# Properties

 Label 22T53 Order $$81749606400$$ n $$22$$ Cyclic No Abelian No Solvable No Primitive No $p$-group No

# Related objects

## Group action invariants

Degree $n$ :  $22$
Transitive number $t$ :  $53$
CHM label :  $t22n53$
Parity:  $-1$
Primitive:  No
Generators:   ( 1, 9, 5,13,22,18,15,12, 8,20, 2,10, 6,14,21,17,16,11, 7,19), ( 1,14,21,10)( 2,13,22, 9)( 3, 5,17)( 4, 6,18)( 7,12,15, 8,11,16)(19,20)
$|\Aut(F/K)|$:  $2$
Low degree resolvents:
 2: 2T1, 2T1, 2T1 4: 4T2 39916800: 11T8 79833600: 22T47 40874803200: 22T50

## Subfields

Degree 2: None

Degree 11: $S_{11}$

## Low degree siblings

22T53b
A number field with this Galois group has no arithmetically equivalent fields.

## Conjugacy Classes

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

## Group invariants

 Order: $81749606400=2^{19} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$ Cyclic: No Abelian: No Solvable: No GAP id: Data not available
 Character table: Group too large