C4^2.180D10 - GroupNames

G = C₄².₁₈₀D₁₀ order 320 = 2⁶·5

180^th non-split extension by C₄² of D₁₀ acting via D₁₀/C₅=C₂²

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C₄².₁₈₀D₁₀, C₁₀.₈₆2₊¹⁺⁴, C₁₀.₄₁2_-¹⁺⁴, C₄⋊Q₈⋊₁₈D₅, C₄⋊C₄.₁₂₇D₁₀, (C₂×Q₈).₉₀D₁₀, D₁₀⋊Q₈⋊₄₉C₂, D₁₀⋊₃Q₈⋊₃₉C₂, C₄²⋊₂D₅⋊₂₀C₂, Dic₅⋊Q₈⋊₂₈C₂, (C₂×C₂₀).₆₄₁C₂³, (C₄×C₂₀).₂₇₄C₂², (C₂×C₁₀).₂₇₉C₂⁴, C₂.₉₀(D₄⋊₆D₁₀), Dic₅.Q₈⋊₄₃C₂, D₁₀.₁₃D₄.₅C₂, C₂₀.₂₃D₄.₁₁C₂, (C₂×D₂₀).₁₈₀C₂², C₄⋊Dic₅.₂₅₆C₂², (Q₈×C₁₀).₁₄₆C₂², C₂².₃₀₀(C₂³×D₅), D₁₀⋊C₄.₇₆C₂², C₅⋊₆(C₂².₅₇C₂⁴), (C₄×Dic₅).₁₇₆C₂², (C₂×Dic₅).₁₄₇C₂³, C₁₀.D₄.₈₈C₂², (C₂²×D₅).₁₂₄C₂³, C₂.₄₂(Q₈.₁₀D₁₀), (C₂×Dic₁₀).₁₉₉C₂², (C₅×C₄⋊Q₈)⋊₂₁C₂, C₄⋊C₄⋊D₅⋊₄₈C₂, (C₂×C₄×D₅).₁₆₁C₂², (C₅×C₄⋊C₄).₂₂₂C₂², (C₂×C₄).₂₂₂(C₂²×D₅), SmallGroup(320,1407)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series

C₁ — C₂×C₁₀ — C₄².₁₈₀D₁₀

Chief series

C₁ — C₅ — C₁₀ — C₂×C₁₀ — C₂²×D₅ — C₂×C₄×D₅ — D₁₀⋊₃Q₈ — C₄².₁₈₀D₁₀

Lower central

C₅ — C₂×C₁₀ — C₄².₁₈₀D₁₀

Upper central

C₁ — C₂² — C₄⋊Q₈

Generators and relations for C₄².₁₈₀D₁₀
G = < a,b,c,d | a⁴=b⁴=1, c¹⁰=d²=a², ab=ba, cac^-1=a^-1, dad^-1=a^-1b², cbc^-1=b^-1, dbd^-1=a²b, dcd^-1=c⁹ >

Subgroups: 678 in 196 conjugacy classes, 91 normal (27 characteristic)
C₁, C₂, C₂, C₂, C₄, C₂², C₂², C₅, C₂×C₄, C₂×C₄, C₂×C₄, D₄, Q₈, C₂³, D₅, C₁₀, C₁₀, C₄², C₄², C₂²⋊C₄, C₄⋊C₄, C₄⋊C₄, C₂²×C₄, C₂×D₄, C₂×Q₈, C₂×Q₈, Dic₅, C₂₀, D₁₀, C₂×C₁₀, C₂²⋊Q₈, C₂².D₄, C₄.₄D₄, C₄².C₂, C₄²⋊₂C₂, C₄⋊Q₈, C₄⋊Q₈, Dic₁₀, C₄×D₅, D₂₀, C₂×Dic₅, C₂×C₂₀, C₂×C₂₀, C₅×Q₈, C₂²×D₅, C₂².₅₇C₂⁴, C₄×Dic₅, C₁₀.D₄, C₄⋊Dic₅, D₁₀⋊C₄, C₄×C₂₀, C₅×C₄⋊C₄, C₂×Dic₁₀, C₂×C₄×D₅, C₂×D₂₀, Q₈×C₁₀, C₄²⋊₂D₅, Dic₅.Q₈, D₁₀.₁₃D₄, D₁₀⋊Q₈, C₄⋊C₄⋊D₅, Dic₅⋊Q₈, D₁₀⋊₃Q₈, C₂₀.₂₃D₄, C₅×C₄⋊Q₈, C₄².₁₈₀D₁₀
Quotients: C₁, C₂, C₂², C₂³, D₅, C₂⁴, D₁₀, 2₊¹⁺⁴, 2_-¹⁺⁴, C₂²×D₅, C₂².₅₇C₂⁴, C₂³×D₅, D₄⋊₆D₁₀, Q₈.₁₀D₁₀, C₄².₁₈₀D₁₀

Smallest permutation representation of C₄².₁₈₀D₁₀
►On 160 points

Generators in S₁₆₀

(1 96 11 86)(2 87 12 97)(3 98 13 88)(4 89 14 99)(5 100 15 90)(6 91 16 81)(7 82 17 92)(8 93 18 83)(9 84 19 94)(10 95 20 85)(21 125 31 135)(22 136 32 126)(23 127 33 137)(24 138 34 128)(25 129 35 139)(26 140 36 130)(27 131 37 121)(28 122 38 132)(29 133 39 123)(30 124 40 134)(41 79 51 69)(42 70 52 80)(43 61 53 71)(44 72 54 62)(45 63 55 73)(46 74 56 64)(47 65 57 75)(48 76 58 66)(49 67 59 77)(50 78 60 68)(101 159 111 149)(102 150 112 160)(103 141 113 151)(104 152 114 142)(105 143 115 153)(106 154 116 144)(107 145 117 155)(108 156 118 146)(109 147 119 157)(110 158 120 148)

(1 27 70 160)(2 141 71 28)(3 29 72 142)(4 143 73 30)(5 31 74 144)(6 145 75 32)(7 33 76 146)(8 147 77 34)(9 35 78 148)(10 149 79 36)(11 37 80 150)(12 151 61 38)(13 39 62 152)(14 153 63 40)(15 21 64 154)(16 155 65 22)(17 23 66 156)(18 157 67 24)(19 25 68 158)(20 159 69 26)(41 140 85 111)(42 112 86 121)(43 122 87 113)(44 114 88 123)(45 124 89 115)(46 116 90 125)(47 126 91 117)(48 118 92 127)(49 128 93 119)(50 120 94 129)(51 130 95 101)(52 102 96 131)(53 132 97 103)(54 104 98 133)(55 134 99 105)(56 106 100 135)(57 136 81 107)(58 108 82 137)(59 138 83 109)(60 110 84 139)

(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 28 29 30 31 32 33 34 35 36 37 38 39 40)(41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60)(61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80)(81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100)(101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120)(121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140)(141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160)

(1 10 11 20)(2 19 12 9)(3 8 13 18)(4 17 14 7)(5 6 15 16)(21 145 31 155)(22 154 32 144)(23 143 33 153)(24 152 34 142)(25 141 35 151)(26 150 36 160)(27 159 37 149)(28 148 38 158)(29 157 39 147)(30 146 40 156)(41 86 51 96)(42 95 52 85)(43 84 53 94)(44 93 54 83)(45 82 55 92)(46 91 56 81)(47 100 57 90)(48 89 58 99)(49 98 59 88)(50 87 60 97)(61 78 71 68)(62 67 72 77)(63 76 73 66)(64 65 74 75)(69 70 79 80)(101 112 111 102)(103 110 113 120)(104 119 114 109)(105 108 115 118)(106 117 116 107)(121 140 131 130)(122 129 132 139)(123 138 133 128)(124 127 134 137)(125 136 135 126)

G:=sub<Sym(160)| (1,96,11,86)(2,87,12,97)(3,98,13,88)(4,89,14,99)(5,100,15,90)(6,91,16,81)(7,82,17,92)(8,93,18,83)(9,84,19,94)(10,95,20,85)(21,125,31,135)(22,136,32,126)(23,127,33,137)(24,138,34,128)(25,129,35,139)(26,140,36,130)(27,131,37,121)(28,122,38,132)(29,133,39,123)(30,124,40,134)(41,79,51,69)(42,70,52,80)(43,61,53,71)(44,72,54,62)(45,63,55,73)(46,74,56,64)(47,65,57,75)(48,76,58,66)(49,67,59,77)(50,78,60,68)(101,159,111,149)(102,150,112,160)(103,141,113,151)(104,152,114,142)(105,143,115,153)(106,154,116,144)(107,145,117,155)(108,156,118,146)(109,147,119,157)(110,158,120,148), (1,27,70,160)(2,141,71,28)(3,29,72,142)(4,143,73,30)(5,31,74,144)(6,145,75,32)(7,33,76,146)(8,147,77,34)(9,35,78,148)(10,149,79,36)(11,37,80,150)(12,151,61,38)(13,39,62,152)(14,153,63,40)(15,21,64,154)(16,155,65,22)(17,23,66,156)(18,157,67,24)(19,25,68,158)(20,159,69,26)(41,140,85,111)(42,112,86,121)(43,122,87,113)(44,114,88,123)(45,124,89,115)(46,116,90,125)(47,126,91,117)(48,118,92,127)(49,128,93,119)(50,120,94,129)(51,130,95,101)(52,102,96,131)(53,132,97,103)(54,104,98,133)(55,134,99,105)(56,106,100,135)(57,136,81,107)(58,108,82,137)(59,138,83,109)(60,110,84,139), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60)(61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100)(101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160), (1,10,11,20)(2,19,12,9)(3,8,13,18)(4,17,14,7)(5,6,15,16)(21,145,31,155)(22,154,32,144)(23,143,33,153)(24,152,34,142)(25,141,35,151)(26,150,36,160)(27,159,37,149)(28,148,38,158)(29,157,39,147)(30,146,40,156)(41,86,51,96)(42,95,52,85)(43,84,53,94)(44,93,54,83)(45,82,55,92)(46,91,56,81)(47,100,57,90)(48,89,58,99)(49,98,59,88)(50,87,60,97)(61,78,71,68)(62,67,72,77)(63,76,73,66)(64,65,74,75)(69,70,79,80)(101,112,111,102)(103,110,113,120)(104,119,114,109)(105,108,115,118)(106,117,116,107)(121,140,131,130)(122,129,132,139)(123,138,133,128)(124,127,134,137)(125,136,135,126)>;

G:=Group( (1,96,11,86)(2,87,12,97)(3,98,13,88)(4,89,14,99)(5,100,15,90)(6,91,16,81)(7,82,17,92)(8,93,18,83)(9,84,19,94)(10,95,20,85)(21,125,31,135)(22,136,32,126)(23,127,33,137)(24,138,34,128)(25,129,35,139)(26,140,36,130)(27,131,37,121)(28,122,38,132)(29,133,39,123)(30,124,40,134)(41,79,51,69)(42,70,52,80)(43,61,53,71)(44,72,54,62)(45,63,55,73)(46,74,56,64)(47,65,57,75)(48,76,58,66)(49,67,59,77)(50,78,60,68)(101,159,111,149)(102,150,112,160)(103,141,113,151)(104,152,114,142)(105,143,115,153)(106,154,116,144)(107,145,117,155)(108,156,118,146)(109,147,119,157)(110,158,120,148), (1,27,70,160)(2,141,71,28)(3,29,72,142)(4,143,73,30)(5,31,74,144)(6,145,75,32)(7,33,76,146)(8,147,77,34)(9,35,78,148)(10,149,79,36)(11,37,80,150)(12,151,61,38)(13,39,62,152)(14,153,63,40)(15,21,64,154)(16,155,65,22)(17,23,66,156)(18,157,67,24)(19,25,68,158)(20,159,69,26)(41,140,85,111)(42,112,86,121)(43,122,87,113)(44,114,88,123)(45,124,89,115)(46,116,90,125)(47,126,91,117)(48,118,92,127)(49,128,93,119)(50,120,94,129)(51,130,95,101)(52,102,96,131)(53,132,97,103)(54,104,98,133)(55,134,99,105)(56,106,100,135)(57,136,81,107)(58,108,82,137)(59,138,83,109)(60,110,84,139), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60)(61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100)(101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160), (1,10,11,20)(2,19,12,9)(3,8,13,18)(4,17,14,7)(5,6,15,16)(21,145,31,155)(22,154,32,144)(23,143,33,153)(24,152,34,142)(25,141,35,151)(26,150,36,160)(27,159,37,149)(28,148,38,158)(29,157,39,147)(30,146,40,156)(41,86,51,96)(42,95,52,85)(43,84,53,94)(44,93,54,83)(45,82,55,92)(46,91,56,81)(47,100,57,90)(48,89,58,99)(49,98,59,88)(50,87,60,97)(61,78,71,68)(62,67,72,77)(63,76,73,66)(64,65,74,75)(69,70,79,80)(101,112,111,102)(103,110,113,120)(104,119,114,109)(105,108,115,118)(106,117,116,107)(121,140,131,130)(122,129,132,139)(123,138,133,128)(124,127,134,137)(125,136,135,126) );

G=PermutationGroup([[(1,96,11,86),(2,87,12,97),(3,98,13,88),(4,89,14,99),(5,100,15,90),(6,91,16,81),(7,82,17,92),(8,93,18,83),(9,84,19,94),(10,95,20,85),(21,125,31,135),(22,136,32,126),(23,127,33,137),(24,138,34,128),(25,129,35,139),(26,140,36,130),(27,131,37,121),(28,122,38,132),(29,133,39,123),(30,124,40,134),(41,79,51,69),(42,70,52,80),(43,61,53,71),(44,72,54,62),(45,63,55,73),(46,74,56,64),(47,65,57,75),(48,76,58,66),(49,67,59,77),(50,78,60,68),(101,159,111,149),(102,150,112,160),(103,141,113,151),(104,152,114,142),(105,143,115,153),(106,154,116,144),(107,145,117,155),(108,156,118,146),(109,147,119,157),(110,158,120,148)], [(1,27,70,160),(2,141,71,28),(3,29,72,142),(4,143,73,30),(5,31,74,144),(6,145,75,32),(7,33,76,146),(8,147,77,34),(9,35,78,148),(10,149,79,36),(11,37,80,150),(12,151,61,38),(13,39,62,152),(14,153,63,40),(15,21,64,154),(16,155,65,22),(17,23,66,156),(18,157,67,24),(19,25,68,158),(20,159,69,26),(41,140,85,111),(42,112,86,121),(43,122,87,113),(44,114,88,123),(45,124,89,115),(46,116,90,125),(47,126,91,117),(48,118,92,127),(49,128,93,119),(50,120,94,129),(51,130,95,101),(52,102,96,131),(53,132,97,103),(54,104,98,133),(55,134,99,105),(56,106,100,135),(57,136,81,107),(58,108,82,137),(59,138,83,109),(60,110,84,139)], [(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20),(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40),(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60),(61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80),(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100),(101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120),(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140),(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160)], [(1,10,11,20),(2,19,12,9),(3,8,13,18),(4,17,14,7),(5,6,15,16),(21,145,31,155),(22,154,32,144),(23,143,33,153),(24,152,34,142),(25,141,35,151),(26,150,36,160),(27,159,37,149),(28,148,38,158),(29,157,39,147),(30,146,40,156),(41,86,51,96),(42,95,52,85),(43,84,53,94),(44,93,54,83),(45,82,55,92),(46,91,56,81),(47,100,57,90),(48,89,58,99),(49,98,59,88),(50,87,60,97),(61,78,71,68),(62,67,72,77),(63,76,73,66),(64,65,74,75),(69,70,79,80),(101,112,111,102),(103,110,113,120),(104,119,114,109),(105,108,115,118),(106,117,116,107),(121,140,131,130),(122,129,132,139),(123,138,133,128),(124,127,134,137),(125,136,135,126)]])

47 conjugacy classes

class	1	2A	2B	2C	2D	2E	4A	···	4G	4H	···	4M	5A	5B	10A	···	10F	20A	···	20L	20M	···	20T
order	1	2	2	2	2	2	4	···	4	4	···	4	5	5	10	···	10	20	···	20	20	···	20
size	1	1	1	1	20	20	4	···	4	20	···	20	2	2	2	···	2	4	···	4	8	···	8

47 irreducible representations

dim

type

image

C₁

C₂

D₅

D₁₀

2₊¹⁺⁴

2_-¹⁺⁴

D₄⋊₆D₁₀

Q₈.₁₀D₁₀

kernel

C₄².₁₈₀D₁₀

C₄²⋊₂D₅

Dic₅.Q₈

D₁₀.₁₃D₄

D₁₀⋊Q₈

C₄⋊C₄⋊D₅

Dic₅⋊Q₈

D₁₀⋊₃Q₈

C₂₀.₂₃D₄

C₅×C₄⋊Q₈

C₄⋊Q₈

C₄²

C₄⋊C₄

C₂×Q₈

C₁₀

C₂

# reps

Matrix representation of C₄².₁₈₀D₁₀ ►in GL₁₀(𝔽₄₁)

1	0	0	0	0	0	0	0	0	0
0	1	0	0	0	0	0	0	0	0
0	0	0	0	1	0	0	0	0	0
0	0	0	0	0	1	0	0	0	0
0	0	40	0	0	0	0	0	0	0
0	0	0	40	0	0	0	0	0	0
0	0	0	0	0	0	0	0	1	0
0	0	0	0	0	0	0	0	0	1
0	0	0	0	0	0	40	0	0	0
0	0	0	0	0	0	0	40	0	0

40	0	0	0	0	0	0	0	0	0
0	40	0	0	0	0	0	0	0	0
0	0	0	1	0	0	0	0	0	0
0	0	40	0	0	0	0	0	0	0
0	0	0	0	0	1	0	0	0	0
0	0	0	0	40	0	0	0	0	0
0	0	0	0	0	0	0	1	0	0
0	0	0	0	0	0	1	0	0	0
0	0	0	0	0	0	0	0	0	1
0	0	0	0	0	0	0	0	1	0

0	35	0	0	0	0	0	0	0	0
7	34	0	0	0	0	0	0	0	0
0	0	0	32	0	0	0	0	0	0
0	0	32	0	0	0	0	0	0	0
0	0	0	0	0	9	0	0	0	0
0	0	0	0	9	0	0	0	0	0
0	0	0	0	0	0	0	0	32	0
0	0	0	0	0	0	0	0	0	32
0	0	0	0	0	0	32	0	0	0
0	0	0	0	0	0	0	32	0	0

7	35	0	0	0	0	0	0	0	0
8	34	0	0	0	0	0	0	0	0
0	0	0	32	0	0	0	0	0	0
0	0	32	0	0	0	0	0	0	0
0	0	0	0	0	32	0	0	0	0
0	0	0	0	32	0	0	0	0	0
0	0	0	0	0	0	0	0	32	0
0	0	0	0	0	0	0	0	0	9
0	0	0	0	0	0	32	0	0	0
0	0	0	0	0	0	0	9	0	0

G:=sub<GL(10,GF(41))| [1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0],[40,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0],[0,7,0,0,0,0,0,0,0,0,35,34,0,0,0,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,0,0,0,0,9,0,0,0,0,0,0,0,0,9,0,0,0,0,0,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,0,0,32,0,0],[7,8,0,0,0,0,0,0,0,0,35,34,0,0,0,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,0,0,9,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,0,0,9,0,0] >;

C₄².₁₈₀D₁₀ in GAP, Magma, Sage, TeX

C_4^2._{180}D_{10}

% in TeX

G:=Group("C4^2.180D10");

// GroupNames label

G:=SmallGroup(320,1407);

// by ID

G=gap.SmallGroup(320,1407);

# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,120,758,219,100,1571,570,136,12550]);

// Polycyclic

G:=Group<a,b,c,d|a^4=b^4=1,c^10=d^2=a^2,a*b=b*a,c*a*c^-1=a^-1,d*a*d^-1=a^-1*b^2,c*b*c^-1=b^-1,d*b*d^-1=a^2*b,d*c*d^-1=c^9>;

// generators/relations

1	0	0	0	0	0	0	0	0	0
0	1	0	0	0	0	0	0	0	0
0	0	0	0	1	0	0	0	0	0
0	0	0	0	0	1	0	0	0	0
0	0	40	0	0	0	0	0	0	0
0	0	0	40	0	0	0	0	0	0
0	0	0	0	0	0	0	0	1	0
0	0	0	0	0	0	0	0	0	1
0	0	0	0	0	0	40	0	0	0
0	0	0	0	0	0	0	40	0	0

40	0	0	0	0	0	0	0	0	0
0	40	0	0	0	0	0	0	0	0
0	0	0	1	0	0	0	0	0	0
0	0	40	0	0	0	0	0	0	0
0	0	0	0	0	1	0	0	0	0
0	0	0	0	40	0	0	0	0	0
0	0	0	0	0	0	0	1	0	0
0	0	0	0	0	0	1	0	0	0
0	0	0	0	0	0	0	0	0	1
0	0	0	0	0	0	0	0	1	0

0	35	0	0	0	0	0	0	0	0
7	34	0	0	0	0	0	0	0	0
0	0	0	32	0	0	0	0	0	0
0	0	32	0	0	0	0	0	0	0
0	0	0	0	0	9	0	0	0	0
0	0	0	0	9	0	0	0	0	0
0	0	0	0	0	0	0	0	32	0
0	0	0	0	0	0	0	0	0	32
0	0	0	0	0	0	32	0	0	0
0	0	0	0	0	0	0	32	0	0

7	35	0	0	0	0	0	0	0	0
8	34	0	0	0	0	0	0	0	0
0	0	0	32	0	0	0	0	0	0
0	0	32	0	0	0	0	0	0	0
0	0	0	0	0	32	0	0	0	0
0	0	0	0	32	0	0	0	0	0
0	0	0	0	0	0	0	0	32	0
0	0	0	0	0	0	0	0	0	9
0	0	0	0	0	0	32	0	0	0
0	0	0	0	0	0	0	9	0	0

1	0	0	0	0	0	0	0	0	0
0	1	0	0	0	0	0	0	0	0
0	0	0	0	1	0	0	0	0	0
0	0	0	0	0	1	0	0	0	0
0	0	40	0	0	0	0	0	0	0
0	0	0	40	0	0	0	0	0	0
0	0	0	0	0	0	0	0	1	0
0	0	0	0	0	0	0	0	0	1
0	0	0	0	0	0	40	0	0	0
0	0	0	0	0	0	0	40	0	0

40	0	0	0	0	0	0	0	0	0
0	40	0	0	0	0	0	0	0	0
0	0	0	1	0	0	0	0	0	0
0	0	40	0	0	0	0	0	0	0
0	0	0	0	0	1	0	0	0	0
0	0	0	0	40	0	0	0	0	0
0	0	0	0	0	0	0	1	0	0
0	0	0	0	0	0	1	0	0	0
0	0	0	0	0	0	0	0	0	1
0	0	0	0	0	0	0	0	1	0

0	35	0	0	0	0	0	0	0	0
7	34	0	0	0	0	0	0	0	0
0	0	0	32	0	0	0	0	0	0
0	0	32	0	0	0	0	0	0	0
0	0	0	0	0	9	0	0	0	0
0	0	0	0	9	0	0	0	0	0
0	0	0	0	0	0	0	0	32	0
0	0	0	0	0	0	0	0	0	32
0	0	0	0	0	0	32	0	0	0
0	0	0	0	0	0	0	32	0	0

7	35	0	0	0	0	0	0	0	0
8	34	0	0	0	0	0	0	0	0
0	0	0	32	0	0	0	0	0	0
0	0	32	0	0	0	0	0	0	0
0	0	0	0	0	32	0	0	0	0
0	0	0	0	32	0	0	0	0	0
0	0	0	0	0	0	0	0	32	0
0	0	0	0	0	0	0	0	0	9
0	0	0	0	0	0	32	0	0	0
0	0	0	0	0	0	0	9	0	0

G = C42.180D10 order 320 = 26·5

180th non-split extension by C42 of D10 acting via D10/C5=C22

G = C₄².₁₈₀D₁₀ order 320 = 2⁶·5

180^th non-split extension by C₄² of D₁₀ acting via D₁₀/C₅=C₂²

1	0	0	0	0	0	0	0	0	0
0	1	0	0	0	0	0	0	0	0
0	0	0	0	1	0	0	0	0	0
0	0	0	0	0	1	0	0	0	0
0	0	40	0	0	0	0	0	0	0
0	0	0	40	0	0	0	0	0	0
0	0	0	0	0	0	0	0	1	0
0	0	0	0	0	0	0	0	0	1
0	0	0	0	0	0	40	0	0	0
0	0	0	0	0	0	0	40	0	0

40	0	0	0	0	0	0	0	0	0
0	40	0	0	0	0	0	0	0	0
0	0	0	1	0	0	0	0	0	0
0	0	40	0	0	0	0	0	0	0
0	0	0	0	0	1	0	0	0	0
0	0	0	0	40	0	0	0	0	0
0	0	0	0	0	0	0	1	0	0
0	0	0	0	0	0	1	0	0	0
0	0	0	0	0	0	0	0	0	1
0	0	0	0	0	0	0	0	1	0

0	35	0	0	0	0	0	0	0	0
7	34	0	0	0	0	0	0	0	0
0	0	0	32	0	0	0	0	0	0
0	0	32	0	0	0	0	0	0	0
0	0	0	0	0	9	0	0	0	0
0	0	0	0	9	0	0	0	0	0
0	0	0	0	0	0	0	0	32	0
0	0	0	0	0	0	0	0	0	32
0	0	0	0	0	0	32	0	0	0
0	0	0	0	0	0	0	32	0	0

7	35	0	0	0	0	0	0	0	0
8	34	0	0	0	0	0	0	0	0
0	0	0	32	0	0	0	0	0	0
0	0	32	0	0	0	0	0	0	0
0	0	0	0	0	32	0	0	0	0
0	0	0	0	32	0	0	0	0	0
0	0	0	0	0	0	0	0	32	0
0	0	0	0	0	0	0	0	0	9
0	0	0	0	0	0	32	0	0	0
0	0	0	0	0	0	0	9	0	0