ $( 1,19, 2,20)( 3,11, 9)( 4,12,10)( 5, 6)( 7,15, 8,16)(13,14)(17,18)(21,22)$ $3, 3, 2, 2, 2, 2, 2, 2, 2, 2$ $1108800$ $6$ $( 1,20)( 2,19)( 3,11, 9)( 4,12,10)( 5, 6)( 7,15)( 8,16)(13,14)(17,18)(21,22)$ $4, 4, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1$ $1108800$ $12$ $( 1,19, 2,20)( 3,12, 9)( 4,11,10)( 7,15, 8,16)$ $6, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1$ $2217600$ $12$ $( 1,20)( 2,19)( 3,12,10, 4,11, 9)( 7,15, 8,16)$ $3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1$ $1108800$ $6$ $( 1,20)( 2,19)( 3,12, 9)( 4,11,10)( 7,15)( 8,16)$ $4, 4, 3, 3, 2, 2, 1, 1, 1, 1$ $53222400$ $12$ $( 1,15,20, 7)( 2,16,19, 8)( 3, 9,12)( 4,10,11)(17,21)(18,22)$ $8, 4, 3, 3, 1, 1, 1, 1$ $53222400$ $24$ $( 1,15,19, 8, 2,16,20, 7)( 3, 9,12)( 4,10,11)(17,22,18,21)$ $6, 4, 4, 4, 1, 1, 1, 1$ $53222400$ $12$ $( 1,15,20, 7)( 2,16,19, 8)( 3,10,11, 4, 9,12)(17,22,18,21)$ $8, 6, 2, 2, 1, 1, 1, 1$ $53222400$ $24$ $( 1,15,19, 8, 2,16,20, 7)( 3,10,11, 4, 9,12)(17,21)(18,22)$ $6, 4, 4, 2, 2, 2, 1, 1$ $106444800$ $12$ $( 1,15,20, 7)( 2,16,19, 8)( 3, 9,11, 4,10,12)(13,14)(17,21)(18,22)$ $8, 6, 4, 2, 1, 1$ $106444800$ $24$ $( 1,15,19, 8, 2,16,20, 7)( 3, 9,11, 4,10,12)(13,14)(17,22,18,21)$ $4, 4, 4, 3, 3, 2, 1, 1$ $106444800$ $12$ $( 1,15,20, 7)( 2,16,19, 8)( 3,10,12)( 4, 9,11)(13,14)(17,22,18,21)$ $8, 3, 3, 2, 2, 2, 1, 1$ $106444800$ $24$ $( 1,15,19, 8, 2,16,20, 7)( 3,10,12)( 4, 9,11)(13,14)(17,21)(18,22)$ $6, 4, 4, 4, 2, 2$ $53222400$ $12$ $( 1,15,20, 7)( 2,16,19, 8)( 3, 9,11, 4,10,12)( 5, 6)(13,14)(17,22,18,21)$ $8, 6, 2, 2, 2, 2$ $53222400$ $24$ $( 1,15,19, 8, 2,16,20, 7)( 3, 9,11, 4,10,12)( 5, 6)(13,14)(17,21)(18,22)$ $4, 4, 3, 3, 2, 2, 2, 2$ $53222400$ $12$ $( 1,15,20, 7)( 2,16,19, 8)( 3,10,12)( 4, 9,11)( 5, 6)(13,14)(17,21)(18,22)$ $8, 4, 3, 3, 2, 2$ $53222400$ $24$ $( 1,15,19, 8, 2,16,20, 7)( 3,10,12)( 4, 9,11)( 5, 6)(13,14)(17,22,18,21)$ $6, 4, 4, 4, 2, 2$ $106444800$ $12$ $( 1,14)( 2,13)( 3,21,10, 4,22, 9)( 5, 8,19,11)( 6, 7,20,12)(15,17,16,18)$ $8, 4, 3, 3, 2, 2$ $106444800$ $24$ $( 1,14)( 2,13)( 3,22, 9)( 4,21,10)( 5, 8,20,12, 6, 7,19,11)(15,17,16,18)$ $8, 6, 4, 4$ $53222400$ $24$ $( 1,13, 2,14)( 3,21,10, 4,22, 9)( 5, 8,19,12, 6, 7,20,11)(15,17,16,18)$ $4, 4, 4, 4, 3, 3$ $53222400$ $12$ $( 1,13, 2,14)( 3,22, 9)( 4,21,10)( 5, 8,20,11)( 6, 7,19,12)(15,17,16,18)$ $4, 4, 3, 3, 2, 2, 2, 2$ $53222400$ $12$ $( 1,14)( 2,13)( 3,22, 9)( 4,21,10)( 5, 8,19,11)( 6, 7,20,12)(15,17)(16,18)$ $8, 6, 2, 2, 2, 2$ $53222400$ $24$ $( 1,14)( 2,13)( 3,21,10, 4,22, 9)( 5, 8,20,12, 6, 7,19,11)(15,17)(16,18)$ $6, 4, 4, 2, 1, 1, 1, 1, 1, 1$ $17740800$ $12$ $( 1,17,14,16)( 2,18,13,15)( 3, 9,22, 4,10,21)(19,20)$ $4, 4, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1$ $4435200$ $12$ $( 1,17,14,16)( 2,18,13,15)( 3, 9,21)( 4,10,22)$ $4, 4, 3, 3, 2, 2, 1, 1, 1, 1$ $26611200$ $12$ $( 1,17,14,16)( 2,18,13,15)( 3, 9,21)( 4,10,22)( 7, 8)(19,20)$ $6, 4, 4, 2, 2, 2, 1, 1$ $17740800$ $12$ $( 1,17,14,16)( 2,18,13,15)( 3, 9,21, 4,10,22)( 7, 8)(11,12)(19,20)$ $8, 6, 2, 2, 1, 1, 1, 1$ $26611200$ $24$ $( 1,17,13,15, 2,18,14,16)( 3, 9,22, 4,10,21)(11,12)(19,20)$ $8, 3, 3, 2, 1, 1, 1, 1, 1, 1$ $17740800$ $24$ $( 1,17,13,15, 2,18,14,16)( 3, 9,21)( 4,10,22)(11,12)$ $8, 3, 3, 2, 2, 2, 1, 1$ $17740800$ $24$ $( 1,17,13,15, 2,18,14,16)( 3, 9,21)( 4,10,22)( 7, 8)(11,12)(19,20)$ $8, 6, 1, 1, 1, 1, 1, 1, 1, 1$ $4435200$ $24$ $( 1,17,13,15, 2,18,14,16)( 3, 9,21, 4,10,22)$ $4, 4, 3, 3, 2, 2, 2, 2$ $4435200$ $12$ $( 1,17,14,16)( 2,18,13,15)( 3, 9,22)( 4,10,21)( 5, 6)( 7, 8)(11,12)(19,20)$ $8, 6, 2, 2, 2, 2$ $4435200$ $24$ $( 1,17,13,15, 2,18,14,16)( 3, 9,22, 4,10,21)( 5, 6)( 7, 8)(11,12)(19,20)$ $6, 4, 2, 2, 2, 2, 1, 1, 1, 1$ $13305600$ $12$ $( 1,13, 2,14)( 3,22,10, 4,21, 9)( 5,11)( 6,12)(15,17)(16,18)$ $4, 3, 3, 2, 2, 2, 2, 2, 1, 1$ $26611200$ $12$ $( 1,13, 2,14)( 3,21, 9)( 4,22,10)( 5,11)( 6,12)(15,17)(16,18)(19,20)$ $6, 4, 2, 2, 2, 2, 2, 2$ $13305600$ $12$ $( 1,13, 2,14)( 3,22,10, 4,21, 9)( 5,11)( 6,12)( 7, 8)(15,17)(16,18)(19,20)$ $4, 4, 3, 3, 2, 2, 1, 1, 1, 1$ $13305600$ $12$ $( 1,13, 2,14)( 3,22,10)( 4,21, 9)( 5,12, 6,11)(15,17)(16,18)$ $6, 4, 4, 2, 2, 2, 1, 1$ $26611200$ $12$ $( 1,13, 2,14)( 3,21, 9, 4,22,10)( 5,12, 6,11)(15,17)(16,18)(19,20)$ $4, 4, 3, 3, 2, 2, 2, 2$ $13305600$ $12$ $( 1,13, 2,14)( 3,22,10)( 4,21, 9)( 5,12, 6,11)( 7, 8)(15,17)(16,18)(19,20)$ $3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1$ $4435200$ $6$ $( 1,14)( 2,13)( 3,22,10)( 4,21, 9)( 5,11)( 6,12)(15,17)(16,18)$ $6, 2, 2, 2, 2, 2, 2, 2, 1, 1$ $8870400$ $6$ $( 1,14)( 2,13)( 3,21, 9, 4,22,10)( 5,11)( 6,12)(15,17)(16,18)(19,20)$ $3, 3, 2, 2, 2, 2, 2, 2, 2, 2$ $4435200$ $6$ $( 1,14)( 2,13)( 3,22,10)( 4,21, 9)( 5,11)( 6,12)( 7, 8)(15,17)(16,18)(19,20)$ $6, 4, 4, 4, 1, 1, 1, 1$ $4435200$ $12$ $( 1,13, 2,14)( 3,21, 9, 4,22,10)( 5,12, 6,11)(15,17,16,18)$ $4, 4, 4, 3, 3, 2, 1, 1$ $8870400$ $12$ $( 1,13, 2,14)( 3,22,10)( 4,21, 9)( 5,12, 6,11)(15,17,16,18)(19,20)$ $6, 4, 4, 4, 2, 2$ $4435200$ $12$ $( 1,13, 2,14)( 3,21, 9, 4,22,10)( 5,12, 6,11)( 7, 8)(15,17,16,18)(19,20)$ $4, 4, 4, 2, 2, 2, 2, 2$ $3326400$ $4$ $( 1,13)( 2,14)( 3, 4)( 5,21)( 6,22)( 7,18, 8,17)( 9,16,10,15)(11,19,12,20)$ $4, 2, 2, 2, 2, 2, 2, 2, 2, 2$ $1663200$ $4$ $( 1,13)( 2,14)( 3, 4)( 5,21)( 6,22)( 7,18, 8,17)( 9,16)(10,15)(11,20)(12,19)$ $4, 4, 2, 2, 2, 2, 2, 2, 1, 1$ $3326400$ $4$ $( 1,13)( 2,14)( 5,21)( 6,22)( 7,18, 8,17)( 9,16,10,15)(11,19)(12,20)$ $4, 4, 4, 4, 2, 2, 1, 1$ $1663200$ $4$ $( 1,13)( 2,14)( 5,22, 6,21)( 7,18, 8,17)( 9,16,10,15)(11,20,12,19)$ $2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1$ $332640$ $2$ $( 1,13)( 2,14)( 5,21)( 6,22)( 7,18)( 8,17)( 9,16)(10,15)(11,19)(12,20)$ $4, 4, 4, 4, 4, 2$ $332640$ $4$ $( 1,14, 2,13)( 3, 4)( 5,22, 6,21)( 7,18, 8,17)( 9,16,10,15)(11,20,12,19)$ $6, 6, 3, 3, 2, 2$ $47308800$ $6$ $( 1,16, 7, 2,15, 8)( 3,11)( 4,12)( 5,17,13)( 6,18,14)( 9,19,22,10,20,21)$ $3, 3, 3, 3, 3, 3, 2, 2$ $15769600$ $6$ $( 1,16, 8)( 2,15, 7)( 3,11)( 4,12)( 5,17,13)( 6,18,14)( 9,19,21)(10,20,22)$ $6, 6, 6, 4$ $15769600$ $12$ $( 1,16, 7, 2,15, 8)( 3,12, 4,11)( 5,17,14, 6,18,13)( 9,19,22,10,20,21)$ $6, 4, 3, 3, 3, 3$ $47308800$ $12$ $( 1,16, 8)( 2,15, 7)( 3,12, 4,11)( 5,17,14, 6,18,13)( 9,19,21)(10,20,22)$ $6, 6, 2, 2, 1, 1, 1, 1, 1, 1$ $17740800$ $6$ $( 1, 2)( 5,10,17,20,13,21)( 6, 9,18,19,14,22)(15,16)$ $12, 2, 2, 2, 1, 1, 1, 1$ $17740800$ $12$ $( 1, 2)( 5,10,17,20,13,22, 6, 9,18,19,14,21)( 7, 8)(15,16)$ $6, 6, 2, 2, 2, 2, 1, 1$ $8870400$ $6$ $( 1, 2)( 3, 4)( 5,10,17,20,13,21)( 6, 9,18,19,14,22)(11,12)(15,16)$ $12, 2, 2, 2, 2, 2$ $1774080$ $12$ $( 1, 2)( 3, 4)( 5,10,17,20,13,22, 6, 9,18,19,14,21)( 7, 8)(11,12)(15,16)$ $12, 2, 1, 1, 1, 1, 1, 1, 1, 1$ $8870400$ $12$ $( 1, 2)( 5,10,17,20,13,22, 6, 9,18,19,14,21)$ $6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $1774080$ $6$ $( 5,10,17,20,13,21)( 6, 9,18,19,14,22)$ $9, 9, 1, 1, 1, 1$ $567705600$ $9$ $( 1,16,21, 6,17,19,14, 7,11)( 2,15,22, 5,18,20,13, 8,12)$ $18, 2, 1, 1$ $1135411200$ $18$ $( 1,16,22, 5,18,20,13, 8,12, 2,15,21, 6,17,19,14, 7,11)( 9,10)$ $9, 9, 2, 2$ $567705600$ $18$ $( 1,16,22, 5,18,20,13, 8,11)( 2,15,21, 6,17,19,14, 7,12)( 3, 4)( 9,10)$ $9, 9, 2, 2$ $1135411200$ $18$ $( 1, 7,20, 5,15,11,14,17,21)( 2, 8,19, 6,16,12,13,18,22)( 3, 9)( 4,10)$ $18, 4$ $1135411200$ $36$ $( 1, 7,20, 5,15,11,14,17,22, 2, 8,19, 6,16,12,13,18,21)( 3,10, 4, 9)$ $11, 11$ $3715891200$ $11$ $( 1, 6,22,16,17,11,10, 4, 8,19,14)( 2, 5,21,15,18,12, 9, 3, 7,20,13)$ $8, 5, 5, 4$ $255467520$ $40$ $( 1,17,11,22, 2,18,12,21)( 3,10,20,14,15)( 4, 9,19,13,16)( 5, 8, 6, 7)$ $10, 4, 4, 4$ $255467520$ $20$ $( 1,17,11,21)( 2,18,12,22)( 3,10,19,13,16, 4, 9,20,14,15)( 5, 8, 6, 7)$ $5, 5, 4, 4, 2, 2$ $255467520$ $20$ $( 1,17,11,21)( 2,18,12,22)( 3,10,20,14,15)( 4, 9,19,13,16)( 5, 7)( 6, 8)$ $10, 8, 2, 2$ $255467520$ $40$ $( 1,17,11,22, 2,18,12,21)( 3,10,19,13,16, 4, 9,20,14,15)( 5, 7)( 6, 8)$ $10, 4, 2, 2, 2, 2$ $63866880$ $20$ $( 1,11)( 2,12)( 3,16,13,19, 9, 4,15,14,20,10)( 5, 8)( 6, 7)(17,22,18,21)$ $5, 5, 2, 2, 2, 2, 2, 2$ $21288960$ $10$ $( 1,11)( 2,12)( 3,16,13,20,10)( 4,15,14,19, 9)( 5, 8)( 6, 7)(17,21)(18,22)$ $5, 5, 4, 4, 2, 2$ $63866880$ $20$ $( 1,11)( 2,12)( 3,16,13,20,10)( 4,15,14,19, 9)( 5, 7, 6, 8)(17,22,18,21)$ $10, 4, 4, 4$ $21288960$ $20$ $( 1,12, 2,11)( 3,16,13,20,10, 4,15,14,19, 9)( 5, 7, 6, 8)(17,22,18,21)$ $16, 2, 2, 2$ $638668800$ $16$ $( 1,19)( 2,20)( 3,15, 5, 7,10,11,13,18, 4,16, 6, 8, 9,12,14,17)(21,22)$ $16, 4, 1, 1$ $638668800$ $16$ $( 1,20, 2,19)( 3,15, 5, 7,10,11,13,18, 4,16, 6, 8, 9,12,14,17)$ $8, 8, 2, 2, 1, 1$ $638668800$ $8$ $( 1,19)( 2,20)( 3,15, 5, 7, 9,12,14,17)( 4,16, 6, 8,10,11,13,18)$ $8, 8, 4, 2$ $638668800$ $8$ $( 1,20, 2,19)( 3,15, 5, 7, 9,12,14,17)( 4,16, 6, 8,10,11,13,18)(21,22)$ $8, 4, 4, 2, 2, 2$ $159667200$ $8$ $( 1,21,17,20, 2,22,18,19)( 3, 9)( 4,10)( 5,14, 7,16)( 6,13, 8,15)(11,12)$ $4, 4, 4, 4, 4, 2$ $79833600$ $4$ $( 1,22,18,19)( 2,21,17,20)( 3,10, 4, 9)( 5,14, 7,16)( 6,13, 8,15)(11,12)$ $8, 8, 4, 2$ $79833600$ $8$ $( 1,21,17,20, 2,22,18,19)( 3,10, 4, 9)( 5,14, 8,15, 6,13, 7,16)(11,12)$ $8, 4, 4, 4, 1, 1$ $159667200$ $8$ $( 1,21,17,20, 2,22,18,19)( 3, 9, 4,10)( 5,14, 7,16)( 6,13, 8,15)$ $4, 4, 4, 4, 2, 2, 1, 1$ $79833600$ $4$ $( 1,22,18,19)( 2,21,17,20)( 3,10)( 4, 9)( 5,14, 7,16)( 6,13, 8,15)$ $8, 8, 2, 2, 1, 1$ $79833600$ $8$ $( 1,21,17,20, 2,22,18,19)( 3,10)( 4, 9)( 5,14, 8,15, 6,13, 7,16)$ $10, 6, 3, 3$ $227082240$ $30$ $( 1,14, 5, 2,13, 6)( 3,22,19,10,11, 4,21,20, 9,12)( 7,17,16)( 8,18,15)$ $6, 6, 5, 5$ $113541120$ $30$ $( 1,14, 5, 2,13, 6)( 3,21,20, 9,12)( 4,22,19,10,11)( 7,17,16, 8,18,15)$ $5, 5, 3, 3, 3, 3$ $113541120$ $15$ $( 1,13, 6)( 2,14, 5)( 3,22,19,10,12)( 4,21,20, 9,11)( 7,17,16)( 8,18,15)$ $6, 6, 5, 5$ $681246720$ $30$ $( 1,16,13, 8, 6,18)( 2,15,14, 7, 5,17)( 3, 9,21,11,19)( 4,10,22,12,20)$ $12, 10$ $681246720$ $60$ $( 1,16,13, 7, 5,17, 2,15,14, 8, 6,18)( 3, 9,22,12,20, 4,10,21,11,19)$ $5, 5, 5, 5, 1, 1$ $204374016$ $5$ $( 1, 7,21,13, 4)( 2, 8,22,14, 3)( 5,16,19,12,10)( 6,15,20,11, 9)$ $10, 10, 1, 1$ $204374016$ $10$ $( 1, 7,22,14, 3, 2, 8,21,13, 4)( 5,16,20,11, 9, 6,15,19,12,10)$ $10, 5, 5, 2$ $408748032$ $10$ $( 1, 7,22,14, 3, 2, 8,21,13, 4)( 5,16,19,12,10)( 6,15,20,11, 9)(17,18)$ $10, 10, 1, 1$ $2043740160$ $10$ $( 1,11, 8,10,21, 6,13,15, 3,19)( 2,12, 7, 9,22, 5,14,16, 4,20)$ $20, 2$ $2043740160$ $20$ $( 1,11, 8,10,22, 5,14,16, 4,20, 2,12, 7, 9,21, 6,13,15, 3,19)(17,18)$ $12, 4, 2, 2, 1, 1$ $212889600$ $12$ $( 1, 7,14,17, 5,15, 2, 8,13,18, 6,16)( 3, 9, 4,10)(11,21)(12,22)$ $12, 4, 4, 2$ $106444800$ $12$ $( 1, 7,14,17, 5,15, 2, 8,13,18, 6,16)( 3, 9, 4,10)(11,22,12,21)(19,20)$ $12, 2, 2, 2, 2, 2$ $106444800$ $12$ $( 1, 7,14,17, 5,15, 2, 8,13,18, 6,16)( 3,10)( 4, 9)(11,21)(12,22)(19,20)$ $6, 6, 4, 4, 1, 1$ $106444800$ $12$ $( 1, 8,13,18, 6,16)( 2, 7,14,17, 5,15)( 3, 9, 4,10)(11,22,12,21)$ $6, 6, 4, 2, 2, 2$ $212889600$ $12$ $( 1, 8,13,18, 6,16)( 2, 7,14,17, 5,15)( 3, 9, 4,10)(11,21)(12,22)(19,20)$ $6, 6, 2, 2, 2, 2, 1, 1$ $106444800$ $6$ $( 1, 8,13,18, 6,16)( 2, 7,14,17, 5,15)( 3,10)( 4, 9)(11,21)(12,22)$ $7, 7, 2, 2, 1, 1, 1, 1$ $91238400$ $14$ $( 1,16,22, 8,12,17, 3)( 2,15,21, 7,11,18, 4)( 5, 6)( 9,10)$ $14, 2, 2, 2, 1, 1$ $60825600$ $14$ $( 1,16,21, 7,11,18, 4, 2,15,22, 8,12,17, 3)( 5, 6)( 9,10)(19,20)$ $14, 2, 1, 1, 1, 1, 1, 1$ $60825600$ $14$ $( 1,16,21, 7,11,18, 4, 2,15,22, 8,12,17, 3)( 5, 6)$ $7, 7, 2, 2, 2, 2$ $15206400$ $14$ $( 1,16,21, 7,12,17, 3)( 2,15,22, 8,11,18, 4)( 5, 6)( 9,10)(13,14)(19,20)$ $7, 7, 1, 1, 1, 1, 1, 1, 1, 1$ $15206400$ $7$ $( 1,16,22, 8,12,17, 3)( 2,15,21, 7,11,18, 4)$ $7, 7, 2, 2, 2, 2$ $182476800$ $14$ $( 1,11,15,18,22, 3, 8)( 2,12,16,17,21, 4, 7)( 5,13)( 6,14)( 9,19)(10,20)$ $14, 4, 2, 2$ $364953600$ $28$ $( 1,11,15,18,21, 4, 7, 2,12,16,17,22, 3, 8)( 5,13)( 6,14)( 9,20,10,19)$ $7, 7, 4, 4$ $182476800$ $28$ $( 1,12,16,17,22, 3, 8)( 2,11,15,18,21, 4, 7)( 5,14, 6,13)( 9,20,10,19)$ $7, 7, 4, 4$ $729907200$ $28$ $( 1,22,12, 4,16, 8,17)( 2,21,11, 3,15, 7,18)( 5,19,14, 9)( 6,20,13,10)$ $14, 8$ $729907200$ $56$ $( 1,21,11, 3,15, 7,18, 2,22,12, 4,16, 8,17)( 5,20,13,10, 6,19,14, 9)$ $7, 7, 4, 2, 1, 1$ $364953600$ $28$ $( 1,16,22, 7,12,18, 4)( 2,15,21, 8,11,17, 3)( 9,20,10,19)(13,14)$ $14, 2, 2, 2, 1, 1$ $364953600$ $14$ $( 1,16,21, 8,11,17, 3, 2,15,22, 7,12,18, 4)( 9,19)(10,20)(13,14)$ $14, 4, 1, 1, 1, 1$ $182476800$ $28$ $( 1,16,22, 7,11,17, 3, 2,15,21, 8,12,18, 4)( 9,20,10,19)$ $7, 7, 2, 2, 1, 1, 1, 1$ $182476800$ $14$ $( 1,16,21, 8,12,18, 4)( 2,15,22, 7,11,17, 3)( 9,19)(10,20)$ $14, 4, 2, 2$ $182476800$ $28$ $( 1,16,21, 8,11,17, 3, 2,15,22, 7,12,18, 4)( 5, 6)( 9,20,10,19)(13,14)$ $7, 7, 2, 2, 2, 2$ $182476800$ $14$ $( 1,16,22, 7,12,18, 4)( 2,15,21, 8,11,17, 3)( 5, 6)( 9,19)(10,20)(13,14)$ $7, 7, 3, 3, 1, 1$ $486604800$ $21$ $( 1,17, 7,15, 3,11,21)( 2,18, 8,16, 4,12,22)( 5, 9,20)( 6,10,19)$ $14, 6, 1, 1$ $486604800$ $42$ $( 1,17, 7,15, 3,11,22, 2,18, 8,16, 4,12,21)( 5, 9,19, 6,10,20)$ $14, 3, 3, 2$ $486604800$ $42$ $( 1,17, 7,15, 3,12,22, 2,18, 8,16, 4,11,21)( 5, 9,20)( 6,10,19)(13,14)$ $7, 7, 6, 2$ $486604800$ $42$ $( 1,17, 7,15, 3,12,21)( 2,18, 8,16, 4,11,22)( 5, 9,19, 6,10,20)(13,14)$ $6, 4, 4, 3, 3, 2$ $141926400$ $12$ $( 1,12,18)( 2,11,17)( 3, 4)( 5,16,22,10)( 6,15,21, 9)( 7,13,20, 8,14,19)$ $8, 3, 3, 3, 3, 2$ $70963200$ $24$ $( 1,12,18)( 2,11,17)( 3, 4)( 5,16,21, 9, 6,15,22,10)( 7,13,19)( 8,14,20)$ $6, 6, 4, 4, 1, 1$ $70963200$ $12$ $( 1,11,17, 2,12,18)( 5,16,22,10)( 6,15,21, 9)( 7,13,20, 8,14,19)$ $8, 6, 3, 3, 1, 1$ $141926400$ $24$ $( 1,11,17, 2,12,18)( 5,16,21, 9, 6,15,22,10)( 7,13,19)( 8,14,20)$ $8, 6, 6, 2$ $70963200$ $24$ $( 1,11,17, 2,12,18)( 3, 4)( 5,16,21, 9, 6,15,22,10)( 7,14,20, 8,13,19)$ $4, 4, 3, 3, 3, 3, 1, 1$ $70963200$ $12$ $( 1,12,18)( 2,11,17)( 5,16,22,10)( 6,15,21, 9)( 7,14,19)( 8,13,20)$

## Group invariants

 Order: $40874803200=2^{18} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$ Cyclic: No Abelian: No Solvable: No GAP id: Data not available
 Character table: Data not available