Properties

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

Related objects

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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 TypeSizeOrderRepresentative
$ 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