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## G = C42.77D6order 192 = 26·3

### 77th non-split extension by C42 of D6 acting via D6/C3=C22

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C12 — C42.77D6
 Chief series C1 — C3 — C6 — C2×C6 — C2×C12 — C2×C3⋊C8 — C42.S3 — C42.77D6
 Lower central C3 — C6 — C2×C12 — C42.77D6
 Upper central C1 — C22 — C42 — C4⋊Q8

Generators and relations for C42.77D6
G = < a,b,c,d | a4=b4=1, c6=b2, d2=a2b2, ab=ba, cac-1=a-1, dad-1=a-1b2, cbc-1=dbd-1=b-1, dcd-1=a2bc5 >

Subgroups: 208 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 [×6], C2×C8 [×2], C2×Q8 [×2], C3⋊C8 [×2], C2×Dic3 [×2], C2×C12, C2×C12 [×2], C2×C12 [×2], C3×Q8 [×4], C8⋊C4, Q8⋊C4 [×4], C42.C2, C4⋊Q8, C2×C3⋊C8 [×2], Dic3⋊C4 [×2], C4⋊Dic3 [×2], C4×C12, C3×C4⋊C4 [×2], C6×Q8 [×2], C42.30C22, C42.S3, Q82Dic3 [×4], C12.6Q8, C3×C4⋊Q8, C42.77D6
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], D42S3 [×2], C2×C3⋊D4, C42.30C22, C23.12D6, Q8.11D6 [×2], C42.77D6

Character table of C42.77D6

 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 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 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 0 -2 0 0 2 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 0 -2 0 0 2 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 0 2 0 0 -2 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 0 2 0 0 -2 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 0 2 0 0 -2 0 0 0 0 symplectic lifted from D4⋊2S3, Schur index 2 ρ24 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 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 D4⋊2S3, 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 Q8.11D6 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 Q8.11D6 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 C42.77D6
Regular action on 192 points
Generators in S192
```(1 35 161 17)(2 18 162 36)(3 25 163 19)(4 20 164 26)(5 27 165 21)(6 22 166 28)(7 29 167 23)(8 24 168 30)(9 31 157 13)(10 14 158 32)(11 33 159 15)(12 16 160 34)(37 138 123 177)(38 178 124 139)(39 140 125 179)(40 180 126 141)(41 142 127 169)(42 170 128 143)(43 144 129 171)(44 172 130 133)(45 134 131 173)(46 174 132 135)(47 136 121 175)(48 176 122 137)(49 106 66 84)(50 73 67 107)(51 108 68 74)(52 75 69 97)(53 98 70 76)(54 77 71 99)(55 100 72 78)(56 79 61 101)(57 102 62 80)(58 81 63 103)(59 104 64 82)(60 83 65 105)(85 113 187 151)(86 152 188 114)(87 115 189 153)(88 154 190 116)(89 117 191 155)(90 156 192 118)(91 119 181 145)(92 146 182 120)(93 109 183 147)(94 148 184 110)(95 111 185 149)(96 150 186 112)
(1 115 7 109)(2 110 8 116)(3 117 9 111)(4 112 10 118)(5 119 11 113)(6 114 12 120)(13 95 19 89)(14 90 20 96)(15 85 21 91)(16 92 22 86)(17 87 23 93)(18 94 24 88)(25 191 31 185)(26 186 32 192)(27 181 33 187)(28 188 34 182)(29 183 35 189)(30 190 36 184)(37 104 43 98)(38 99 44 105)(39 106 45 100)(40 101 46 107)(41 108 47 102)(42 103 48 97)(49 173 55 179)(50 180 56 174)(51 175 57 169)(52 170 58 176)(53 177 59 171)(54 172 60 178)(61 135 67 141)(62 142 68 136)(63 137 69 143)(64 144 70 138)(65 139 71 133)(66 134 72 140)(73 126 79 132)(74 121 80 127)(75 128 81 122)(76 123 82 129)(77 130 83 124)(78 125 84 131)(145 159 151 165)(146 166 152 160)(147 161 153 167)(148 168 154 162)(149 163 155 157)(150 158 156 164)
(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 39 167 131)(2 77 168 105)(3 37 157 129)(4 75 158 103)(5 47 159 127)(6 73 160 101)(7 45 161 125)(8 83 162 99)(9 43 163 123)(10 81 164 97)(11 41 165 121)(12 79 166 107)(13 138 25 171)(14 52 26 63)(15 136 27 169)(16 50 28 61)(17 134 29 179)(18 60 30 71)(19 144 31 177)(20 58 32 69)(21 142 33 175)(22 56 34 67)(23 140 35 173)(24 54 36 65)(38 116 130 148)(40 114 132 146)(42 112 122 156)(44 110 124 154)(46 120 126 152)(48 118 128 150)(49 93 72 189)(51 91 62 187)(53 89 64 185)(55 87 66 183)(57 85 68 181)(59 95 70 191)(74 113 102 145)(76 111 104 155)(78 109 106 153)(80 119 108 151)(82 117 98 149)(84 115 100 147)(86 180 182 135)(88 178 184 133)(90 176 186 143)(92 174 188 141)(94 172 190 139)(96 170 192 137)```

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

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

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

Matrix representation of C42.77D6 in GL8(𝔽73)

 22 8 35 1 0 0 0 0 65 14 72 34 0 0 0 0 38 72 51 65 0 0 0 0 1 39 8 59 0 0 0 0 0 0 0 0 30 60 0 0 0 0 0 0 13 43 0 0 0 0 0 0 0 0 30 60 0 0 0 0 0 0 13 43
,
 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 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 72 0 0 0 0 0 0 0 0 72 0 0
,
 0 0 72 72 0 0 0 0 0 0 1 0 0 0 0 0 72 72 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 6 68 9 26 0 0 0 0 5 11 47 56 0 0 0 0 9 26 67 5 0 0 0 0 47 56 68 62
,
 36 6 41 19 0 0 0 0 43 37 51 32 0 0 0 0 32 54 37 67 0 0 0 0 22 41 30 36 0 0 0 0 0 0 0 0 38 2 7 58 0 0 0 0 37 35 51 66 0 0 0 0 7 58 35 71 0 0 0 0 51 66 36 38

`G:=sub<GL(8,GF(73))| [22,65,38,1,0,0,0,0,8,14,72,39,0,0,0,0,35,72,51,8,0,0,0,0,1,34,65,59,0,0,0,0,0,0,0,0,30,13,0,0,0,0,0,0,60,43,0,0,0,0,0,0,0,0,30,13,0,0,0,0,0,0,60,43],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,72,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0],[0,0,72,1,0,0,0,0,0,0,72,0,0,0,0,0,72,1,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,0,0,0,6,5,9,47,0,0,0,0,68,11,26,56,0,0,0,0,9,47,67,68,0,0,0,0,26,56,5,62],[36,43,32,22,0,0,0,0,6,37,54,41,0,0,0,0,41,51,37,30,0,0,0,0,19,32,67,36,0,0,0,0,0,0,0,0,38,37,7,51,0,0,0,0,2,35,58,66,0,0,0,0,7,51,35,36,0,0,0,0,58,66,71,38] >;`

C42.77D6 in GAP, Magma, Sage, TeX

`C_4^2._{77}D_6`
`% in TeX`

`G:=Group("C4^2.77D6");`
`// GroupNames label`

`G:=SmallGroup(192,641);`
`// by ID`

`G=gap.SmallGroup(192,641);`
`# by ID`

`G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,112,477,64,590,135,184,438,102,6278]);`
`// Polycyclic`

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

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