C3^4:5C6 - GroupNames

G = C₃⁴⋊₅C₆ order 486 = 2·3⁵

5^th semidirect product of C₃⁴ and C₆ acting faithfully

Aliases: C₃⁴⋊₅C₆, C₃≀C₃⋊₄S₃, C₃⋊(C₃³⋊C₆), He₃⋊₁(C₃⋊S₃), (C₃×He₃)⋊₁₀S₃, C₃³⋊₁₂(C₃×S₃), C₃⁴⋊C₂⋊₂C₃, C₃.₆(He₃⋊₄S₃), C₃².₁₇(C₃²⋊C₆), (C₃×C₃≀C₃)⋊₇C₂, C₃².₁₆(C₃×C₃⋊S₃), SmallGroup(486,167)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series

C₁ — C₃⁴ — C₃⁴⋊₅C₆

Chief series

C₁ — C₃ — C₃² — C₃³ — C₃⁴ — C₃×C₃≀C₃ — C₃⁴⋊₅C₆

Lower central

C₃⁴ — C₃⁴⋊₅C₆

Upper central

C₁

Generators and relations for C₃⁴⋊₅C₆
G = < a,b,c,d,e | a³=b³=c³=d³=e⁶=1, ab=ba, ac=ca, ad=da, eae^-1=a^-1c^-1, bc=cb, bd=db, ebe^-1=b^-1, cd=dc, ece^-1=c^-1d^-1, ede^-1=d^-1 >

Subgroups: 3032 in 204 conjugacy classes, 22 normal (11 characteristic)
C₁, C₂, C₃, C₃, C₃, S₃, C₆, C₉, C₃², C₃², C₃², C₃×S₃, C₃⋊S₃, C₃×C₉, He₃, He₃, 3_-¹⁺², C₃³, C₃³, C₃³, C₃²⋊C₆, C₃×C₃⋊S₃, C₃³⋊C₂, C₃≀C₃, C₃≀C₃, C₃×He₃, C₃×3_-¹⁺², C₃⁴, C₃³⋊C₆, He₃⋊₄S₃, C₃⁴⋊C₂, C₃×C₃≀C₃, C₃⁴⋊₅C₆
Quotients: C₁, C₂, C₃, S₃, C₆, C₃×S₃, C₃⋊S₃, C₃²⋊C₆, C₃×C₃⋊S₃, C₃³⋊C₆, He₃⋊₄S₃, C₃⁴⋊₅C₆

Character table of C₃⁴⋊₅C₆

class	1	2	3A	3B	3C	3D	3E	3F	3G	3H	3I	3J	3K	3L	3M	3N	3O	3P	3Q	3R	3S	3T	6A	6B	9A	9B	9C	9D	9E	9F
size	1	81	2	2	2	2	6	6	6	6	6	6	6	6	6	6	6	6	9	9	18	18	81	81	18	18	18	18	18	18
ρ₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	trivial
ρ₂	1	-1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	1	1	1	1	1	1	linear of order 2
ρ₃	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	ζ₃	ζ₃²	ζ₃	ζ₃²	ζ₃	ζ₃²	ζ₃	ζ₃	ζ₃	ζ₃²	ζ₃²	ζ₃²	linear of order 3
ρ₄	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	ζ₃²	ζ₃	ζ₃²	ζ₃	ζ₃²	ζ₃	ζ₃²	ζ₃²	ζ₃²	ζ₃	ζ₃	ζ₃	linear of order 3
ρ₅	1	-1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	ζ₃²	ζ₃	ζ₃²	ζ₃	ζ₆	ζ₆⁵	ζ₃²	ζ₃²	ζ₃²	ζ₃	ζ₃	ζ₃	linear of order 6
ρ₆	1	-1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	ζ₃	ζ₃²	ζ₃	ζ₃²	ζ₆⁵	ζ₆	ζ₃	ζ₃	ζ₃	ζ₃²	ζ₃²	ζ₃²	linear of order 6
ρ₇	2	0	2	2	2	2	-1	2	-1	-1	-1	-1	-1	-1	-1	2	-1	2	2	2	2	2	0	0	-1	-1	-1	-1	-1	-1	orthogonal lifted from S₃
ρ₈	2	0	-1	-1	-1	2	-1	-1	-1	-1	-1	2	2	2	-1	2	-1	-1	2	2	-1	-1	0	0	-1	2	-1	-1	-1	2	orthogonal lifted from S₃
ρ₉	2	0	-1	-1	-1	2	2	-1	-1	-1	-1	-1	-1	-1	2	2	2	-1	2	2	-1	-1	0	0	-1	-1	2	2	-1	-1	orthogonal lifted from S₃
ρ₁₀	2	0	-1	-1	-1	2	-1	-1	2	2	2	-1	-1	-1	-1	2	-1	-1	2	2	-1	-1	0	0	2	-1	-1	-1	2	-1	orthogonal lifted from S₃
ρ₁₁	2	0	-1	-1	-1	2	-1	-1	2	2	2	-1	-1	-1	-1	2	-1	-1	-1-√-3	-1+√-3	ζ₆	ζ₆⁵	0	0	-1-√-3	ζ₆	ζ₆	ζ₆⁵	-1+√-3	ζ₆⁵	complex lifted from C₃×S₃
ρ₁₂	2	0	-1	-1	-1	2	2	-1	-1	-1	-1	-1	-1	-1	2	2	2	-1	-1+√-3	-1-√-3	ζ₆⁵	ζ₆	0	0	ζ₆⁵	ζ₆⁵	-1+√-3	-1-√-3	ζ₆	ζ₆	complex lifted from C₃×S₃
ρ₁₃	2	0	2	2	2	2	-1	2	-1	-1	-1	-1	-1	-1	-1	2	-1	2	-1-√-3	-1+√-3	-1-√-3	-1+√-3	0	0	ζ₆	ζ₆	ζ₆	ζ₆⁵	ζ₆⁵	ζ₆⁵	complex lifted from C₃×S₃
ρ₁₄	2	0	-1	-1	-1	2	2	-1	-1	-1	-1	-1	-1	-1	2	2	2	-1	-1-√-3	-1+√-3	ζ₆	ζ₆⁵	0	0	ζ₆	ζ₆	-1-√-3	-1+√-3	ζ₆⁵	ζ₆⁵	complex lifted from C₃×S₃
ρ₁₅	2	0	-1	-1	-1	2	-1	-1	2	2	2	-1	-1	-1	-1	2	-1	-1	-1+√-3	-1-√-3	ζ₆⁵	ζ₆	0	0	-1+√-3	ζ₆⁵	ζ₆⁵	ζ₆	-1-√-3	ζ₆	complex lifted from C₃×S₃
ρ₁₆	2	0	-1	-1	-1	2	-1	-1	-1	-1	-1	2	2	2	-1	2	-1	-1	-1-√-3	-1+√-3	ζ₆	ζ₆⁵	0	0	ζ₆	-1-√-3	ζ₆	ζ₆⁵	ζ₆⁵	-1+√-3	complex lifted from C₃×S₃
ρ₁₇	2	0	-1	-1	-1	2	-1	-1	-1	-1	-1	2	2	2	-1	2	-1	-1	-1+√-3	-1-√-3	ζ₆⁵	ζ₆	0	0	ζ₆⁵	-1+√-3	ζ₆⁵	ζ₆	ζ₆	-1-√-3	complex lifted from C₃×S₃
ρ₁₈	2	0	2	2	2	2	-1	2	-1	-1	-1	-1	-1	-1	-1	2	-1	2	-1+√-3	-1-√-3	-1+√-3	-1-√-3	0	0	ζ₆⁵	ζ₆⁵	ζ₆⁵	ζ₆	ζ₆	ζ₆	complex lifted from C₃×S₃
ρ₁₉	6	0	6	6	6	6	0	-3	0	0	0	0	0	0	0	-3	0	-3	0	0	0	0	0	0	0	0	0	0	0	0	orthogonal lifted from C₃²⋊C₆
ρ₂₀	6	0	-3	6	-3	-3	3	0	-3	0	3	3	-3	0	0	0	-3	0	0	0	0	0	0	0	0	0	0	0	0	0	orthogonal lifted from C₃³⋊C₆
ρ₂₁	6	0	6	-3	-3	-3	0	0	-3	0	3	-3	0	3	-3	0	3	0	0	0	0	0	0	0	0	0	0	0	0	0	orthogonal lifted from C₃³⋊C₆
ρ₂₂	6	0	-3	-3	-3	6	0	6	0	0	0	0	0	0	0	-3	0	-3	0	0	0	0	0	0	0	0	0	0	0	0	orthogonal lifted from C₃²⋊C₆
ρ₂₃	6	0	-3	-3	6	-3	3	0	3	-3	0	-3	0	3	0	0	-3	0	0	0	0	0	0	0	0	0	0	0	0	0	orthogonal lifted from C₃³⋊C₆
ρ₂₄	6	0	-3	-3	6	-3	0	0	0	3	-3	3	-3	0	-3	0	3	0	0	0	0	0	0	0	0	0	0	0	0	0	orthogonal lifted from C₃³⋊C₆
ρ₂₅	6	0	-3	-3	-3	6	0	-3	0	0	0	0	0	0	0	-3	0	6	0	0	0	0	0	0	0	0	0	0	0	0	orthogonal lifted from C₃²⋊C₆
ρ₂₆	6	0	-3	6	-3	-3	0	0	3	-3	0	0	3	-3	-3	0	3	0	0	0	0	0	0	0	0	0	0	0	0	0	orthogonal lifted from C₃³⋊C₆
ρ₂₇	6	0	-3	-3	6	-3	-3	0	-3	0	3	0	3	-3	3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	orthogonal lifted from C₃³⋊C₆
ρ₂₈	6	0	-3	6	-3	-3	-3	0	0	3	-3	-3	0	3	3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	orthogonal lifted from C₃³⋊C₆
ρ₂₉	6	0	6	-3	-3	-3	3	0	0	3	-3	0	3	-3	0	0	-3	0	0	0	0	0	0	0	0	0	0	0	0	0	orthogonal lifted from C₃³⋊C₆
ρ₃₀	6	0	6	-3	-3	-3	-3	0	3	-3	0	3	-3	0	3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	orthogonal lifted from C₃³⋊C₆

Permutation representations of C₃⁴⋊₅C₆
►On 27 points - transitive group 27T202

Generators in S₂₇

(1 7 4)(10 26 21)(13 18 23)

(1 21 18)(2 19 16)(3 17 20)(4 26 13)(5 14 27)(6 22 15)(7 10 23)(8 24 11)(9 12 25)

(1 4 7)(3 9 6)(10 21 26)(12 22 17)(13 23 18)(15 20 25)

(1 7 4)(2 5 8)(3 9 6)(10 26 21)(11 16 27)(12 22 17)(13 18 23)(14 24 19)(15 20 25)

(1 2 3)(4 5 6 7 8 9)(10 11 12 13 14 15)(16 17 18 19 20 21)(22 23 24 25 26 27)

G:=sub<Sym(27)| (1,7,4)(10,26,21)(13,18,23), (1,21,18)(2,19,16)(3,17,20)(4,26,13)(5,14,27)(6,22,15)(7,10,23)(8,24,11)(9,12,25), (1,4,7)(3,9,6)(10,21,26)(12,22,17)(13,23,18)(15,20,25), (1,7,4)(2,5,8)(3,9,6)(10,26,21)(11,16,27)(12,22,17)(13,18,23)(14,24,19)(15,20,25), (1,2,3)(4,5,6,7,8,9)(10,11,12,13,14,15)(16,17,18,19,20,21)(22,23,24,25,26,27)>;

G:=Group( (1,7,4)(10,26,21)(13,18,23), (1,21,18)(2,19,16)(3,17,20)(4,26,13)(5,14,27)(6,22,15)(7,10,23)(8,24,11)(9,12,25), (1,4,7)(3,9,6)(10,21,26)(12,22,17)(13,23,18)(15,20,25), (1,7,4)(2,5,8)(3,9,6)(10,26,21)(11,16,27)(12,22,17)(13,18,23)(14,24,19)(15,20,25), (1,2,3)(4,5,6,7,8,9)(10,11,12,13,14,15)(16,17,18,19,20,21)(22,23,24,25,26,27) );

G=PermutationGroup([[(1,7,4),(10,26,21),(13,18,23)], [(1,21,18),(2,19,16),(3,17,20),(4,26,13),(5,14,27),(6,22,15),(7,10,23),(8,24,11),(9,12,25)], [(1,4,7),(3,9,6),(10,21,26),(12,22,17),(13,23,18),(15,20,25)], [(1,7,4),(2,5,8),(3,9,6),(10,26,21),(11,16,27),(12,22,17),(13,18,23),(14,24,19),(15,20,25)], [(1,2,3),(4,5,6,7,8,9),(10,11,12,13,14,15),(16,17,18,19,20,21),(22,23,24,25,26,27)]])

G:=TransitiveGroup(27,202);

►On 27 points - transitive group 27T205

Generators in S₂₇

(1 26 23)(2 7 4)(3 13 10)(5 22 16)(6 11 20)(8 19 25)(9 17 14)(12 18 27)(15 24 21)

(1 11 14)(2 15 12)(3 13 10)(4 21 27)(5 22 16)(6 17 23)(7 24 18)(8 19 25)(9 26 20)

(1 14 11)(2 21 18)(3 5 8)(4 24 12)(6 23 17)(7 15 27)(9 20 26)(10 16 25)(13 22 19)

(1 23 26)(2 27 24)(3 25 22)(4 18 15)(5 10 19)(6 20 11)(7 12 21)(8 16 13)(9 14 17)

(1 2 3)(4 5 6 7 8 9)(10 11 12 13 14 15)(16 17 18 19 20 21)(22 23 24 25 26 27)

G:=sub<Sym(27)| (1,26,23)(2,7,4)(3,13,10)(5,22,16)(6,11,20)(8,19,25)(9,17,14)(12,18,27)(15,24,21), (1,11,14)(2,15,12)(3,13,10)(4,21,27)(5,22,16)(6,17,23)(7,24,18)(8,19,25)(9,26,20), (1,14,11)(2,21,18)(3,5,8)(4,24,12)(6,23,17)(7,15,27)(9,20,26)(10,16,25)(13,22,19), (1,23,26)(2,27,24)(3,25,22)(4,18,15)(5,10,19)(6,20,11)(7,12,21)(8,16,13)(9,14,17), (1,2,3)(4,5,6,7,8,9)(10,11,12,13,14,15)(16,17,18,19,20,21)(22,23,24,25,26,27)>;

G:=Group( (1,26,23)(2,7,4)(3,13,10)(5,22,16)(6,11,20)(8,19,25)(9,17,14)(12,18,27)(15,24,21), (1,11,14)(2,15,12)(3,13,10)(4,21,27)(5,22,16)(6,17,23)(7,24,18)(8,19,25)(9,26,20), (1,14,11)(2,21,18)(3,5,8)(4,24,12)(6,23,17)(7,15,27)(9,20,26)(10,16,25)(13,22,19), (1,23,26)(2,27,24)(3,25,22)(4,18,15)(5,10,19)(6,20,11)(7,12,21)(8,16,13)(9,14,17), (1,2,3)(4,5,6,7,8,9)(10,11,12,13,14,15)(16,17,18,19,20,21)(22,23,24,25,26,27) );

G=PermutationGroup([[(1,26,23),(2,7,4),(3,13,10),(5,22,16),(6,11,20),(8,19,25),(9,17,14),(12,18,27),(15,24,21)], [(1,11,14),(2,15,12),(3,13,10),(4,21,27),(5,22,16),(6,17,23),(7,24,18),(8,19,25),(9,26,20)], [(1,14,11),(2,21,18),(3,5,8),(4,24,12),(6,23,17),(7,15,27),(9,20,26),(10,16,25),(13,22,19)], [(1,23,26),(2,27,24),(3,25,22),(4,18,15),(5,10,19),(6,20,11),(7,12,21),(8,16,13),(9,14,17)], [(1,2,3),(4,5,6,7,8,9),(10,11,12,13,14,15),(16,17,18,19,20,21),(22,23,24,25,26,27)]])

G:=TransitiveGroup(27,205);

Matrix representation of C₃⁴⋊₅C₆ ►in GL₈(𝔽₁₉)

1	0	0	0	0	0	0	0
0	1	0	0	0	0	0	0
0	0	0	18	0	0	0	0
0	0	1	18	0	0	0	0
0	0	0	12	0	1	0	0
0	0	7	0	18	18	0	0
0	0	0	8	0	0	0	1
0	0	11	0	0	0	18	18

18	18	0	0	0	0	0	0
1	0	0	0	0	0	0	0
0	0	18	1	0	0	0	0
0	0	18	0	0	0	0	0
0	0	12	0	0	1	0	0
0	0	0	7	18	18	0	0
0	0	8	0	0	0	0	1
0	0	0	11	0	0	18	18

1	0	0	0	0	0	0	0
0	1	0	0	0	0	0	0
0	0	0	18	0	0	0	0
0	0	1	18	0	0	0	0
0	0	0	12	1	0	0	0
0	0	0	12	0	1	0	0
0	0	0	8	0	0	0	1
0	0	11	0	0	0	18	18

1	0	0	0	0	0	0	0
0	1	0	0	0	0	0	0
0	0	18	1	0	0	0	0
0	0	18	0	0	0	0	0
0	0	12	0	0	1	0	0
0	0	0	7	18	18	0	0
0	0	8	0	0	0	0	1
0	0	0	11	0	0	18	18

11	0	0	0	0	0	0	0
8	8	0	0	0	0	0	0
0	0	0	0	0	0	1	18
0	0	11	11	0	0	18	17
0	0	1	0	0	0	0	12
0	0	0	0	0	0	0	12
0	0	0	0	0	1	0	8
0	0	0	0	1	0	0	8

G:=sub<GL(8,GF(19))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,7,0,11,0,0,18,18,12,0,8,0,0,0,0,0,0,18,0,0,0,0,0,0,1,18,0,0,0,0,0,0,0,0,0,18,0,0,0,0,0,0,1,18],[18,1,0,0,0,0,0,0,18,0,0,0,0,0,0,0,0,0,18,18,12,0,8,0,0,0,1,0,0,7,0,11,0,0,0,0,0,18,0,0,0,0,0,0,1,18,0,0,0,0,0,0,0,0,0,18,0,0,0,0,0,0,1,18],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,11,0,0,18,18,12,12,8,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,18,0,0,0,0,0,0,1,18],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,18,18,12,0,8,0,0,0,1,0,0,7,0,11,0,0,0,0,0,18,0,0,0,0,0,0,1,18,0,0,0,0,0,0,0,0,0,18,0,0,0,0,0,0,1,18],[11,8,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,11,1,0,0,0,0,0,0,11,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,18,0,0,0,0,0,0,18,17,12,12,8,8] >;

C₃⁴⋊₅C₆ in GAP, Magma, Sage, TeX

C_3^4\rtimes_5C_6

% in TeX

G:=Group("C3^4:5C6");

// GroupNames label

G:=SmallGroup(486,167);

// by ID

G=gap.SmallGroup(486,167);

# by ID

G:=PCGroup([6,-2,-3,-3,-3,-3,-3,218,548,867,3244,3250,11669]);

// Polycyclic

G:=Group<a,b,c,d,e|a^3=b^3=c^3=d^3=e^6=1,a*b=b*a,a*c=c*a,a*d=d*a,e*a*e^-1=a^-1*c^-1,b*c=c*b,b*d=d*b,e*b*e^-1=b^-1,c*d=d*c,e*c*e^-1=c^-1*d^-1,e*d*e^-1=d^-1>;

// generators/relations

Export

Character table of C₃⁴⋊₅C₆ in TeX

1	0	0	0	0	0	0	0
0	1	0	0	0	0	0	0
0	0	0	18	0	0	0	0
0	0	1	18	0	0	0	0
0	0	0	12	0	1	0	0
0	0	7	0	18	18	0	0
0	0	0	8	0	0	0	1
0	0	11	0	0	0	18	18

18	18	0	0	0	0	0	0
1	0	0	0	0	0	0	0
0	0	18	1	0	0	0	0
0	0	18	0	0	0	0	0
0	0	12	0	0	1	0	0
0	0	0	7	18	18	0	0
0	0	8	0	0	0	0	1
0	0	0	11	0	0	18	18

1	0	0	0	0	0	0	0
0	1	0	0	0	0	0	0
0	0	0	18	0	0	0	0
0	0	1	18	0	0	0	0
0	0	0	12	1	0	0	0
0	0	0	12	0	1	0	0
0	0	0	8	0	0	0	1
0	0	11	0	0	0	18	18

1	0	0	0	0	0	0	0
0	1	0	0	0	0	0	0
0	0	18	1	0	0	0	0
0	0	18	0	0	0	0	0
0	0	12	0	0	1	0	0
0	0	0	7	18	18	0	0
0	0	8	0	0	0	0	1
0	0	0	11	0	0	18	18

11	0	0	0	0	0	0	0
8	8	0	0	0	0	0	0
0	0	0	0	0	0	1	18
0	0	11	11	0	0	18	17
0	0	1	0	0	0	0	12
0	0	0	0	0	0	0	12
0	0	0	0	0	1	0	8
0	0	0	0	1	0	0	8

1	0	0	0	0	0	0	0
0	1	0	0	0	0	0	0
0	0	0	18	0	0	0	0
0	0	1	18	0	0	0	0
0	0	0	12	0	1	0	0
0	0	7	0	18	18	0	0
0	0	0	8	0	0	0	1
0	0	11	0	0	0	18	18

18	18	0	0	0	0	0	0
1	0	0	0	0	0	0	0
0	0	18	1	0	0	0	0
0	0	18	0	0	0	0	0
0	0	12	0	0	1	0	0
0	0	0	7	18	18	0	0
0	0	8	0	0	0	0	1
0	0	0	11	0	0	18	18

1	0	0	0	0	0	0	0
0	1	0	0	0	0	0	0
0	0	0	18	0	0	0	0
0	0	1	18	0	0	0	0
0	0	0	12	1	0	0	0
0	0	0	12	0	1	0	0
0	0	0	8	0	0	0	1
0	0	11	0	0	0	18	18

1	0	0	0	0	0	0	0
0	1	0	0	0	0	0	0
0	0	18	1	0	0	0	0
0	0	18	0	0	0	0	0
0	0	12	0	0	1	0	0
0	0	0	7	18	18	0	0
0	0	8	0	0	0	0	1
0	0	0	11	0	0	18	18

11	0	0	0	0	0	0	0
8	8	0	0	0	0	0	0
0	0	0	0	0	0	1	18
0	0	11	11	0	0	18	17
0	0	1	0	0	0	0	12
0	0	0	0	0	0	0	12
0	0	0	0	0	1	0	8
0	0	0	0	1	0	0	8

G = C34⋊5C6 order 486 = 2·35

5th semidirect product of C34 and C6 acting faithfully

G = C₃⁴⋊₅C₆ order 486 = 2·3⁵

5^th semidirect product of C₃⁴ and C₆ acting faithfully

1	0	0	0	0	0	0	0
0	1	0	0	0	0	0	0
0	0	0	18	0	0	0	0
0	0	1	18	0	0	0	0
0	0	0	12	0	1	0	0
0	0	7	0	18	18	0	0
0	0	0	8	0	0	0	1
0	0	11	0	0	0	18	18

18	18	0	0	0	0	0	0
1	0	0	0	0	0	0	0
0	0	18	1	0	0	0	0
0	0	18	0	0	0	0	0
0	0	12	0	0	1	0	0
0	0	0	7	18	18	0	0
0	0	8	0	0	0	0	1
0	0	0	11	0	0	18	18

1	0	0	0	0	0	0	0
0	1	0	0	0	0	0	0
0	0	0	18	0	0	0	0
0	0	1	18	0	0	0	0
0	0	0	12	1	0	0	0
0	0	0	12	0	1	0	0
0	0	0	8	0	0	0	1
0	0	11	0	0	0	18	18

1	0	0	0	0	0	0	0
0	1	0	0	0	0	0	0
0	0	18	1	0	0	0	0
0	0	18	0	0	0	0	0
0	0	12	0	0	1	0	0
0	0	0	7	18	18	0	0
0	0	8	0	0	0	0	1
0	0	0	11	0	0	18	18

11	0	0	0	0	0	0	0
8	8	0	0	0	0	0	0
0	0	0	0	0	0	1	18
0	0	11	11	0	0	18	17
0	0	1	0	0	0	0	12
0	0	0	0	0	0	0	12
0	0	0	0	0	1	0	8
0	0	0	0	1	0	0	8