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## G = C42.71D6order 192 = 26·3

### 71st non-split extension by C42 of D6 acting via D6/C3=C22

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C12 — C42.71D6
 Chief series C1 — C3 — C6 — C12 — C2×C12 — C2×Dic6 — C12⋊2Q8 — C42.71D6
 Lower central C3 — C6 — C2×C12 — C42.71D6
 Upper central C1 — C22 — C42 — C42.C2

Generators and relations for C42.71D6
G = < a,b,c,d | a4=b4=1, c6=a2, d2=a2b, ab=ba, cac-1=a-1b2, dad-1=ab2, cbc-1=b-1, bd=db, dcd-1=b-1c5 >

Subgroups: 224 in 90 conjugacy classes, 39 normal (15 characteristic)
C1, C2, C2 [×2], C3, C4 [×2], C4 [×6], C22, C6, C6 [×2], C8 [×2], C2×C4, C2×C4 [×2], C2×C4 [×4], Q8 [×4], Dic3 [×2], C12 [×2], C12 [×4], C2×C6, C42, C4⋊C4 [×2], C4⋊C4 [×4], C2×C8 [×2], C2×Q8 [×2], C3⋊C8 [×2], Dic6 [×4], C2×Dic3 [×2], C2×C12, C2×C12 [×2], C2×C12 [×2], C8⋊C4, Q8⋊C4 [×4], C42.C2, C4⋊Q8, C2×C3⋊C8 [×2], C4⋊Dic3 [×2], C4×C12, C3×C4⋊C4 [×2], C3×C4⋊C4 [×2], C2×Dic6 [×2], C42.30C22, C42.S3, C6.SD16 [×4], C122Q8, C3×C42.C2, C42.71D6
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D6 [×3], C2×D4, C4○D4 [×2], C3⋊D4 [×2], C22×S3, C4.4D4, C8.C22 [×2], Q83S3 [×2], C2×C3⋊D4, C42.30C22, C12.23D4, Q8.14D6 [×2], C42.71D6

Character table of C42.71D6

 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 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 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 -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 ρ15 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 ρ16 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 ρ17 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 ρ18 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 ρ19 2 -2 2 -2 2 2 -2 0 0 0 0 0 0 -2 2 -2 0 2i -2i 0 0 -2 2 0 0 0 0 0 0 0 complex lifted from C4○D4 ρ20 2 -2 2 -2 2 2 -2 0 0 0 0 0 0 -2 2 -2 0 -2i 2i 0 0 -2 2 0 0 0 0 0 0 0 complex lifted from C4○D4 ρ21 2 -2 2 -2 2 -2 2 0 0 0 0 0 0 -2 2 -2 2i 0 0 -2i 0 2 -2 0 0 0 0 0 0 0 complex lifted from C4○D4 ρ22 2 -2 2 -2 2 -2 2 0 0 0 0 0 0 -2 2 -2 -2i 0 0 2i 0 2 -2 0 0 0 0 0 0 0 complex lifted from C4○D4 ρ23 4 -4 4 -4 -2 -4 4 0 0 0 0 0 0 2 -2 2 0 0 0 0 0 -2 2 0 0 0 0 0 0 0 orthogonal lifted from Q8⋊3S3, Schur index 2 ρ24 4 -4 4 -4 -2 4 -4 0 0 0 0 0 0 2 -2 2 0 0 0 0 0 2 -2 0 0 0 0 0 0 0 orthogonal lifted from Q8⋊3S3, 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 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 ρ27 4 4 -4 -4 -2 0 0 0 0 0 0 0 0 -2 2 2 0 0 0 0 -2√3 0 0 2√3 0 0 0 0 0 0 symplectic lifted from Q8.14D6, Schur index 2 ρ28 4 4 -4 -4 -2 0 0 0 0 0 0 0 0 -2 2 2 0 0 0 0 2√3 0 0 -2√3 0 0 0 0 0 0 symplectic lifted from Q8.14D6, Schur index 2 ρ29 4 -4 -4 4 -2 0 0 0 0 0 0 0 0 2 2 -2 0 0 0 0 0 0 0 0 2√3 -2√3 0 0 0 0 symplectic lifted from Q8.14D6, Schur index 2 ρ30 4 -4 -4 4 -2 0 0 0 0 0 0 0 0 2 2 -2 0 0 0 0 0 0 0 0 -2√3 2√3 0 0 0 0 symplectic lifted from Q8.14D6, Schur index 2

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

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

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

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

Matrix representation of C42.71D6 in GL8(𝔽73)

 30 11 0 0 0 0 0 0 11 43 0 0 0 0 0 0 0 0 72 0 0 0 0 0 0 0 0 72 0 0 0 0 0 0 0 0 28 0 16 69 0 0 0 0 0 28 69 57 0 0 0 0 57 4 45 0 0 0 0 0 4 16 0 45
,
 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 0 1 0 0 0 0 0 0 72 0 0 0 0 0 0 0 0 0 0 72 0 0 0 0 0 0 1 0
,
 0 1 0 0 0 0 0 0 72 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 72 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 1 0 0 0 0 0 0 0 0 1 0 0
,
 46 0 0 0 0 0 0 0 0 46 0 0 0 0 0 0 0 0 29 54 0 0 0 0 0 0 25 44 0 0 0 0 0 0 0 0 58 58 35 63 0 0 0 0 15 58 63 38 0 0 0 0 63 38 15 58 0 0 0 0 38 10 15 15

`G:=sub<GL(8,GF(73))| [30,11,0,0,0,0,0,0,11,43,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,28,0,57,4,0,0,0,0,0,28,4,16,0,0,0,0,16,69,45,0,0,0,0,0,69,57,0,45],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,72,0],[0,72,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,72,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0],[46,0,0,0,0,0,0,0,0,46,0,0,0,0,0,0,0,0,29,25,0,0,0,0,0,0,54,44,0,0,0,0,0,0,0,0,58,15,63,38,0,0,0,0,58,58,38,10,0,0,0,0,35,63,15,15,0,0,0,0,63,38,58,15] >;`

C42.71D6 in GAP, Magma, Sage, TeX

`C_4^2._{71}D_6`
`% in TeX`

`G:=Group("C4^2.71D6");`
`// GroupNames label`

`G:=SmallGroup(192,628);`
`// by ID`

`G=gap.SmallGroup(192,628);`
`# by ID`

`G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,224,253,120,254,555,100,1123,297,136,6278]);`
`// Polycyclic`

`G:=Group<a,b,c,d|a^4=b^4=1,c^6=a^2,d^2=a^2*b,a*b=b*a,c*a*c^-1=a^-1*b^2,d*a*d^-1=a*b^2,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=b^-1*c^5>;`
`// generators/relations`

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