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: 2T1
39916800: 11T8

Subfields

Degree 2: None

Degree 11: $S_{11}$

Low degree siblings

22T50
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 $ $11$ $2$ $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(19,20)(21,22)$
$ 4, 4, 2, 2, 2, 2, 2, 2, 1, 1 $ $4989600$ $4$ $( 1,14, 2,13)( 3, 8)( 4, 7)( 9,16,10,15)(11,12)(17,20)(18,19)(21,22)$
$ 4, 4, 4, 2, 2, 2, 1, 1, 1, 1 $ $3326400$ $4$ $( 1,14, 2,13)( 3, 8)( 4, 7)( 9,16,10,15)(11,12)(17,19,18,20)$
$ 4, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1 $ $3326400$ $4$ $( 1,14, 2,13)( 3, 8)( 4, 7)( 9,16)(10,15)(11,12)(17,20)(18,19)$
$ 4, 4, 4, 4, 2, 2, 1, 1 $ $831600$ $4$ $( 1,14, 2,13)( 3, 7, 4, 8)( 9,16,10,15)(11,12)(17,19,18,20)(21,22)$
$ 4, 4, 4, 4, 1, 1, 1, 1, 1, 1 $ $277200$ $4$ $( 1,14, 2,13)( 3, 8, 4, 7)( 9,16,10,15)(17,19,18,20)$
$ 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $1663200$ $4$ $( 1,14, 2,13)( 3, 8, 4, 7)( 9,16)(10,15)(17,20)(18,19)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $277200$ $2$ $( 1,13)( 2,14)( 3, 8)( 4, 7)( 9,16)(10,15)(17,20)(18,19)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ $831600$ $2$ $( 1,13)( 2,14)( 3, 7)( 4, 8)( 9,16)(10,15)(11,12)(17,20)(18,19)(21,22)$
$ 4, 4, 4, 2, 2, 2, 2, 2 $ $1108800$ $4$ $( 1,14, 2,13)( 3, 8)( 4, 7)( 5, 6)( 9,16,10,15)(11,12)(17,19,18,20)(21,22)$
$ 4, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $1108800$ $4$ $( 1,14, 2,13)( 3, 8)( 4, 7)( 5, 6)( 9,16)(10,15)(11,12)(17,20)(18,19)(21,22)$
$ 6, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $10560$ $6$ $( 5,22,11, 6,21,12)(15,16)$
$ 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $36960$ $6$ $( 5,21,12)( 6,22,11)(15,16)(19,20)$
$ 6, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $73920$ $6$ $( 5,22,11, 6,21,12)( 9,10)(15,16)(19,20)$
$ 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $92400$ $6$ $( 5,21,12)( 6,22,11)( 7, 8)( 9,10)(15,16)(19,20)$
$ 6, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $73920$ $6$ $( 3, 4)( 5,21,11, 6,22,12)( 7, 8)( 9,10)(15,16)(19,20)$
$ 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1 $ $36960$ $6$ $( 3, 4)( 5,21,12)( 6,22,11)( 7, 8)( 9,10)(13,14)(15,16)(19,20)$
$ 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1320$ $3$ $( 5,21,12)( 6,22,11)$
$ 6, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ $10560$ $6$ $( 1, 2)( 3, 4)( 5,22,11, 6,21,12)( 7, 8)( 9,10)(13,14)(15,16)(19,20)$
$ 3, 3, 2, 2, 2, 2, 2, 2, 2, 2 $ $1320$ $6$ $( 1, 2)( 3, 4)( 5,21,12)( 6,22,11)( 7, 8)( 9,10)(13,14)(15,16)(17,18)(19,20)$
$ 8, 8, 2, 2, 1, 1 $ $39916800$ $8$ $( 1,20,14,17, 2,19,13,18)( 3,10, 8,15, 4, 9, 7,16)( 5, 6)(11,12)$
$ 8, 4, 4, 2, 2, 2 $ $26611200$ $8$ $( 1,19,13,18)( 2,20,14,17)( 3,10, 8,15, 4, 9, 7,16)( 5, 6)(11,12)(21,22)$
$ 4, 4, 4, 4, 2, 2, 1, 1 $ $39916800$ $4$ $( 1,19,13,18)( 2,20,14,17)( 3, 9, 7,16)( 4,10, 8,15)( 5, 6)(11,12)$
$ 8, 4, 4, 2, 1, 1, 1, 1 $ $79833600$ $8$ $( 1,20,14,17, 2,19,13,18)( 3,10, 8,15)( 4, 9, 7,16)( 5, 6)$
$ 4, 4, 4, 4, 1, 1, 1, 1, 1, 1 $ $13305600$ $4$ $( 1,19,13,18)( 2,20,14,17)( 3,10, 8,15)( 4, 9, 7,16)$
$ 8, 8, 1, 1, 1, 1, 1, 1 $ $13305600$ $8$ $( 1,20,14,17, 2,19,13,18)( 3, 9, 7,16, 4,10, 8,15)$
$ 4, 4, 3, 3, 2, 2, 2, 2 $ $13305600$ $12$ $( 1,13)( 2,14)( 3, 7)( 4, 8)( 5,12,22)( 6,11,21)( 9,16,10,15)(17,19,18,20)$
$ 6, 4, 2, 2, 2, 2, 2, 2 $ $8870400$ $12$ $( 1,13)( 2,14)( 3, 7)( 4, 8)( 5,12,21, 6,11,22)( 9,16,10,15)(17,20)(18,19)$
$ 3, 3, 2, 2, 2, 2, 2, 2, 2, 2 $ $2217600$ $6$ $( 1,13)( 2,14)( 3, 7)( 4, 8)( 5,12,22)( 6,11,21)( 9,16)(10,15)(17,20)(18,19)$
$ 6, 4, 4, 4, 2, 2 $ $8870400$ $12$ $( 1,13)( 2,14)( 3, 8, 4, 7)( 5,12,21, 6,11,22)( 9,16,10,15)(17,19,18,20)$
$ 4, 4, 4, 4, 3, 3 $ $2217600$ $12$ $( 1,14, 2,13)( 3, 8, 4, 7)( 5,11,22)( 6,12,21)( 9,16,10,15)(17,19,18,20)$
$ 8, 8, 2, 2, 1, 1 $ $319334400$ $8$ $( 1, 7,19,16,13, 4,18, 9)( 2, 8,20,15,14, 3,17,10)( 5, 6)(21,22)$
$ 16, 2, 1, 1, 1, 1 $ $319334400$ $16$ $( 1, 7,20,15,14, 3,17,10, 2, 8,19,16,13, 4,18, 9)( 5, 6)$
$ 16, 2, 2, 2 $ $106444800$ $16$ $( 1, 7,19,16,13, 3,17,10, 2, 8,20,15,14, 4,18, 9)( 5, 6)(11,12)(21,22)$
$ 8, 8, 1, 1, 1, 1, 1, 1 $ $106444800$ $8$ $( 1, 7,19,16,13, 4,18, 9)( 2, 8,20,15,14, 3,17,10)$
$ 8, 6, 4, 4 $ $212889600$ $24$ $( 1,18,13,19, 2,17,14,20)( 3,15, 8, 9)( 4,16, 7,10)( 5,21,12, 6,22,11)$
$ 4, 4, 4, 4, 3, 3 $ $106444800$ $12$ $( 1,18,13,20)( 2,17,14,19)( 3,15, 8, 9)( 4,16, 7,10)( 5,22,11)( 6,21,12)$
$ 8, 8, 3, 3 $ $106444800$ $24$ $( 1,18,13,19, 2,17,14,20)( 3,15, 8,10, 4,16, 7, 9)( 5,22,11)( 6,21,12)$
$ 8, 8, 3, 3 $ $851558400$ $24$ $( 1,16,17, 7,13, 9,19, 4)( 2,15,18, 8,14,10,20, 3)( 5,12,21)( 6,11,22)$
$ 16, 6 $ $851558400$ $48$ $( 1,16,17, 7,13, 9,20, 3, 2,15,18, 8,14,10,19, 4)( 5,12,22, 6,11,21)$
$ 4, 4, 2, 2, 2, 2, 2, 2, 1, 1 $ $27720$ $4$ $( 1,14, 2,13)( 3, 4)( 7, 8)( 9,10)(11,12)(15,16)(17,20,18,19)(21,22)$
$ 4, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1 $ $166320$ $4$ $( 1,14, 2,13)( 3, 4)( 7, 8)( 9,10)(11,12)(15,16)(17,19)(18,20)$
$ 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $138600$ $4$ $( 1,14, 2,13)( 3, 4)( 7, 8)(11,12)(15,16)(17,20,18,19)$
$ 4, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $277200$ $4$ $( 1,14, 2,13)( 3, 4)(11,12)(15,16)(17,19)(18,20)$
$ 4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $83160$ $4$ $( 1,14, 2,13)( 7, 8)(15,16)(17,20,18,19)$
$ 4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $55440$ $4$ $( 1,14, 2,13)(15,16)(17,19)(18,20)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $138600$ $2$ $( 1,13)( 2,14)( 3, 4)( 7, 8)( 9,10)(15,16)(17,19)(18,20)$
$ 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $83160$ $2$ $( 1,13)( 2,14)( 3, 4)(15,16)(17,19)(18,20)$
$ 4, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $7920$ $4$ $( 1,14, 2,13)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(15,16)(17,19)(18,20)(21,22)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ $27720$ $2$ $( 1,13)( 2,14)( 3, 4)( 5, 6)( 7, 8)( 9,10)(15,16)(17,19)(18,20)(21,22)$
$ 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $3960$ $4$ $( 1,14, 2,13)(17,20,18,19)$
$ 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $3960$ $2$ $( 1,13)( 2,14)(17,19)(18,20)$
$ 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $554400$ $4$ $( 1,17,13,19)( 2,18,14,20)( 3, 4)( 7, 8)(11,12)(21,22)$
$ 8, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $554400$ $8$ $( 1,17,13,20, 2,18,14,19)( 3, 4)( 7, 8)(11,12)$
$ 8, 2, 2, 2, 2, 2, 1, 1, 1, 1 $ $332640$ $8$ $( 1,17,13,20, 2,18,14,19)( 3, 4)( 7, 8)( 9,10)(11,12)(21,22)$
$ 4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $332640$ $4$ $( 1,17,13,19)( 2,18,14,20)( 3, 4)(11,12)$
$ 8, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $110880$ $8$ $( 1,17,13,20, 2,18,14,19)( 7, 8)$
$ 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $15840$ $4$ $( 1,17,13,19)( 2,18,14,20)$
$ 4, 4, 2, 2, 2, 2, 2, 2, 1, 1 $ $110880$ $4$ $( 1,17,13,19)( 2,18,14,20)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(21,22)$
$ 8, 2, 2, 2, 2, 2, 2, 2 $ $15840$ $8$ $( 1,17,13,20, 2,18,14,19)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(15,16)(21,22)$
$ 5, 5, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $2661120$ $10$ $( 1, 2)( 3, 4)( 5, 9, 8,22,12)( 6,10, 7,21,11)$
$ 10, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $3548160$ $10$ $( 1, 2)( 3, 4)( 5, 9, 8,21,11, 6,10, 7,22,12)(19,20)$
$ 10, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1064448$ $10$ $( 1, 2)( 5, 9, 8,22,11, 6,10, 7,21,12)$
$ 5, 5, 2, 2, 2, 2, 1, 1, 1, 1 $ $2661120$ $10$ $( 1, 2)( 3, 4)( 5, 9, 8,21,12)( 6,10, 7,22,11)(13,14)(19,20)$
$ 10, 2, 2, 2, 2, 2, 1, 1 $ $1064448$ $10$ $( 1, 2)( 3, 4)( 5, 9, 8,22,11, 6,10, 7,21,12)(13,14)(15,16)(19,20)$
$ 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $177408$ $5$ $( 5, 9, 8,21,12)( 6,10, 7,22,11)$
$ 5, 5, 2, 2, 2, 2, 2, 2 $ $177408$ $10$ $( 1, 2)( 3, 4)( 5, 9, 8,21,12)( 6,10, 7,22,11)(13,14)(15,16)(17,18)(19,20)$
$ 4, 4, 4, 2, 2, 2, 1, 1, 1, 1 $ $6652800$ $4$ $( 1,20,13,18)( 2,19,14,17)( 3,16, 4,15)( 5, 6)( 7, 8)(21,22)$
$ 8, 4, 2, 2, 1, 1, 1, 1, 1, 1 $ $6652800$ $8$ $( 1,19,14,17, 2,20,13,18)( 3,16, 4,15)( 5, 6)( 7, 8)$
$ 8, 4, 2, 2, 2, 2, 1, 1 $ $3326400$ $8$ $( 1,19,14,17, 2,20,13,18)( 3,16, 4,15)( 5, 6)( 7, 8)( 9,10)(21,22)$
$ 4, 4, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $3326400$ $4$ $( 1,20,13,18)( 2,19,14,17)( 3,16, 4,15)( 5, 6)$
$ 4, 4, 2, 2, 2, 2, 2, 2, 1, 1 $ $3326400$ $4$ $( 1,20,13,18)( 2,19,14,17)( 3,16)( 4,15)( 5, 6)( 7, 8)(11,12)(21,22)$
$ 8, 2, 2, 2, 2, 2, 1, 1, 1, 1 $ $6652800$ $8$ $( 1,19,14,17, 2,20,13,18)( 3,16)( 4,15)( 5, 6)( 7, 8)(11,12)$
$ 8, 2, 2, 2, 2, 2, 2, 2 $ $665280$ $8$ $( 1,19,14,17, 2,20,13,18)( 3,16)( 4,15)( 5, 6)( 7, 8)( 9,10)(11,12)(21,22)$
$ 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $6652800$ $4$ $( 1,20,13,18)( 2,19,14,17)( 3,16)( 4,15)( 5, 6)(11,12)$
$ 4, 4, 4, 2, 2, 2, 2, 2 $ $665280$ $4$ $( 1,19,13,18)( 2,20,14,17)( 3,16, 4,15)( 5, 6)( 7, 8)( 9,10)(11,12)(21,22)$
$ 8, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $3326400$ $8$ $( 1,20,14,17, 2,19,13,18)( 3,16)( 4,15)( 5, 6)$
$ 8, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $665280$ $8$ $( 1,19,14,17, 2,20,13,18)( 3,16, 4,15)$
$ 4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $665280$ $4$ $( 1,19,13,18)( 2,20,14,17)( 3,16)( 4,15)$
$ 5, 5, 2, 2, 2, 2, 1, 1, 1, 1 $ $31933440$ $10$ $( 1,13)( 2,14)( 5,22,10,12, 7)( 6,21, 9,11, 8)(17,20)(18,19)$
$ 10, 4, 2, 2, 1, 1, 1, 1 $ $63866880$ $20$ $( 1,13)( 2,14)( 5,21, 9,11, 8, 6,22,10,12, 7)(17,19,18,20)$
$ 10, 2, 2, 2, 2, 2, 1, 1 $ $63866880$ $10$ $( 1,13)( 2,14)( 3, 4)( 5,22,10,11, 8, 6,21, 9,12, 7)(17,20)(18,19)$
$ 5, 5, 4, 2, 2, 2, 1, 1 $ $127733760$ $20$ $( 1,13)( 2,14)( 3, 4)( 5,21, 9,12, 7)( 6,22,10,11, 8)(17,19,18,20)$
$ 5, 5, 4, 4, 1, 1, 1, 1 $ $31933440$ $20$ $( 1,14, 2,13)( 5,21, 9,12, 7)( 6,22,10,11, 8)(17,19,18,20)$
$ 10, 4, 4, 2, 1, 1 $ $63866880$ $20$ $( 1,14, 2,13)( 3, 4)( 5,21, 9,11, 8, 6,22,10,12, 7)(17,19,18,20)$
$ 5, 5, 2, 2, 2, 2, 2, 2 $ $31933440$ $10$ $( 1,13)( 2,14)( 3, 4)( 5,21, 9,12, 7)( 6,22,10,11, 8)(15,16)(17,20)(18,19)$
$ 10, 4, 2, 2, 2, 2 $ $63866880$ $20$ $( 1,13)( 2,14)( 3, 4)( 5,22,10,11, 8, 6,21, 9,12, 7)(15,16)(17,19,18,20)$
$ 5, 5, 4, 4, 2, 2 $ $31933440$ $20$ $( 1,14, 2,13)( 3, 4)( 5,22,10,12, 7)( 6,21, 9,11, 8)(15,16)(17,19,18,20)$
$ 10, 8, 2, 2 $ $255467520$ $40$ $( 1,20,14,18, 2,19,13,17)( 3,16)( 4,15)( 5,12,22, 8,10, 6,11,21, 7, 9)$
$ 5, 5, 4, 4, 2, 2 $ $255467520$ $20$ $( 1,19,13,17)( 2,20,14,18)( 3,16)( 4,15)( 5,12,21, 7, 9)( 6,11,22, 8,10)$
$ 8, 5, 5, 4 $ $255467520$ $40$ $( 1,20,14,18, 2,19,13,17)( 3,16, 4,15)( 5,11,21, 7, 9)( 6,12,22, 8,10)$
$ 10, 4, 4, 4 $ $255467520$ $20$ $( 1,19,13,17)( 2,20,14,18)( 3,16, 4,15)( 5,11,22, 8,10, 6,12,21, 7, 9)$
$ 10, 4, 4, 2, 1, 1 $ $255467520$ $20$ $( 1,19,15,13)( 2,20,16,14)( 5, 8,11, 9,22, 6, 7,12,10,21)(17,18)$
$ 8, 5, 5, 2, 1, 1 $ $255467520$ $40$ $( 1,20,16,14, 2,19,15,13)( 5, 8,11, 9,21)( 6, 7,12,10,22)(17,18)$
$ 5, 5, 4, 4, 2, 2 $ $127733760$ $20$ $( 1,19,15,13)( 2,20,16,14)( 3, 4)( 5, 8,12,10,21)( 6, 7,11, 9,22)(17,18)$
$ 10, 8, 2, 2 $ $127733760$ $40$ $( 1,20,16,14, 2,19,15,13)( 3, 4)( 5, 8,12,10,22, 6, 7,11, 9,21)(17,18)$
$ 5, 5, 4, 4, 1, 1, 1, 1 $ $127733760$ $20$ $( 1,19,15,13)( 2,20,16,14)( 5, 8,11, 9,21)( 6, 7,12,10,22)$
$ 10, 8, 1, 1, 1, 1 $ $127733760$ $40$ $( 1,20,16,14, 2,19,15,13)( 5, 8,11, 9,22, 6, 7,12,10,21)$
$ 3, 3, 3, 3, 2, 2, 2, 2, 1, 1 $ $1478400$ $6$ $( 1, 2)( 3, 7,22)( 4, 8,21)( 5, 9,11)( 6,10,12)(13,14)(15,16)(17,18)$
$ 6, 3, 3, 2, 2, 2, 2, 2 $ $591360$ $6$ $( 1, 2)( 3, 7,21, 4, 8,22)( 5, 9,11)( 6,10,12)(13,14)(15,16)(17,18)(19,20)$
$ 6, 6, 2, 2, 2, 2, 1, 1 $ $1478400$ $6$ $( 1, 2)( 3, 7,21, 4, 8,22)( 5,10,12, 6, 9,11)(13,14)(15,16)(17,18)$
$ 6, 3, 3, 2, 2, 2, 1, 1, 1, 1 $ $5913600$ $6$ $( 1, 2)( 3, 7,22)( 4, 8,21)( 5, 9,12, 6,10,11)(15,16)(17,18)$
$ 6, 6, 2, 2, 1, 1, 1, 1, 1, 1 $ $2956800$ $6$ $( 1, 2)( 3, 7,21, 4, 8,22)( 5, 9,12, 6,10,11)(17,18)$
$ 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1 $ $2956800$ $6$ $( 1, 2)( 3, 7,22)( 4, 8,21)( 5,10,11)( 6, 9,12)(17,18)$
$ 6, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $2956800$ $6$ $( 3, 7,22)( 4, 8,21)( 5, 9,12, 6,10,11)(17,18)$
$ 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $295680$ $6$ $( 3, 7,21, 4, 8,22)( 5, 9,12, 6,10,11)$
$ 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $295680$ $3$ $( 3, 7,22)( 4, 8,21)( 5,10,11)( 6, 9,12)$
$ 6, 6, 4, 2, 2, 2 $ $35481600$ $12$ $( 1, 2)( 3,10, 8,12,21, 5)( 4, 9, 7,11,22, 6)(13,14)(15,16)(17,19,18,20)$
$ 12, 2, 2, 2, 2, 2 $ $35481600$ $12$ $( 1, 2)( 3,10, 8,12,22, 6, 4, 9, 7,11,21, 5)(13,14)(15,16)(17,20)(18,19)$
$ 12, 4, 2, 2, 1, 1 $ $106444800$ $12$ $( 1, 2)( 3,10, 8,11,22, 6, 4, 9, 7,12,21, 5)(15,16)(17,19,18,20)$
$ 6, 6, 2, 2, 2, 2, 1, 1 $ $106444800$ $6$ $( 1, 2)( 3,10, 8,11,21, 5)( 4, 9, 7,12,22, 6)(15,16)(17,20)(18,19)$
$ 6, 6, 4, 2, 1, 1, 1, 1 $ $106444800$ $12$ $( 1, 2)( 3,10, 8,11,21, 5)( 4, 9, 7,12,22, 6)(17,19,18,20)$
$ 12, 2, 2, 2, 1, 1, 1, 1 $ $106444800$ $12$ $( 1, 2)( 3,10, 8,11,22, 6, 4, 9, 7,12,21, 5)(17,20)(18,19)$
$ 12, 4, 1, 1, 1, 1, 1, 1 $ $35481600$ $12$ $( 3,10, 8,11,22, 6, 4, 9, 7,12,21, 5)(17,19,18,20)$
$ 6, 6, 2, 2, 1, 1, 1, 1, 1, 1 $ $35481600$ $6$ $( 3,10, 8,11,21, 5)( 4, 9, 7,12,22, 6)(17,20)(18,19)$
$ 4, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1 $ $1663200$ $4$ $( 3,11)( 4,12)( 5, 8, 6, 7)( 9,21)(10,22)(15,16)(17,18)(19,20)$
$ 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $1663200$ $4$ $( 3,11)( 4,12)( 5, 8, 6, 7)( 9,22,10,21)(15,16)(17,18)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $554400$ $2$ $( 3,11)( 4,12)( 5, 7)( 6, 8)( 9,21)(10,22)(15,16)(17,18)$
$ 4, 4, 2, 2, 2, 2, 2, 2, 1, 1 $ $831600$ $4$ $( 3,12, 4,11)( 5, 8, 6, 7)( 9,21)(10,22)(13,14)(15,16)(17,18)(19,20)$
$ 4, 4, 4, 2, 2, 2, 1, 1, 1, 1 $ $554400$ $4$ $( 3,12, 4,11)( 5, 8, 6, 7)( 9,22,10,21)(13,14)(15,16)(17,18)$
$ 4, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $831600$ $4$ $( 3,11)( 4,12)( 5, 8, 6, 7)( 9,21)(10,22)(17,18)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ $277200$ $2$ $( 3,11)( 4,12)( 5, 7)( 6, 8)( 9,21)(10,22)(13,14)(15,16)(17,18)(19,20)$
$ 4, 4, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $277200$ $4$ $( 3,12, 4,11)( 5, 8, 6, 7)( 9,22,10,21)(17,18)$
$ 4, 4, 4, 2, 2, 2, 2, 2 $ $55440$ $4$ $( 1, 2)( 3,12, 4,11)( 5, 8, 6, 7)( 9,22,10,21)(13,14)(15,16)(17,18)(19,20)$
$ 4, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $166320$ $4$ $( 1, 2)( 3,12, 4,11)( 5, 7)( 6, 8)( 9,21)(10,22)(13,14)(15,16)(17,18)(19,20)$
$ 4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $166320$ $4$ $( 3,11)( 4,12)( 5, 8, 6, 7)( 9,22,10,21)$
$ 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $55440$ $2$ $( 3,11)( 4,12)( 5, 7)( 6, 8)( 9,21)(10,22)$
$ 10, 6, 3, 3 $ $227082240$ $30$ $( 1,17,15,19,14, 2,18,16,20,13)( 3,21, 6)( 4,22, 5)( 7,11, 9, 8,12,10)$
$ 6, 6, 5, 5 $ $113541120$ $30$ $( 1,17,15,20,13)( 2,18,16,19,14)( 3,22, 5, 4,21, 6)( 7,11, 9, 8,12,10)$
$ 5, 5, 3, 3, 3, 3 $ $113541120$ $15$ $( 1,17,15,20,13)( 2,18,16,19,14)( 3,21, 6)( 4,22, 5)( 7,11,10)( 8,12, 9)$
$ 12, 2, 2, 2, 1, 1, 1, 1 $ $17740800$ $12$ $( 3,11, 5, 8,22,10, 4,12, 6, 7,21, 9)(15,16)(17,18)(19,20)$
$ 6, 6, 2, 2, 1, 1, 1, 1, 1, 1 $ $17740800$ $6$ $( 3,11, 5, 8,21, 9)( 4,12, 6, 7,22,10)(15,16)(17,18)$
$ 6, 6, 2, 2, 2, 2, 1, 1 $ $8870400$ $6$ $( 3,12, 6, 7,21, 9)( 4,11, 5, 8,22,10)(13,14)(15,16)(17,18)(19,20)$
$ 12, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $8870400$ $12$ $( 3,11, 5, 8,22,10, 4,12, 6, 7,21, 9)(17,18)$
$ 12, 2, 2, 2, 2, 2 $ $1774080$ $12$ $( 1, 2)( 3,12, 6, 7,22,10, 4,11, 5, 8,21, 9)(13,14)(15,16)(17,18)(19,20)$
$ 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1774080$ $6$ $( 3,11, 5, 8,21, 9)( 4,12, 6, 7,22,10)$
$ 5, 5, 4, 4, 2, 2 $ $63866880$ $20$ $( 1,18,16,20,13)( 2,17,15,19,14)( 3, 7, 4, 8)( 5, 9, 6,10)(11,22)(12,21)$
$ 10, 4, 4, 4 $ $21288960$ $20$ $( 1,18,16,19,14, 2,17,15,20,13)( 3, 7, 4, 8)( 5, 9, 6,10)(11,21,12,22)$
$ 10, 4, 2, 2, 2, 2 $ $63866880$ $20$ $( 1,18,16,19,14, 2,17,15,20,13)( 3, 7, 4, 8)( 5,10)( 6, 9)(11,22)(12,21)$
$ 5, 5, 2, 2, 2, 2, 2, 2 $ $21288960$ $10$ $( 1,18,16,20,13)( 2,17,15,19,14)( 3, 8)( 4, 7)( 5,10)( 6, 9)(11,22)(12,21)$
$ 6, 6, 5, 5 $ $681246720$ $30$ $( 1,15,13,18,19)( 2,16,14,17,20)( 3,10,21, 8, 5,11)( 4, 9,22, 7, 6,12)$
$ 12, 10 $ $681246720$ $60$ $( 1,15,13,18,20, 2,16,14,17,19)( 3,10,22, 7, 6,12, 4, 9,21, 8, 5,11)$
$ 4, 4, 4, 4, 2, 2, 1, 1 $ $1663200$ $4$ $( 1,12, 2,11)( 3,18, 4,17)( 5,22, 6,21)( 7, 9, 8,10)(15,19)(16,20)$
$ 4, 4, 2, 2, 2, 2, 2, 2, 1, 1 $ $3326400$ $4$ $( 1,12, 2,11)( 3,18, 4,17)( 5,21)( 6,22)( 7,10)( 8, 9)(15,19)(16,20)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ $332640$ $2$ $( 1,11)( 2,12)( 3,18)( 4,17)( 5,21)( 6,22)( 7,10)( 8, 9)(15,19)(16,20)$
$ 4, 4, 4, 2, 2, 2, 2, 2 $ $3326400$ $4$ $( 1,11)( 2,12)( 3,18, 4,17)( 5,22, 6,21)( 7, 9, 8,10)(13,14)(15,19)(16,20)$
$ 4, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $1663200$ $4$ $( 1,11)( 2,12)( 3,18, 4,17)( 5,21)( 6,22)( 7,10)( 8, 9)(13,14)(15,19)(16,20)$
$ 4, 4, 4, 4, 4, 2 $ $332640$ $4$ $( 1,12, 2,11)( 3,18, 4,17)( 5,22, 6,21)( 7, 9, 8,10)(13,14)(15,20,16,19)$
$ 10, 5, 5, 2 $ $408748032$ $10$ $( 1, 5, 3,20, 8, 2, 6, 4,19, 7)( 9,12,22,18,15)(10,11,21,17,16)(13,14)$
$ 10, 10, 1, 1 $ $204374016$ $10$ $( 1, 5, 3,20, 8, 2, 6, 4,19, 7)( 9,11,21,17,16,10,12,22,18,15)$
$ 5, 5, 5, 5, 1, 1 $ $204374016$ $5$ $( 1, 5, 3,19, 7)( 2, 6, 4,20, 8)( 9,11,22,18,15)(10,12,21,17,16)$
$ 20, 2 $ $2043740160$ $20$ $( 1,15, 6,10, 3,12,20,22, 8,17, 2,16, 5, 9, 4,11,19,21, 7,18)(13,14)$
$ 10, 10, 1, 1 $ $2043740160$ $10$ $( 1,15, 6,10, 3,11,19,21, 7,18)( 2,16, 5, 9, 4,12,20,22, 8,17)$
$ 6, 6, 3, 3, 1, 1, 1, 1 $ $23654400$ $6$ $( 1, 6,18)( 2, 5,17)( 3, 9,19, 4,10,20)(13,15,22,14,16,21)$
$ 3, 3, 3, 3, 3, 3, 1, 1, 1, 1 $ $7884800$ $3$ $( 1, 6,18)( 2, 5,17)( 3, 9,20)( 4,10,19)(13,15,21)(14,16,22)$
$ 6, 3, 3, 3, 3, 2, 1, 1 $ $47308800$ $6$ $( 1, 6,18)( 2, 5,17)( 3, 9,19, 4,10,20)( 7, 8)(13,15,21)(14,16,22)$
$ 3, 3, 3, 3, 3, 3, 2, 2 $ $7884800$ $6$ $( 1, 6,18)( 2, 5,17)( 3, 9,19)( 4,10,20)( 7, 8)(11,12)(13,15,21)(14,16,22)$
$ 6, 6, 3, 3, 2, 2 $ $23654400$ $6$ $( 1, 6,18)( 2, 5,17)( 3, 9,20, 4,10,19)( 7, 8)(11,12)(13,15,22,14,16,21)$
$ 6, 6, 6, 2, 1, 1 $ $15769600$ $6$ $( 1, 5,17, 2, 6,18)( 3, 9,19, 4,10,20)( 7, 8)(13,15,22,14,16,21)$
$ 12, 6, 2, 2 $ $283852800$ $12$ $( 1,17, 5, 2,18, 6)( 3,14,10,15,20,21, 4,13, 9,16,19,22)( 7,12)( 8,11)$
$ 6, 6, 6, 4 $ $283852800$ $12$ $( 1,17, 5, 2,18, 6)( 3,14,10,15,20,22)( 4,13, 9,16,19,21)( 7,12, 8,11)$
$ 6, 6, 3, 3, 2, 2 $ $283852800$ $6$ $( 1,17, 6)( 2,18, 5)( 3,14,10,15,20,22)( 4,13, 9,16,19,21)( 7,12)( 8,11)$
$ 12, 4, 3, 3 $ $283852800$ $12$ $( 1,17, 6)( 2,18, 5)( 3,14,10,15,20,21, 4,13, 9,16,19,22)( 7,12, 8,11)$
$ 6, 4, 2, 2, 2, 2, 2, 2 $ $13305600$ $12$ $( 1,17, 6, 2,18, 5)( 3,15, 4,16)( 7, 8)( 9,21)(10,22)(11,12)(13,20)(14,19)$
$ 6, 4, 4, 4, 2, 2 $ $4435200$ $12$ $( 1,17, 6, 2,18, 5)( 3,15, 4,16)( 7, 8)( 9,22,10,21)(11,12)(13,19,14,20)$
$ 6, 4, 4, 2, 2, 2, 1, 1 $ $26611200$ $12$ $( 1,17, 6, 2,18, 5)( 3,15, 4,16)( 9,22,10,21)(11,12)(13,20)(14,19)$
$ 6, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ $8870400$ $6$ $( 1,17, 6, 2,18, 5)( 3,15)( 4,16)( 7, 8)( 9,21)(10,22)(13,20)(14,19)$
$ 6, 4, 2, 2, 2, 2, 1, 1, 1, 1 $ $13305600$ $12$ $( 1,17, 6, 2,18, 5)( 3,15)( 4,16)( 9,22,10,21)(13,20)(14,19)$
$ 6, 4, 4, 4, 1, 1, 1, 1 $ $4435200$ $12$ $( 1,17, 6, 2,18, 5)( 3,15, 4,16)( 9,22,10,21)(13,20,14,19)$
$ 4, 4, 3, 3, 2, 2, 2, 2 $ $13305600$ $12$ $( 1,17, 5)( 2,18, 6)( 3,15, 4,16)( 7, 8)( 9,22,10,21)(11,12)(13,20)(14,19)$
$ 4, 3, 3, 2, 2, 2, 2, 2, 1, 1 $ $26611200$ $12$ $( 1,17, 5)( 2,18, 6)( 3,15, 4,16)( 9,21)(10,22)(11,12)(13,20)(14,19)$
$ 4, 4, 4, 3, 3, 2, 1, 1 $ $8870400$ $12$ $( 1,17, 5)( 2,18, 6)( 3,15, 4,16)( 9,22,10,21)(11,12)(13,19,14,20)$
$ 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1 $ $4435200$ $6$ $( 1,17, 5)( 2,18, 6)( 3,15)( 4,16)( 9,21)(10,22)(13,20)(14,19)$
$ 4, 4, 3, 3, 2, 2, 1, 1, 1, 1 $ $13305600$ $12$ $( 1,17, 5)( 2,18, 6)( 3,15)( 4,16)( 9,22,10,21)(13,19,14,20)$
$ 3, 3, 2, 2, 2, 2, 2, 2, 2, 2 $ $4435200$ $6$ $( 1,17, 5)( 2,18, 6)( 3,15)( 4,16)( 7, 8)( 9,21)(10,22)(11,12)(13,19)(14,20)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ $990$ $2$ $( 3, 4)( 5, 6)( 7,12)( 8,11)( 9,10)(13,14)(15,16)(17,18)(19,20)(21,22)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $9240$ $2$ $( 3, 4)( 5, 6)( 7,12)( 8,11)( 9,10)(13,14)(15,16)(17,18)$
$ 4, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1 $ $3960$ $4$ $( 3, 4)( 5, 6)( 7,12, 8,11)( 9,10)(13,14)(15,16)(17,18)(19,20)$
$ 4, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $13860$ $4$ $( 3, 4)( 5, 6)( 7,12, 8,11)(13,14)(15,16)(17,18)$
$ 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $13860$ $2$ $( 5, 6)( 7,11)( 8,12)(13,14)(15,16)(17,18)$
$ 4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $9240$ $4$ $( 5, 6)( 7,12, 8,11)(15,16)(17,18)$
$ 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $3960$ $2$ $( 7,12)( 8,11)(15,16)(17,18)$
$ 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $990$ $4$ $( 7,12, 8,11)(17,18)$
$ 4, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $110$ $4$ $( 1, 2)( 3, 4)( 5, 6)( 7,12, 8,11)( 9,10)(13,14)(15,16)(17,18)(19,20)(21,22)$
$ 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $110$ $2$ $( 7,12)( 8,11)$
$ 6, 6, 3, 3, 2, 2 $ $47308800$ $6$ $( 1, 6,17, 2, 5,18)( 3,10,19)( 4, 9,20)( 7,11)( 8,12)(13,16,22,14,15,21)$
$ 6, 4, 3, 3, 3, 3 $ $47308800$ $12$ $( 1, 6,17, 2, 5,18)( 3,10,19)( 4, 9,20)( 7,11, 8,12)(13,16,21)(14,15,22)$
$ 6, 6, 6, 4 $ $15769600$ $12$ $( 1, 6,17, 2, 5,18)( 3,10,20, 4, 9,19)( 7,11, 8,12)(13,16,22,14,15,21)$
$ 3, 3, 3, 3, 3, 3, 2, 2 $ $15769600$ $6$ $( 1, 5,18)( 2, 6,17)( 3,10,19)( 4, 9,20)( 7,11)( 8,12)(13,16,21)(14,15,22)$
$ 7, 7, 2, 2, 2, 2 $ $15206400$ $14$ $( 1, 2)( 3,22,15, 5, 8,11,10)( 4,21,16, 6, 7,12, 9)(13,14)(17,18)(19,20)$
$ 14, 2, 2, 2, 1, 1 $ $60825600$ $14$ $( 1, 2)( 3,21,16, 6, 7,12, 9, 4,22,15, 5, 8,11,10)(13,14)(17,18)$
$ 7, 7, 2, 2, 1, 1, 1, 1 $ $91238400$ $14$ $( 1, 2)( 3,21,16, 6, 7,11,10)( 4,22,15, 5, 8,12, 9)(17,18)$
$ 14, 2, 1, 1, 1, 1, 1, 1 $ $60825600$ $14$ $( 3,22,15, 5, 8,12, 9, 4,21,16, 6, 7,11,10)(17,18)$
$ 7, 7, 1, 1, 1, 1, 1, 1, 1, 1 $ $15206400$ $7$ $( 3,21,16, 6, 7,11,10)( 4,22,15, 5, 8,12, 9)$
$ 14, 4, 2, 2 $ $364953600$ $28$ $( 1,13)( 2,14)( 3, 7,22,11,16, 9, 5, 4, 8,21,12,15,10, 6)(17,20,18,19)$
$ 7, 7, 2, 2, 2, 2 $ $182476800$ $14$ $( 1,13)( 2,14)( 3, 7,21,12,15,10, 6)( 4, 8,22,11,16, 9, 5)(17,19)(18,20)$
$ 7, 7, 4, 4 $ $182476800$ $28$ $( 1,14, 2,13)( 3, 7,22,12,15,10, 6)( 4, 8,21,11,16, 9, 5)(17,20,18,19)$
$ 7, 7, 4, 4 $ $729907200$ $28$ $( 1,18,14,19)( 2,17,13,20)( 3,16, 7,10,22, 6,11)( 4,15, 8, 9,21, 5,12)$
$ 14, 8 $ $729907200$ $56$ $( 1,18,14,20, 2,17,13,19)( 3,16, 7,10,21, 5,12, 4,15, 8, 9,22, 6,11)$
$ 8, 2, 2, 2, 2, 2, 1, 1, 1, 1 $ $19958400$ $8$ $( 1, 2)( 3, 9, 7, 5, 4,10, 8, 6)(11,16)(12,15)(17,19)(18,20)$
$ 8, 4, 2, 2, 2, 2, 1, 1 $ $39916800$ $8$ $( 1, 2)( 3, 9, 7, 5, 4,10, 8, 6)(11,16)(12,15)(17,20,18,19)(21,22)$
$ 4, 4, 2, 2, 2, 2, 2, 2, 1, 1 $ $19958400$ $4$ $( 1, 2)( 3,10, 8, 6)( 4, 9, 7, 5)(11,16)(12,15)(17,19)(18,20)(21,22)$
$ 4, 4, 4, 2, 2, 2, 1, 1, 1, 1 $ $39916800$ $4$ $( 1, 2)( 3,10, 8, 6)( 4, 9, 7, 5)(11,16)(12,15)(17,20,18,19)$
$ 4, 4, 4, 4, 2, 2, 1, 1 $ $19958400$ $4$ $( 1, 2)( 3, 9, 7, 5)( 4,10, 8, 6)(11,16,12,15)(17,20,18,19)(21,22)$
$ 8, 4, 4, 2, 1, 1, 1, 1 $ $19958400$ $8$ $( 1, 2)( 3,10, 8, 6, 4, 9, 7, 5)(11,16,12,15)(17,20,18,19)$
$ 8, 4, 4, 2, 2, 2 $ $6652800$ $8$ $( 1, 2)( 3, 9, 7, 5, 4,10, 8, 6)(11,16,12,15)(13,14)(17,20,18,19)(21,22)$
$ 4, 4, 4, 2, 2, 2, 2, 2 $ $13305600$ $4$ $( 1, 2)( 3,10, 8, 6)( 4, 9, 7, 5)(11,16,12,15)(13,14)(17,19)(18,20)(21,22)$
$ 8, 2, 2, 2, 2, 2, 2, 2 $ $6652800$ $8$ $( 1, 2)( 3,10, 8, 6, 4, 9, 7, 5)(11,16)(12,15)(13,14)(17,19)(18,20)(21,22)$
$ 8, 4, 2, 2, 1, 1, 1, 1, 1, 1 $ $13305600$ $8$ $( 3, 9, 7, 5, 4,10, 8, 6)(11,16)(12,15)(17,20,18,19)$
$ 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $6652800$ $4$ $( 3,10, 8, 6)( 4, 9, 7, 5)(11,16)(12,15)(17,19)(18,20)$
$ 4, 4, 4, 4, 1, 1, 1, 1, 1, 1 $ $6652800$ $4$ $( 3, 9, 7, 5)( 4,10, 8, 6)(11,16,12,15)(17,20,18,19)$
$ 8, 4, 4, 2, 2, 2 $ $39916800$ $8$ $( 1,18,13,19, 2,17,14,20)( 3,12, 4,11)( 5,16, 6,15)( 7,21)( 8,22)( 9,10)$
$ 4, 4, 4, 4, 4, 2 $ $13305600$ $4$ $( 1,18,13,20)( 2,17,14,19)( 3,12, 4,11)( 5,16, 6,15)( 7,22, 8,21)( 9,10)$
$ 8, 4, 4, 4, 1, 1 $ $13305600$ $8$ $( 1,18,13,19, 2,17,14,20)( 3,12, 4,11)( 5,16, 6,15)( 7,22, 8,21)$
$ 4, 4, 4, 4, 2, 2, 1, 1 $ $39916800$ $4$ $( 1,18,13,20)( 2,17,14,19)( 3,12, 4,11)( 5,16, 6,15)( 7,21)( 8,22)$
$ 4, 4, 4, 2, 2, 2, 2, 2 $ $39916800$ $4$ $( 1,18,14,20)( 2,17,13,19)( 3,11)( 4,12)( 5,16, 6,15)( 7,21)( 8,22)( 9,10)$
$ 8, 4, 2, 2, 2, 2, 1, 1 $ $39916800$ $8$ $( 1,18,14,19, 2,17,13,20)( 3,11)( 4,12)( 5,16, 6,15)( 7,21)( 8,22)$
$ 8, 2, 2, 2, 2, 2, 2, 2 $ $13305600$ $8$ $( 1,18,14,19, 2,17,13,20)( 3,11)( 4,12)( 5,16)( 6,15)( 7,21)( 8,22)( 9,10)$
$ 4, 4, 2, 2, 2, 2, 2, 2, 1, 1 $ $13305600$ $4$ $( 1,18,14,20)( 2,17,13,19)( 3,11)( 4,12)( 5,16)( 6,15)( 7,21)( 8,22)$
$ 6, 6, 4, 2, 2, 2 $ $35481600$ $12$ $( 1,13, 2,14)( 3, 7,16, 4, 8,15)( 5,12,22, 6,11,21)( 9,10)(17,19)(18,20)$
$ 6, 4, 4, 3, 3, 2 $ $35481600$ $12$ $( 1,13, 2,14)( 3, 7,16, 4, 8,15)( 5,12,21)( 6,11,22)( 9,10)(17,20,18,19)$
$ 6, 4, 3, 3, 2, 2, 1, 1 $ $70963200$ $12$ $( 1,13, 2,14)( 3, 7,16, 4, 8,15)( 5,12,21)( 6,11,22)(17,19)(18,20)$
$ 6, 6, 4, 4, 1, 1 $ $17740800$ $12$ $( 1,13, 2,14)( 3, 7,16, 4, 8,15)( 5,12,22, 6,11,21)(17,20,18,19)$
$ 4, 3, 3, 3, 3, 2, 2, 2 $ $35481600$ $12$ $( 1,13, 2,14)( 3, 8,15)( 4, 7,16)( 5,12,21)( 6,11,22)( 9,10)(17,19)(18,20)$
$ 4, 4, 3, 3, 3, 3, 1, 1 $ $17740800$ $12$ $( 1,13, 2,14)( 3, 8,15)( 4, 7,16)( 5,12,21)( 6,11,22)(17,20,18,19)$
$ 6, 3, 3, 2, 2, 2, 2, 2 $ $35481600$ $6$ $( 1,14)( 2,13)( 3, 7,16, 4, 8,15)( 5,11,21)( 6,12,22)( 9,10)(17,19)(18,20)$
$ 6, 6, 2, 2, 2, 2, 1, 1 $ $17740800$ $6$ $( 1,14)( 2,13)( 3, 7,16, 4, 8,15)( 5,11,22, 6,12,21)(17,19)(18,20)$
$ 3, 3, 3, 3, 2, 2, 2, 2, 1, 1 $ $17740800$ $6$ $( 1,14)( 2,13)( 3, 8,15)( 4, 7,16)( 5,11,21)( 6,12,22)(17,19)(18,20)$
$ 6, 6, 4, 4, 1, 1 $ $425779200$ $12$ $( 1,19,14,17)( 2,20,13,18)( 3, 6, 8,12,16,21)( 4, 5, 7,11,15,22)$
$ 12, 8, 1, 1 $ $425779200$ $24$ $( 1,20,13,18, 2,19,14,17)( 3, 6, 8,12,16,22, 4, 5, 7,11,15,21)$
$ 12, 4, 4, 2 $ $425779200$ $12$ $( 1,19,14,17)( 2,20,13,18)( 3, 6, 8,12,16,22, 4, 5, 7,11,15,21)( 9,10)$
$ 8, 6, 6, 2 $ $425779200$ $24$ $( 1,20,13,18, 2,19,14,17)( 3, 6, 8,12,16,21)( 4, 5, 7,11,15,22)( 9,10)$
$ 8, 4, 4, 2, 2, 2 $ $159667200$ $8$ $( 1,19,13,18, 2,20,14,17)( 3, 7, 9,16)( 4, 8,10,15)( 5, 6)(11,22)(12,21)$
$ 4, 4, 4, 4, 4, 2 $ $79833600$ $4$ $( 1,20,14,17)( 2,19,13,18)( 3, 7, 9,16)( 4, 8,10,15)( 5, 6)(11,21,12,22)$
$ 8, 8, 4, 2 $ $79833600$ $8$ $( 1,19,13,18, 2,20,14,17)( 3, 7,10,15, 4, 8, 9,16)( 5, 6)(11,21,12,22)$
$ 8, 4, 4, 4, 1, 1 $ $159667200$ $8$ $( 1,19,13,18, 2,20,14,17)( 3, 7, 9,16)( 4, 8,10,15)(11,21,12,22)$
$ 4, 4, 4, 4, 2, 2, 1, 1 $ $79833600$ $4$ $( 1,20,14,17)( 2,19,13,18)( 3, 7, 9,16)( 4, 8,10,15)(11,22)(12,21)$
$ 8, 8, 2, 2, 1, 1 $ $79833600$ $8$ $( 1,19,13,18, 2,20,14,17)( 3, 7,10,15, 4, 8, 9,16)(11,22)(12,21)$
$ 6, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $443520$ $6$ $( 1,22,14, 2,21,13)( 3, 4)(11,16)(12,15)$
$ 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $1108800$ $6$ $( 1,21,13)( 2,22,14)( 3, 4)(11,16)(12,15)(19,20)$
$ 6, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $1478400$ $6$ $( 1,22,14, 2,21,13)( 3, 4)( 9,10)(11,16)(12,15)(19,20)$
$ 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1 $ $1108800$ $6$ $( 1,21,13)( 2,22,14)( 3, 4)( 7, 8)( 9,10)(11,16)(12,15)(19,20)$
$ 6, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $73920$ $12$ $( 1,22,14, 2,21,13)(11,16,12,15)$
$ 4, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $443520$ $12$ $( 1,21,13)( 2,22,14)(11,16,12,15)(19,20)$
$ 6, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $1108800$ $12$ $( 1,22,14, 2,21,13)( 9,10)(11,16,12,15)(19,20)$
$ 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $1478400$ $12$ $( 1,21,13)( 2,22,14)( 7, 8)( 9,10)(11,16,12,15)(19,20)$
$ 6, 4, 2, 2, 2, 2, 1, 1, 1, 1 $ $1108800$ $12$ $( 1,21,14, 2,22,13)( 3, 4)( 7, 8)( 9,10)(11,16,12,15)(19,20)$
$ 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $73920$ $6$ $( 1,22,13)( 2,21,14)(11,16)(12,15)$
$ 6, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ $443520$ $6$ $( 1,22,14, 2,21,13)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,16)(12,15)(19,20)$
$ 4, 3, 3, 2, 2, 2, 2, 2, 1, 1 $ $443520$ $12$ $( 1,22,13)( 2,21,14)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,16,12,15)(19,20)$
$ 3, 3, 2, 2, 2, 2, 2, 2, 2, 2 $ $73920$ $6$ $( 1,21,13)( 2,22,14)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,16)(12,15)(17,18)(19,20)$
$ 6, 4, 2, 2, 2, 2, 2, 2 $ $73920$ $12$ $( 1,21,14, 2,22,13)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,16,12,15)(17,18)(19,20)$
$ 6, 4, 4, 2, 2, 2, 1, 1 $ $4435200$ $12$ $( 1,14,21, 2,13,22)( 3, 4)( 5, 9, 6,10)( 7, 8)(15,16)(17,19,18,20)$
$ 4, 3, 3, 2, 2, 2, 2, 2, 1, 1 $ $8870400$ $12$ $( 1,14,22)( 2,13,21)( 3, 4)( 5, 9, 6,10)( 7, 8)(15,16)(17,20)(18,19)$
$ 6, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ $4435200$ $6$ $( 1,14,21, 2,13,22)( 3, 4)( 5,10)( 6, 9)( 7, 8)(15,16)(17,20)(18,19)$
$ 4, 4, 3, 3, 2, 2, 1, 1, 1, 1 $ $6652800$ $12$ $( 1,14,22)( 2,13,21)( 3, 4)( 5, 9, 6,10)(15,16)(17,19,18,20)$
$ 6, 4, 2, 2, 2, 2, 1, 1, 1, 1 $ $13305600$ $12$ $( 1,14,21, 2,13,22)( 3, 4)( 5, 9, 6,10)(15,16)(17,20)(18,19)$
$ 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1 $ $6652800$ $6$ $( 1,14,22)( 2,13,21)( 3, 4)( 5,10)( 6, 9)(15,16)(17,20)(18,19)$
$ 4, 4, 3, 3, 2, 2, 2, 2 $ $1108800$ $12$ $( 1,13,22)( 2,14,21)( 3, 4)( 5, 9, 6,10)( 7, 8)(11,12)(15,16)(17,19,18,20)$
$ 6, 4, 2, 2, 2, 2, 2, 2 $ $2217600$ $12$ $( 1,13,21, 2,14,22)( 3, 4)( 5, 9, 6,10)( 7, 8)(11,12)(15,16)(17,20)(18,19)$
$ 3, 3, 2, 2, 2, 2, 2, 2, 2, 2 $ $1108800$ $6$ $( 1,13,22)( 2,14,21)( 3, 4)( 5,10)( 6, 9)( 7, 8)(11,12)(15,16)(17,20)(18,19)$
$ 6, 4, 4, 2, 1, 1, 1, 1, 1, 1 $ $4435200$ $12$ $( 1,13,21, 2,14,22)( 5, 9, 6,10)(15,16)(17,19,18,20)$
$ 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $8870400$ $12$ $( 1,13,22)( 2,14,21)( 5, 9, 6,10)(15,16)(17,20)(18,19)$
$ 6, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $4435200$ $6$ $( 1,13,21, 2,14,22)( 5,10)( 6, 9)(15,16)(17,20)(18,19)$
$ 4, 4, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1 $ $1108800$ $12$ $( 1,13,22)( 2,14,21)( 5, 9, 6,10)(17,19,18,20)$
$ 6, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $2217600$ $12$ $( 1,13,21, 2,14,22)( 5, 9, 6,10)(17,20)(18,19)$
$ 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $1108800$ $6$ $( 1,13,22)( 2,14,21)( 5,10)( 6, 9)(17,20)(18,19)$
$ 6, 4, 4, 2, 2, 2, 1, 1 $ $17740800$ $12$ $( 1,22,13, 2,21,14)( 3, 4)( 5,18,10,20)( 6,17, 9,19)(11,12)(15,16)$
$ 8, 3, 3, 2, 2, 2, 1, 1 $ $17740800$ $24$ $( 1,21,14)( 2,22,13)( 3, 4)( 5,18,10,19, 6,17, 9,20)(11,12)(15,16)$
$ 4, 4, 3, 3, 2, 2, 2, 2 $ $4435200$ $12$ $( 1,21,14)( 2,22,13)( 3, 4)( 5,18,10,20)( 6,17, 9,19)( 7, 8)(11,12)(15,16)$
$ 8, 6, 2, 2, 2, 2 $ $4435200$ $24$ $( 1,22,13, 2,21,14)( 3, 4)( 5,18,10,19, 6,17, 9,20)( 7, 8)(11,12)(15,16)$
$ 6, 4, 4, 2, 1, 1, 1, 1, 1, 1 $ $17740800$ $12$ $( 1,22,13, 2,21,14)( 5,18,10,20)( 6,17, 9,19)(15,16)$
$ 8, 3, 3, 2, 1, 1, 1, 1, 1, 1 $ $17740800$ $24$ $( 1,21,14)( 2,22,13)( 5,18,10,19, 6,17, 9,20)(15,16)$
$ 4, 4, 3, 3, 2, 2, 1, 1, 1, 1 $ $26611200$ $12$ $( 1,21,14)( 2,22,13)( 5,18,10,20)( 6,17, 9,19)( 7, 8)(15,16)$
$ 8, 6, 2, 2, 1, 1, 1, 1 $ $26611200$ $24$ $( 1,22,13, 2,21,14)( 5,18,10,19, 6,17, 9,20)( 7, 8)(15,16)$
$ 4, 4, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1 $ $4435200$ $12$ $( 1,21,14)( 2,22,13)( 5,18,10,20)( 6,17, 9,19)$
$ 8, 6, 1, 1, 1, 1, 1, 1, 1, 1 $ $4435200$ $24$ $( 1,22,13, 2,21,14)( 5,18,10,19, 6,17, 9,20)$
$ 8, 8, 4, 2 $ $638668800$ $8$ $( 1,16,20, 3,13, 9,18, 8)( 2,15,19, 4,14,10,17, 7)( 5, 6)(11,22,12,21)$
$ 16, 2, 2, 2 $ $638668800$ $16$ $( 1,16,19, 4,14,10,17, 7, 2,15,20, 3,13, 9,18, 8)( 5, 6)(11,21)(12,22)$
$ 8, 8, 2, 2, 1, 1 $ $638668800$ $8$ $( 1,16,20, 3,13, 9,18, 8)( 2,15,19, 4,14,10,17, 7)(11,21)(12,22)$
$ 16, 4, 1, 1 $ $638668800$ $16$ $( 1,16,19, 4,14,10,17, 7, 2,15,20, 3,13, 9,18, 8)(11,22,12,21)$
$ 10, 6, 2, 2, 1, 1 $ $85155840$ $30$ $( 1,21,14,10,19, 2,22,13, 9,20)( 3,17,15, 4,18,16)( 7, 8)(11,12)$
$ 6, 5, 5, 2, 1, 1, 1, 1 $ $85155840$ $30$ $( 1,22,13, 9,20)( 2,21,14,10,19)( 3,17,15, 4,18,16)(11,12)$
$ 10, 3, 3, 2, 1, 1, 1, 1 $ $85155840$ $30$ $( 1,21,14,10,19, 2,22,13, 9,20)( 3,17,15)( 4,18,16)( 7, 8)$
$ 5, 5, 3, 3, 1, 1, 1, 1, 1, 1 $ $28385280$ $15$ $( 1,22,13, 9,20)( 2,21,14,10,19)( 3,17,15)( 4,18,16)$
$ 10, 6, 1, 1, 1, 1, 1, 1 $ $28385280$ $30$ $( 1,22,14,10,19, 2,21,13, 9,20)( 3,17,15, 4,18,16)$
$ 5, 5, 3, 3, 2, 2, 1, 1 $ $85155840$ $30$ $( 1,21,13, 9,20)( 2,22,14,10,19)( 3,17,15)( 4,18,16)( 7, 8)(11,12)$
$ 6, 5, 5, 2, 2, 2 $ $28385280$ $30$ $( 1,22,13, 9,20)( 2,21,14,10,19)( 3,17,15, 4,18,16)( 5, 6)( 7, 8)(11,12)$
$ 10, 3, 3, 2, 2, 2 $ $28385280$ $30$ $( 1,22,14,10,19, 2,21,13, 9,20)( 3,17,15)( 4,18,16)( 5, 6)( 7, 8)(11,12)$
$ 5, 5, 4, 2, 1, 1, 1, 1, 1, 1 $ $21288960$ $20$ $( 1,14,19,22,10)( 2,13,20,21, 9)( 5, 8, 6, 7)(15,16)$
$ 10, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $21288960$ $10$ $( 1,14,19,21, 9, 2,13,20,22,10)( 5, 7)( 6, 8)(15,16)$
$ 5, 5, 4, 2, 2, 2, 1, 1 $ $21288960$ $20$ $( 1,14,19,22,10)( 2,13,20,21, 9)( 3, 4)( 5, 8, 6, 7)(11,12)(15,16)$
$ 10, 2, 2, 2, 2, 2, 1, 1 $ $21288960$ $10$ $( 1,14,19,21, 9, 2,13,20,22,10)( 3, 4)( 5, 7)( 6, 8)(11,12)(15,16)$
$ 10, 4, 2, 2, 1, 1, 1, 1 $ $31933440$ $20$ $( 1,13,20,21, 9, 2,14,19,22,10)( 5, 8, 6, 7)(11,12)(15,16)$
$ 5, 5, 2, 2, 2, 2, 1, 1, 1, 1 $ $31933440$ $10$ $( 1,13,20,22,10)( 2,14,19,21, 9)( 5, 7)( 6, 8)(11,12)(15,16)$
$ 10, 4, 1, 1, 1, 1, 1, 1, 1, 1 $ $5322240$ $20$ $( 1,14,19,21, 9, 2,13,20,22,10)( 5, 8, 6, 7)$
$ 5, 5, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $5322240$ $10$ $( 1,14,19,22,10)( 2,13,20,21, 9)( 5, 7)( 6, 8)$
$ 10, 4, 2, 2, 2, 2 $ $5322240$ $20$ $( 1,14,19,21, 9, 2,13,20,22,10)( 3, 4)( 5, 8, 6, 7)(11,12)(15,16)(17,18)$
$ 5, 5, 2, 2, 2, 2, 2, 2 $ $5322240$ $10$ $( 1,14,19,22,10)( 2,13,20,21, 9)( 3, 4)( 5, 7)( 6, 8)(11,12)(15,16)(17,18)$
$ 10, 6, 2, 2, 1, 1 $ $170311680$ $30$ $( 1,19,10,13,21, 2,20, 9,14,22)( 3,17,15, 4,18,16)( 5, 8)( 6, 7)$
$ 6, 5, 5, 4, 1, 1 $ $170311680$ $60$ $( 1,19,10,13,22)( 2,20, 9,14,21)( 3,17,15, 4,18,16)( 5, 7, 6, 8)$
$ 10, 3, 3, 2, 2, 2 $ $170311680$ $30$ $( 1,19,10,13,21, 2,20, 9,14,22)( 3,17,15)( 4,18,16)( 5, 8)( 6, 7)(11,12)$
$ 5, 5, 4, 3, 3, 2 $ $170311680$ $60$ $( 1,19,10,13,22)( 2,20, 9,14,21)( 3,17,15)( 4,18,16)( 5, 7, 6, 8)(11,12)$
$ 6, 5, 5, 2, 2, 2 $ $170311680$ $30$ $( 1,19,10,14,22)( 2,20, 9,13,21)( 3,17,15, 4,18,16)( 5, 8)( 6, 7)(11,12)$
$ 10, 6, 4, 2 $ $170311680$ $60$ $( 1,19,10,14,21, 2,20, 9,13,22)( 3,17,15, 4,18,16)( 5, 7, 6, 8)(11,12)$
$ 5, 5, 3, 3, 2, 2, 1, 1 $ $170311680$ $30$ $( 1,19,10,14,22)( 2,20, 9,13,21)( 3,17,15)( 4,18,16)( 5, 8)( 6, 7)$
$ 10, 4, 3, 3, 1, 1 $ $170311680$ $60$ $( 1,19,10,14,21, 2,20, 9,13,22)( 3,17,15)( 4,18,16)( 5, 7, 6, 8)$
$ 14, 4, 2, 2 $ $182476800$ $28$ $( 1,14, 2,13)( 3,16, 5,12, 7,21,10, 4,15, 6,11, 8,22, 9)(17,18)(19,20)$
$ 7, 7, 4, 2, 1, 1 $ $364953600$ $28$ $( 1,14, 2,13)( 3,16, 5,12, 7,22, 9)( 4,15, 6,11, 8,21,10)(17,18)$
$ 7, 7, 2, 2, 2, 2 $ $182476800$ $14$ $( 1,13)( 2,14)( 3,16, 5,11, 8,22, 9)( 4,15, 6,12, 7,21,10)(17,18)(19,20)$
$ 14, 2, 2, 2, 1, 1 $ $364953600$ $14$ $( 1,13)( 2,14)( 3,16, 5,11, 8,21,10, 4,15, 6,12, 7,22, 9)(17,18)$
$ 14, 4, 1, 1, 1, 1 $ $182476800$ $28$ $( 1,14, 2,13)( 3,16, 5,12, 7,21,10, 4,15, 6,11, 8,22, 9)$
$ 7, 7, 2, 2, 1, 1, 1, 1 $ $182476800$ $14$ $( 1,13)( 2,14)( 3,16, 5,11, 8,22, 9)( 4,15, 6,12, 7,21,10)$
$ 4, 4, 4, 3, 3, 2, 1, 1 $ $106444800$ $12$ $( 1,17,14)( 2,18,13)( 3,16,21,10)( 4,15,22, 9)( 5,20, 6,19)(11,12)$
$ 8, 3, 3, 2, 2, 2, 1, 1 $ $106444800$ $24$ $( 1,17,14)( 2,18,13)( 3,16,22, 9, 4,15,21,10)( 5,19)( 6,20)(11,12)$
$ 8, 4, 3, 3, 2, 2 $ $53222400$ $24$ $( 1,17,14)( 2,18,13)( 3,16,22, 9, 4,15,21,10)( 5,20, 6,19)( 7, 8)(11,12)$
$ 4, 4, 3, 3, 2, 2, 2, 2 $ $53222400$ $12$ $( 1,17,14)( 2,18,13)( 3,16,21,10)( 4,15,22, 9)( 5,19)( 6,20)( 7, 8)(11,12)$
$ 8, 4, 3, 3, 1, 1, 1, 1 $ $53222400$ $24$ $( 1,17,14)( 2,18,13)( 3,16,21,10, 4,15,22, 9)( 5,20, 6,19)$
$ 4, 4, 3, 3, 2, 2, 1, 1, 1, 1 $ $53222400$ $12$ $( 1,17,14)( 2,18,13)( 3,16,22, 9)( 4,15,21,10)( 5,19)( 6,20)$
$ 6, 4, 4, 4, 1, 1, 1, 1 $ $53222400$ $12$ $( 1,17,13, 2,18,14)( 3,16,21,10)( 4,15,22, 9)( 5,20, 6,19)$
$ 8, 6, 2, 2, 1, 1, 1, 1 $ $53222400$ $24$ $( 1,17,13, 2,18,14)( 3,16,22, 9, 4,15,21,10)( 5,19)( 6,20)$
$ 8, 6, 4, 2, 1, 1 $ $106444800$ $24$ $( 1,17,13, 2,18,14)( 3,16,22, 9, 4,15,21,10)( 5,20, 6,19)( 7, 8)$
$ 6, 4, 4, 2, 2, 2, 1, 1 $ $106444800$ $12$ $( 1,17,13, 2,18,14)( 3,16,21,10)( 4,15,22, 9)( 5,19)( 6,20)( 7, 8)$
$ 6, 4, 4, 4, 2, 2 $ $53222400$ $12$ $( 1,17,13, 2,18,14)( 3,16,22, 9)( 4,15,21,10)( 5,20, 6,19)( 7, 8)(11,12)$
$ 8, 6, 2, 2, 2, 2 $ $53222400$ $24$ $( 1,17,13, 2,18,14)( 3,16,21,10, 4,15,22, 9)( 5,19)( 6,20)( 7, 8)(11,12)$
$ 8, 6, 3, 3, 1, 1 $ $141926400$ $24$ $( 1,20,13,18, 2,19,14,17)( 3,15, 8, 4,16, 7)( 5,21,12)( 6,22,11)$
$ 6, 6, 4, 4, 1, 1 $ $70963200$ $12$ $( 1,19,14,17)( 2,20,13,18)( 3,15, 8, 4,16, 7)( 5,22,11, 6,21,12)$
$ 8, 6, 6, 2 $ $70963200$ $24$ $( 1,20,13,18, 2,19,14,17)( 3,15, 8, 4,16, 7)( 5,22,11, 6,21,12)( 9,10)$
$ 6, 4, 4, 3, 3, 2 $ $141926400$ $12$ $( 1,19,14,17)( 2,20,13,18)( 3,15, 8, 4,16, 7)( 5,21,12)( 6,22,11)( 9,10)$
$ 4, 4, 3, 3, 3, 3, 1, 1 $ $70963200$ $12$ $( 1,19,14,17)( 2,20,13,18)( 3,15, 7)( 4,16, 8)( 5,21,12)( 6,22,11)$
$ 8, 3, 3, 3, 3, 2 $ $70963200$ $24$ $( 1,20,13,18, 2,19,14,17)( 3,15, 7)( 4,16, 8)( 5,21,12)( 6,22,11)( 9,10)$
$ 6, 6, 2, 2, 2, 2, 1, 1 $ $17740800$ $6$ $( 3, 5,21, 4, 6,22)( 7,10,12, 8, 9,11)(13,14)(15,18)(16,17)(19,20)$
$ 6, 3, 3, 2, 2, 2, 1, 1, 1, 1 $ $35481600$ $6$ $( 3, 5,22)( 4, 6,21)( 7,10,12, 8, 9,11)(13,14)(15,18)(16,17)$
$ 3, 3, 3, 3, 2, 2, 2, 2, 1, 1 $ $17740800$ $6$ $( 3, 5,22)( 4, 6,21)( 7, 9,11)( 8,10,12)(13,14)(15,18)(16,17)(19,20)$
$ 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1 $ $5913600$ $6$ $( 3, 5,22)( 4, 6,21)( 7,10,11)( 8, 9,12)(15,18)(16,17)$
$ 6, 6, 2, 2, 1, 1, 1, 1, 1, 1 $ $5913600$ $6$ $( 3, 5,21, 4, 6,22)( 7, 9,12, 8,10,11)(15,18)(16,17)$
$ 6, 4, 3, 3, 2, 2, 1, 1 $ $35481600$ $12$ $( 3, 5,22)( 4, 6,21)( 7,10,12, 8, 9,11)(13,14)(15,18,16,17)(19,20)$
$ 6, 6, 4, 2, 1, 1, 1, 1 $ $17740800$ $12$ $( 3, 5,21, 4, 6,22)( 7,10,12, 8, 9,11)(13,14)(15,18,16,17)$
$ 4, 3, 3, 3, 3, 2, 1, 1, 1, 1 $ $17740800$ $12$ $( 3, 5,22)( 4, 6,21)( 7, 9,11)( 8,10,12)(13,14)(15,18,16,17)$
$ 6, 4, 3, 3, 1, 1, 1, 1, 1, 1 $ $11827200$ $12$ $( 3, 5,21, 4, 6,22)( 7,10,11)( 8, 9,12)(15,18,16,17)$
$ 6, 3, 3, 2, 2, 2, 2, 2 $ $11827200$ $6$ $( 1, 2)( 3, 5,22)( 4, 6,21)( 7,10,12, 8, 9,11)(13,14)(15,18)(16,17)(19,20)$
$ 6, 6, 4, 2, 2, 2 $ $5913600$ $12$ $( 1, 2)( 3, 5,21, 4, 6,22)( 7,10,12, 8, 9,11)(13,14)(15,18,16,17)(19,20)$
$ 4, 3, 3, 3, 3, 2, 2, 2 $ $5913600$ $12$ $( 1, 2)( 3, 5,22)( 4, 6,21)( 7, 9,11)( 8,10,12)(13,14)(15,18,16,17)(19,20)$
$ 12, 2, 2, 2, 2, 2 $ $106444800$ $12$ $( 1,17)( 2,18)( 3,12, 7,22,16, 6, 4,11, 8,21,15, 5)( 9,10)(13,19)(14,20)$
$ 6, 6, 4, 2, 2, 2 $ $212889600$ $12$ $( 1,17)( 2,18)( 3,12, 7,21,15, 5)( 4,11, 8,22,16, 6)( 9,10)(13,20,14,19)$
$ 6, 6, 2, 2, 2, 2, 1, 1 $ $106444800$ $6$ $( 1,17)( 2,18)( 3,12, 7,21,15, 5)( 4,11, 8,22,16, 6)(13,19)(14,20)$
$ 12, 4, 2, 2, 1, 1 $ $212889600$ $12$ $( 1,17)( 2,18)( 3,12, 7,22,16, 6, 4,11, 8,21,15, 5)(13,20,14,19)$
$ 12, 4, 4, 2 $ $106444800$ $12$ $( 1,17, 2,18)( 3,12, 7,22,16, 6, 4,11, 8,21,15, 5)( 9,10)(13,20,14,19)$
$ 6, 6, 4, 4, 1, 1 $ $106444800$ $12$ $( 1,17, 2,18)( 3,12, 7,21,15, 5)( 4,11, 8,22,16, 6)(13,20,14,19)$
$ 7, 7, 6, 2 $ $486604800$ $42$ $( 1, 2)( 3,20,10,16, 8,18,14)( 4,19, 9,15, 7,17,13)( 5,21,11, 6,22,12)$
$ 14, 3, 3, 2 $ $486604800$ $42$ $( 1, 2)( 3,19, 9,15, 7,17,13, 4,20,10,16, 8,18,14)( 5,22,12)( 6,21,11)$
$ 7, 7, 3, 3, 1, 1 $ $486604800$ $21$ $( 3,20,10,16, 8,18,14)( 4,19, 9,15, 7,17,13)( 5,22,12)( 6,21,11)$
$ 14, 6, 1, 1 $ $486604800$ $42$ $( 3,19, 9,15, 7,17,13, 4,20,10,16, 8,18,14)( 5,21,11, 6,22,12)$
$ 6, 6, 3, 3, 2, 2 $ $141926400$ $6$ $( 1, 6,17)( 2, 5,18)( 3,21,19,15, 9,14)( 4,22,20,16,10,13)( 7, 8)(11,12)$
$ 12, 3, 3, 2, 1, 1 $ $283852800$ $12$ $( 1, 6,17)( 2, 5,18)( 3,22,20,16,10,13, 4,21,19,15, 9,14)(11,12)$
$ 6, 6, 3, 3, 1, 1, 1, 1 $ $141926400$ $6$ $( 1, 6,17)( 2, 5,18)( 3,22,20,16,10,13)( 4,21,19,15, 9,14)$
$ 12, 6, 2, 2 $ $141926400$ $12$ $( 1, 5,18, 2, 6,17)( 3,22,20,16,10,13, 4,21,19,15, 9,14)( 7, 8)(11,12)$
$ 6, 6, 6, 2, 1, 1 $ $283852800$ $6$ $( 1, 5,18, 2, 6,17)( 3,21,19,15, 9,14)( 4,22,20,16,10,13)(11,12)$
$ 12, 6, 1, 1, 1, 1 $ $141926400$ $12$ $( 1, 5,18, 2, 6,17)( 3,21,19,15, 9,14, 4,22,20,16,10,13)$
$ 18, 2, 1, 1 $ $1135411200$ $18$ $( 1,14,21, 4,17, 9, 6,20,16, 2,13,22, 3,18,10, 5,19,15)(11,12)$
$ 9, 9, 2, 2 $ $567705600$ $18$ $( 1,14,22, 3,18,10, 5,19,15)( 2,13,21, 4,17, 9, 6,20,16)( 7, 8)(11,12)$
$ 9, 9, 1, 1, 1, 1 $ $567705600$ $9$ $( 1,14,21, 3,18,10, 5,19,15)( 2,13,22, 4,17, 9, 6,20,16)$
$ 9, 9, 2, 2 $ $1135411200$ $18$ $( 1,10,14, 6,22,20, 3,16,17)( 2, 9,13, 5,21,19, 4,15,18)( 7,12)( 8,11)$
$ 18, 4 $ $1135411200$ $36$ $( 1,10,14, 6,21,19, 4,15,18, 2, 9,13, 5,22,20, 3,16,17)( 7,12, 8,11)$
$ 6, 4, 4, 4, 2, 2 $ $106444800$ $12$ $( 1,17, 2,18)( 3, 6, 9,19)( 4, 5,10,20)( 7,11)( 8,12)(13,15,22,14,16,21)$
$ 8, 4, 3, 3, 2, 2 $ $106444800$ $24$ $( 1,17, 2,18)( 3, 6, 9,20, 4, 5,10,19)( 7,11)( 8,12)(13,15,21)(14,16,22)$
$ 4, 4, 4, 4, 3, 3 $ $53222400$ $12$ $( 1,17, 2,18)( 3, 6, 9,19)( 4, 5,10,20)( 7,11, 8,12)(13,15,21)(14,16,22)$
$ 8, 6, 4, 4 $ $53222400$ $24$ $( 1,17, 2,18)( 3, 6, 9,20, 4, 5,10,19)( 7,11, 8,12)(13,15,22,14,16,21)$
$ 4, 4, 3, 3, 2, 2, 2, 2 $ $53222400$ $12$ $( 1,17)( 2,18)( 3, 6, 9,19)( 4, 5,10,20)( 7,11)( 8,12)(13,15,21)(14,16,22)$
$ 8, 6, 2, 2, 2, 2 $ $53222400$ $24$ $( 1,17)( 2,18)( 3, 6, 9,20, 4, 5,10,19)( 7,11)( 8,12)(13,15,22,14,16,21)$
$ 11, 11 $ $3715891200$ $11$ $( 1, 5,11,13,19,22,18,16, 3,10, 7)( 2, 6,12,14,20,21,17,15, 4, 9, 8)$

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:  
Group too large