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## G = C42.76D6order 192 = 26·3

### 76th non-split extension by C42 of D6 acting via D6/C3=C22

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C12 — C42.76D6
 Chief series C1 — C3 — C6 — C2×C6 — C2×C12 — C2×C3⋊C8 — C42.S3 — C42.76D6
 Lower central C3 — C6 — C2×C12 — C42.76D6
 Upper central C1 — C22 — C42 — C4⋊Q8

Generators and relations for C42.76D6
G = < a,b,c,d | a4=b4=1, c6=d2=a2, ab=ba, cac-1=a-1, dad-1=a-1b2, cbc-1=dbd-1=b-1, dcd-1=bc5 >

Subgroups: 208 in 90 conjugacy classes, 43 normal (25 characteristic)
C1, C2 [×3], C3, C4 [×2], C4 [×6], C22, C6 [×3], C8 [×4], C2×C4 [×3], C2×C4 [×4], Q8 [×2], Dic3 [×2], C12 [×2], C12 [×4], C2×C6, C42, C4⋊C4 [×2], C4⋊C4 [×5], C2×C8 [×2], C2×Q8, C3⋊C8 [×4], C2×Dic3 [×2], C2×C12 [×3], C2×C12 [×2], C3×Q8 [×2], C8⋊C4, C4.Q8 [×2], C2.D8 [×2], C42.C2, C4⋊Q8, C2×C3⋊C8 [×2], Dic3⋊C4 [×2], C4⋊Dic3 [×2], C4×C12, C3×C4⋊C4 [×2], C3×C4⋊C4, C6×Q8, C8⋊Q8, C42.S3, C6.Q16 [×2], C12.Q8 [×2], C12.6Q8, C3×C4⋊Q8, C42.76D6
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], Q8 [×4], C23, D6 [×3], C2×D4, C2×Q8 [×2], C3⋊D4 [×2], C22×S3, C4⋊Q8, C8⋊C22, C8.C22, S3×Q8 [×2], C2×C3⋊D4, C8⋊Q8, D126C22, Q8.11D6, Dic3⋊Q8, C42.76D6

Character table of C42.76D6

 class 1 2A 2B 2C 3 4A 4B 4C 4D 4E 4F 4G 4H 6A 6B 6C 8A 8B 8C 8D 12A 12B 12C 12D 12E 12F 12G 12H 12I 12J size 1 1 1 1 2 2 2 4 4 8 8 24 24 2 2 2 12 12 12 12 4 4 4 4 4 4 8 8 8 8 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 -1 1 -1 -1 1 -1 -1 1 1 -1 1 -1 linear of order 2 ρ4 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 ρ5 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 ρ6 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 ρ7 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 ρ8 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 ρ9 2 2 2 2 2 -2 -2 2 -2 0 0 0 0 2 2 2 0 0 0 0 2 2 -2 -2 -2 -2 0 0 0 0 orthogonal lifted from D4 ρ10 2 2 2 2 -1 2 2 2 2 2 2 0 0 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 orthogonal lifted from S3 ρ11 2 2 2 2 -1 2 2 -2 -2 -2 2 0 0 -1 -1 -1 0 0 0 0 1 1 -1 1 1 -1 1 -1 1 -1 orthogonal lifted from D6 ρ12 2 2 2 2 -1 2 2 -2 -2 2 -2 0 0 -1 -1 -1 0 0 0 0 1 1 -1 1 1 -1 -1 1 -1 1 orthogonal lifted from D6 ρ13 2 2 2 2 -1 2 2 2 2 -2 -2 0 0 -1 -1 -1 0 0 0 0 -1 -1 -1 -1 -1 -1 1 1 1 1 orthogonal lifted from D6 ρ14 2 2 2 2 2 -2 -2 -2 2 0 0 0 0 2 2 2 0 0 0 0 -2 -2 -2 2 2 -2 0 0 0 0 orthogonal lifted from D4 ρ15 2 2 -2 -2 2 -2 2 0 0 0 0 0 0 -2 -2 2 0 -2 2 0 0 0 2 0 0 -2 0 0 0 0 symplectic lifted from Q8, Schur index 2 ρ16 2 2 -2 -2 2 2 -2 0 0 0 0 0 0 -2 -2 2 -2 0 0 2 0 0 -2 0 0 2 0 0 0 0 symplectic lifted from Q8, Schur index 2 ρ17 2 2 -2 -2 2 -2 2 0 0 0 0 0 0 -2 -2 2 0 2 -2 0 0 0 2 0 0 -2 0 0 0 0 symplectic lifted from Q8, Schur index 2 ρ18 2 2 -2 -2 2 2 -2 0 0 0 0 0 0 -2 -2 2 2 0 0 -2 0 0 -2 0 0 2 0 0 0 0 symplectic lifted from Q8, Schur index 2 ρ19 2 2 2 2 -1 -2 -2 -2 2 0 0 0 0 -1 -1 -1 0 0 0 0 1 1 1 -1 -1 1 √-3 -√-3 -√-3 √-3 complex lifted from C3⋊D4 ρ20 2 2 2 2 -1 -2 -2 2 -2 0 0 0 0 -1 -1 -1 0 0 0 0 -1 -1 1 1 1 1 √-3 √-3 -√-3 -√-3 complex lifted from C3⋊D4 ρ21 2 2 2 2 -1 -2 -2 2 -2 0 0 0 0 -1 -1 -1 0 0 0 0 -1 -1 1 1 1 1 -√-3 -√-3 √-3 √-3 complex lifted from C3⋊D4 ρ22 2 2 2 2 -1 -2 -2 -2 2 0 0 0 0 -1 -1 -1 0 0 0 0 1 1 1 -1 -1 1 -√-3 √-3 √-3 -√-3 complex lifted from C3⋊D4 ρ23 4 -4 4 -4 4 0 0 0 0 0 0 0 0 -4 4 -4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 orthogonal lifted from C8⋊C22 ρ24 4 4 -4 -4 -2 4 -4 0 0 0 0 0 0 2 2 -2 0 0 0 0 0 0 2 0 0 -2 0 0 0 0 symplectic lifted from S3×Q8, Schur index 2 ρ25 4 -4 -4 4 4 0 0 0 0 0 0 0 0 4 -4 -4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 symplectic lifted from C8.C22, Schur index 2 ρ26 4 4 -4 -4 -2 -4 4 0 0 0 0 0 0 2 2 -2 0 0 0 0 0 0 -2 0 0 2 0 0 0 0 symplectic lifted from S3×Q8, Schur index 2 ρ27 4 -4 4 -4 -2 0 0 0 0 0 0 0 0 2 -2 2 0 0 0 0 2√-3 -2√-3 0 0 0 0 0 0 0 0 complex lifted from D12⋊6C22 ρ28 4 -4 4 -4 -2 0 0 0 0 0 0 0 0 2 -2 2 0 0 0 0 -2√-3 2√-3 0 0 0 0 0 0 0 0 complex lifted from D12⋊6C22 ρ29 4 -4 -4 4 -2 0 0 0 0 0 0 0 0 -2 2 2 0 0 0 0 0 0 0 2√-3 -2√-3 0 0 0 0 0 complex lifted from Q8.11D6 ρ30 4 -4 -4 4 -2 0 0 0 0 0 0 0 0 -2 2 2 0 0 0 0 0 0 0 -2√-3 2√-3 0 0 0 0 0 complex lifted from Q8.11D6

Smallest permutation representation of C42.76D6
Regular action on 192 points
Generators in S192
```(1 18 7 24)(2 13 8 19)(3 20 9 14)(4 15 10 21)(5 22 11 16)(6 17 12 23)(25 122 31 128)(26 129 32 123)(27 124 33 130)(28 131 34 125)(29 126 35 132)(30 121 36 127)(37 144 43 138)(38 139 44 133)(39 134 45 140)(40 141 46 135)(41 136 47 142)(42 143 48 137)(49 98 55 104)(50 105 56 99)(51 100 57 106)(52 107 58 101)(53 102 59 108)(54 97 60 103)(61 81 67 75)(62 76 68 82)(63 83 69 77)(64 78 70 84)(65 73 71 79)(66 80 72 74)(85 174 91 180)(86 169 92 175)(87 176 93 170)(88 171 94 177)(89 178 95 172)(90 173 96 179)(109 158 115 164)(110 165 116 159)(111 160 117 166)(112 167 118 161)(113 162 119 168)(114 157 120 163)(145 190 151 184)(146 185 152 191)(147 192 153 186)(148 187 154 181)(149 182 155 188)(150 189 156 183)
(1 176 65 147)(2 148 66 177)(3 178 67 149)(4 150 68 179)(5 180 69 151)(6 152 70 169)(7 170 71 153)(8 154 72 171)(9 172 61 155)(10 156 62 173)(11 174 63 145)(12 146 64 175)(13 187 80 88)(14 89 81 188)(15 189 82 90)(16 91 83 190)(17 191 84 92)(18 93 73 192)(19 181 74 94)(20 95 75 182)(21 183 76 96)(22 85 77 184)(23 185 78 86)(24 87 79 186)(25 112 39 58)(26 59 40 113)(27 114 41 60)(28 49 42 115)(29 116 43 50)(30 51 44 117)(31 118 45 52)(32 53 46 119)(33 120 47 54)(34 55 48 109)(35 110 37 56)(36 57 38 111)(97 130 163 142)(98 143 164 131)(99 132 165 144)(100 133 166 121)(101 122 167 134)(102 135 168 123)(103 124 157 136)(104 137 158 125)(105 126 159 138)(106 139 160 127)(107 128 161 140)(108 141 162 129)
(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)(157 158 159 160 161 162 163 164 165 166 167 168)(169 170 171 172 173 174 175 176 177 178 179 180)(181 182 183 184 185 186 187 188 189 190 191 192)
(1 56 7 50)(2 28 8 34)(3 54 9 60)(4 26 10 32)(5 52 11 58)(6 36 12 30)(13 137 19 143)(14 163 20 157)(15 135 21 141)(16 161 22 167)(17 133 23 139)(18 159 24 165)(25 151 31 145)(27 149 33 155)(29 147 35 153)(37 170 43 176)(38 64 44 70)(39 180 45 174)(40 62 46 68)(41 178 47 172)(42 72 48 66)(49 171 55 177)(51 169 57 175)(53 179 59 173)(61 114 67 120)(63 112 69 118)(65 110 71 116)(73 105 79 99)(74 131 80 125)(75 103 81 97)(76 129 82 123)(77 101 83 107)(78 127 84 121)(85 122 91 128)(86 160 92 166)(87 132 93 126)(88 158 94 164)(89 130 95 124)(90 168 96 162)(98 187 104 181)(100 185 106 191)(102 183 108 189)(109 148 115 154)(111 146 117 152)(113 156 119 150)(134 190 140 184)(136 188 142 182)(138 186 144 192)```

`G:=sub<Sym(192)| (1,18,7,24)(2,13,8,19)(3,20,9,14)(4,15,10,21)(5,22,11,16)(6,17,12,23)(25,122,31,128)(26,129,32,123)(27,124,33,130)(28,131,34,125)(29,126,35,132)(30,121,36,127)(37,144,43,138)(38,139,44,133)(39,134,45,140)(40,141,46,135)(41,136,47,142)(42,143,48,137)(49,98,55,104)(50,105,56,99)(51,100,57,106)(52,107,58,101)(53,102,59,108)(54,97,60,103)(61,81,67,75)(62,76,68,82)(63,83,69,77)(64,78,70,84)(65,73,71,79)(66,80,72,74)(85,174,91,180)(86,169,92,175)(87,176,93,170)(88,171,94,177)(89,178,95,172)(90,173,96,179)(109,158,115,164)(110,165,116,159)(111,160,117,166)(112,167,118,161)(113,162,119,168)(114,157,120,163)(145,190,151,184)(146,185,152,191)(147,192,153,186)(148,187,154,181)(149,182,155,188)(150,189,156,183), (1,176,65,147)(2,148,66,177)(3,178,67,149)(4,150,68,179)(5,180,69,151)(6,152,70,169)(7,170,71,153)(8,154,72,171)(9,172,61,155)(10,156,62,173)(11,174,63,145)(12,146,64,175)(13,187,80,88)(14,89,81,188)(15,189,82,90)(16,91,83,190)(17,191,84,92)(18,93,73,192)(19,181,74,94)(20,95,75,182)(21,183,76,96)(22,85,77,184)(23,185,78,86)(24,87,79,186)(25,112,39,58)(26,59,40,113)(27,114,41,60)(28,49,42,115)(29,116,43,50)(30,51,44,117)(31,118,45,52)(32,53,46,119)(33,120,47,54)(34,55,48,109)(35,110,37,56)(36,57,38,111)(97,130,163,142)(98,143,164,131)(99,132,165,144)(100,133,166,121)(101,122,167,134)(102,135,168,123)(103,124,157,136)(104,137,158,125)(105,126,159,138)(106,139,160,127)(107,128,161,140)(108,141,162,129), (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)(157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180)(181,182,183,184,185,186,187,188,189,190,191,192), (1,56,7,50)(2,28,8,34)(3,54,9,60)(4,26,10,32)(5,52,11,58)(6,36,12,30)(13,137,19,143)(14,163,20,157)(15,135,21,141)(16,161,22,167)(17,133,23,139)(18,159,24,165)(25,151,31,145)(27,149,33,155)(29,147,35,153)(37,170,43,176)(38,64,44,70)(39,180,45,174)(40,62,46,68)(41,178,47,172)(42,72,48,66)(49,171,55,177)(51,169,57,175)(53,179,59,173)(61,114,67,120)(63,112,69,118)(65,110,71,116)(73,105,79,99)(74,131,80,125)(75,103,81,97)(76,129,82,123)(77,101,83,107)(78,127,84,121)(85,122,91,128)(86,160,92,166)(87,132,93,126)(88,158,94,164)(89,130,95,124)(90,168,96,162)(98,187,104,181)(100,185,106,191)(102,183,108,189)(109,148,115,154)(111,146,117,152)(113,156,119,150)(134,190,140,184)(136,188,142,182)(138,186,144,192)>;`

`G:=Group( (1,18,7,24)(2,13,8,19)(3,20,9,14)(4,15,10,21)(5,22,11,16)(6,17,12,23)(25,122,31,128)(26,129,32,123)(27,124,33,130)(28,131,34,125)(29,126,35,132)(30,121,36,127)(37,144,43,138)(38,139,44,133)(39,134,45,140)(40,141,46,135)(41,136,47,142)(42,143,48,137)(49,98,55,104)(50,105,56,99)(51,100,57,106)(52,107,58,101)(53,102,59,108)(54,97,60,103)(61,81,67,75)(62,76,68,82)(63,83,69,77)(64,78,70,84)(65,73,71,79)(66,80,72,74)(85,174,91,180)(86,169,92,175)(87,176,93,170)(88,171,94,177)(89,178,95,172)(90,173,96,179)(109,158,115,164)(110,165,116,159)(111,160,117,166)(112,167,118,161)(113,162,119,168)(114,157,120,163)(145,190,151,184)(146,185,152,191)(147,192,153,186)(148,187,154,181)(149,182,155,188)(150,189,156,183), (1,176,65,147)(2,148,66,177)(3,178,67,149)(4,150,68,179)(5,180,69,151)(6,152,70,169)(7,170,71,153)(8,154,72,171)(9,172,61,155)(10,156,62,173)(11,174,63,145)(12,146,64,175)(13,187,80,88)(14,89,81,188)(15,189,82,90)(16,91,83,190)(17,191,84,92)(18,93,73,192)(19,181,74,94)(20,95,75,182)(21,183,76,96)(22,85,77,184)(23,185,78,86)(24,87,79,186)(25,112,39,58)(26,59,40,113)(27,114,41,60)(28,49,42,115)(29,116,43,50)(30,51,44,117)(31,118,45,52)(32,53,46,119)(33,120,47,54)(34,55,48,109)(35,110,37,56)(36,57,38,111)(97,130,163,142)(98,143,164,131)(99,132,165,144)(100,133,166,121)(101,122,167,134)(102,135,168,123)(103,124,157,136)(104,137,158,125)(105,126,159,138)(106,139,160,127)(107,128,161,140)(108,141,162,129), (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)(157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180)(181,182,183,184,185,186,187,188,189,190,191,192), (1,56,7,50)(2,28,8,34)(3,54,9,60)(4,26,10,32)(5,52,11,58)(6,36,12,30)(13,137,19,143)(14,163,20,157)(15,135,21,141)(16,161,22,167)(17,133,23,139)(18,159,24,165)(25,151,31,145)(27,149,33,155)(29,147,35,153)(37,170,43,176)(38,64,44,70)(39,180,45,174)(40,62,46,68)(41,178,47,172)(42,72,48,66)(49,171,55,177)(51,169,57,175)(53,179,59,173)(61,114,67,120)(63,112,69,118)(65,110,71,116)(73,105,79,99)(74,131,80,125)(75,103,81,97)(76,129,82,123)(77,101,83,107)(78,127,84,121)(85,122,91,128)(86,160,92,166)(87,132,93,126)(88,158,94,164)(89,130,95,124)(90,168,96,162)(98,187,104,181)(100,185,106,191)(102,183,108,189)(109,148,115,154)(111,146,117,152)(113,156,119,150)(134,190,140,184)(136,188,142,182)(138,186,144,192) );`

`G=PermutationGroup([(1,18,7,24),(2,13,8,19),(3,20,9,14),(4,15,10,21),(5,22,11,16),(6,17,12,23),(25,122,31,128),(26,129,32,123),(27,124,33,130),(28,131,34,125),(29,126,35,132),(30,121,36,127),(37,144,43,138),(38,139,44,133),(39,134,45,140),(40,141,46,135),(41,136,47,142),(42,143,48,137),(49,98,55,104),(50,105,56,99),(51,100,57,106),(52,107,58,101),(53,102,59,108),(54,97,60,103),(61,81,67,75),(62,76,68,82),(63,83,69,77),(64,78,70,84),(65,73,71,79),(66,80,72,74),(85,174,91,180),(86,169,92,175),(87,176,93,170),(88,171,94,177),(89,178,95,172),(90,173,96,179),(109,158,115,164),(110,165,116,159),(111,160,117,166),(112,167,118,161),(113,162,119,168),(114,157,120,163),(145,190,151,184),(146,185,152,191),(147,192,153,186),(148,187,154,181),(149,182,155,188),(150,189,156,183)], [(1,176,65,147),(2,148,66,177),(3,178,67,149),(4,150,68,179),(5,180,69,151),(6,152,70,169),(7,170,71,153),(8,154,72,171),(9,172,61,155),(10,156,62,173),(11,174,63,145),(12,146,64,175),(13,187,80,88),(14,89,81,188),(15,189,82,90),(16,91,83,190),(17,191,84,92),(18,93,73,192),(19,181,74,94),(20,95,75,182),(21,183,76,96),(22,85,77,184),(23,185,78,86),(24,87,79,186),(25,112,39,58),(26,59,40,113),(27,114,41,60),(28,49,42,115),(29,116,43,50),(30,51,44,117),(31,118,45,52),(32,53,46,119),(33,120,47,54),(34,55,48,109),(35,110,37,56),(36,57,38,111),(97,130,163,142),(98,143,164,131),(99,132,165,144),(100,133,166,121),(101,122,167,134),(102,135,168,123),(103,124,157,136),(104,137,158,125),(105,126,159,138),(106,139,160,127),(107,128,161,140),(108,141,162,129)], [(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),(157,158,159,160,161,162,163,164,165,166,167,168),(169,170,171,172,173,174,175,176,177,178,179,180),(181,182,183,184,185,186,187,188,189,190,191,192)], [(1,56,7,50),(2,28,8,34),(3,54,9,60),(4,26,10,32),(5,52,11,58),(6,36,12,30),(13,137,19,143),(14,163,20,157),(15,135,21,141),(16,161,22,167),(17,133,23,139),(18,159,24,165),(25,151,31,145),(27,149,33,155),(29,147,35,153),(37,170,43,176),(38,64,44,70),(39,180,45,174),(40,62,46,68),(41,178,47,172),(42,72,48,66),(49,171,55,177),(51,169,57,175),(53,179,59,173),(61,114,67,120),(63,112,69,118),(65,110,71,116),(73,105,79,99),(74,131,80,125),(75,103,81,97),(76,129,82,123),(77,101,83,107),(78,127,84,121),(85,122,91,128),(86,160,92,166),(87,132,93,126),(88,158,94,164),(89,130,95,124),(90,168,96,162),(98,187,104,181),(100,185,106,191),(102,183,108,189),(109,148,115,154),(111,146,117,152),(113,156,119,150),(134,190,140,184),(136,188,142,182),(138,186,144,192)])`

Matrix representation of C42.76D6 in GL8(𝔽73)

 17 21 2 62 0 0 0 0 52 38 11 64 0 0 0 0 57 10 56 52 0 0 0 0 63 67 21 35 0 0 0 0 0 0 0 0 61 47 58 69 0 0 0 0 0 25 22 45 0 0 0 0 58 23 12 0 0 0 0 0 56 30 3 48
,
 1 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 1 0 0 0 0 0 0 0 0 1 48 0 0 0 0 0 0 3 72 0 0 0 0 0 0 0 13 72 2 0 0 0 0 17 13 72 1
,
 0 1 0 2 0 0 0 0 72 1 71 2 0 0 0 0 0 72 0 72 0 0 0 0 1 72 1 72 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 56 0 3 0 0 0 0 72 0 0 0 0 0 0 0 0 25 0 17
,
 51 56 70 47 0 0 0 0 34 22 44 3 0 0 0 0 38 13 54 9 0 0 0 0 51 35 63 19 0 0 0 0 0 0 0 0 45 46 68 5 0 0 0 0 68 28 29 0 0 0 0 0 0 1 24 21 0 0 0 0 35 1 65 49

`G:=sub<GL(8,GF(73))| [17,52,57,63,0,0,0,0,21,38,10,67,0,0,0,0,2,11,56,21,0,0,0,0,62,64,52,35,0,0,0,0,0,0,0,0,61,0,58,56,0,0,0,0,47,25,23,30,0,0,0,0,58,22,12,3,0,0,0,0,69,45,0,48],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,3,0,17,0,0,0,0,48,72,13,13,0,0,0,0,0,0,72,72,0,0,0,0,0,0,2,1],[0,72,0,1,0,0,0,0,1,1,72,72,0,0,0,0,0,71,0,1,0,0,0,0,2,2,72,72,0,0,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,56,0,25,0,0,0,0,1,0,0,0,0,0,0,0,0,3,0,17],[51,34,38,51,0,0,0,0,56,22,13,35,0,0,0,0,70,44,54,63,0,0,0,0,47,3,9,19,0,0,0,0,0,0,0,0,45,68,0,35,0,0,0,0,46,28,1,1,0,0,0,0,68,29,24,65,0,0,0,0,5,0,21,49] >;`

C42.76D6 in GAP, Magma, Sage, TeX

`C_4^2._{76}D_6`
`% in TeX`

`G:=Group("C4^2.76D6");`
`// GroupNames label`

`G:=SmallGroup(192,640);`
`// by ID`

`G=gap.SmallGroup(192,640);`
`# by ID`

`G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,112,477,64,422,135,58,438,102,6278]);`
`// Polycyclic`

`G:=Group<a,b,c,d|a^4=b^4=1,c^6=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=d*b*d^-1=b^-1,d*c*d^-1=b*c^5>;`
`// generators/relations`

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