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

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