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## G = C3⋊Q64order 192 = 26·3

### The semidirect product of C3 and Q64 acting via Q64/Q32=C2

Aliases: C32Q64, Q32.S3, C16.7D6, C12.8D8, C6.11D16, C24.12D4, C48.5C22, Dic24.2C2, C3⋊C32.C2, C4.4(D4⋊S3), (C3×Q32).1C2, C2.7(C3⋊D16), C8.12(C3⋊D4), SmallGroup(192,81)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C48 — C3⋊Q64
 Chief series C1 — C3 — C6 — C12 — C24 — C48 — Dic24 — C3⋊Q64
 Lower central C3 — C6 — C12 — C24 — C48 — C3⋊Q64
 Upper central C1 — C2 — C4 — C8 — C16 — Q32

Generators and relations for C3⋊Q64
G = < a,b,c | a3=b32=1, c2=b16, bab-1=a-1, ac=ca, cbc-1=b-1 >

Character table of C3⋊Q64

 class 1 2 3 4A 4B 4C 6 8A 8B 12A 12B 12C 16A 16B 16C 16D 24A 24B 32A 32B 32C 32D 32E 32F 32G 32H 48A 48B 48C 48D size 1 1 2 2 16 48 2 2 2 4 16 16 2 2 2 2 4 4 6 6 6 6 6 6 6 6 4 4 4 4 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 2 2 -1 2 2 0 -1 2 2 -1 -1 -1 2 2 2 2 -1 -1 0 0 0 0 0 0 0 0 -1 -1 -1 -1 orthogonal lifted from S3 ρ6 2 2 -1 2 -2 0 -1 2 2 -1 1 1 2 2 2 2 -1 -1 0 0 0 0 0 0 0 0 -1 -1 -1 -1 orthogonal lifted from D6 ρ7 2 2 2 2 0 0 2 2 2 2 0 0 -2 -2 -2 -2 2 2 0 0 0 0 0 0 0 0 -2 -2 -2 -2 orthogonal lifted from D4 ρ8 2 2 2 -2 0 0 2 0 0 -2 0 0 √2 -√2 -√2 √2 0 0 -ζ167+ζ16 -ζ165+ζ163 ζ165-ζ163 ζ165-ζ163 ζ167-ζ16 ζ167-ζ16 -ζ167+ζ16 -ζ165+ζ163 -√2 √2 -√2 √2 orthogonal lifted from D16 ρ9 2 2 2 -2 0 0 2 0 0 -2 0 0 -√2 √2 √2 -√2 0 0 ζ165-ζ163 -ζ167+ζ16 ζ167-ζ16 ζ167-ζ16 -ζ165+ζ163 -ζ165+ζ163 ζ165-ζ163 -ζ167+ζ16 √2 -√2 √2 -√2 orthogonal lifted from D16 ρ10 2 2 2 2 0 0 2 -2 -2 2 0 0 0 0 0 0 -2 -2 -√2 √2 √2 √2 -√2 -√2 -√2 √2 0 0 0 0 orthogonal lifted from D8 ρ11 2 2 2 2 0 0 2 -2 -2 2 0 0 0 0 0 0 -2 -2 √2 -√2 -√2 -√2 √2 √2 √2 -√2 0 0 0 0 orthogonal lifted from D8 ρ12 2 2 2 -2 0 0 2 0 0 -2 0 0 -√2 √2 √2 -√2 0 0 -ζ165+ζ163 ζ167-ζ16 -ζ167+ζ16 -ζ167+ζ16 ζ165-ζ163 ζ165-ζ163 -ζ165+ζ163 ζ167-ζ16 √2 -√2 √2 -√2 orthogonal lifted from D16 ρ13 2 2 2 -2 0 0 2 0 0 -2 0 0 √2 -√2 -√2 √2 0 0 ζ167-ζ16 ζ165-ζ163 -ζ165+ζ163 -ζ165+ζ163 -ζ167+ζ16 -ζ167+ζ16 ζ167-ζ16 ζ165-ζ163 -√2 √2 -√2 √2 orthogonal lifted from D16 ρ14 2 -2 2 0 0 0 -2 √2 -√2 0 0 0 -ζ3214+ζ322 ζ3210-ζ326 -ζ3210+ζ326 ζ3214-ζ322 √2 -√2 ζ329-ζ327 -ζ3227+ζ3221 ζ3213-ζ323 -ζ3213+ζ323 -ζ3231+ζ3217 ζ3231-ζ3217 -ζ329+ζ327 ζ3227-ζ3221 ζ3210-ζ326 ζ3214-ζ322 -ζ3210+ζ326 -ζ3214+ζ322 symplectic lifted from Q64, Schur index 2 ρ15 2 -2 2 0 0 0 -2 √2 -√2 0 0 0 ζ3214-ζ322 -ζ3210+ζ326 ζ3210-ζ326 -ζ3214+ζ322 √2 -√2 -ζ3231+ζ3217 -ζ3213+ζ323 -ζ3227+ζ3221 ζ3227-ζ3221 -ζ329+ζ327 ζ329-ζ327 ζ3231-ζ3217 ζ3213-ζ323 -ζ3210+ζ326 -ζ3214+ζ322 ζ3210-ζ326 ζ3214-ζ322 symplectic lifted from Q64, Schur index 2 ρ16 2 -2 2 0 0 0 -2 √2 -√2 0 0 0 ζ3214-ζ322 -ζ3210+ζ326 ζ3210-ζ326 -ζ3214+ζ322 √2 -√2 ζ3231-ζ3217 ζ3213-ζ323 ζ3227-ζ3221 -ζ3227+ζ3221 ζ329-ζ327 -ζ329+ζ327 -ζ3231+ζ3217 -ζ3213+ζ323 -ζ3210+ζ326 -ζ3214+ζ322 ζ3210-ζ326 ζ3214-ζ322 symplectic lifted from Q64, Schur index 2 ρ17 2 -2 2 0 0 0 -2 √2 -√2 0 0 0 -ζ3214+ζ322 ζ3210-ζ326 -ζ3210+ζ326 ζ3214-ζ322 √2 -√2 -ζ329+ζ327 ζ3227-ζ3221 -ζ3213+ζ323 ζ3213-ζ323 ζ3231-ζ3217 -ζ3231+ζ3217 ζ329-ζ327 -ζ3227+ζ3221 ζ3210-ζ326 ζ3214-ζ322 -ζ3210+ζ326 -ζ3214+ζ322 symplectic lifted from Q64, Schur index 2 ρ18 2 -2 2 0 0 0 -2 -√2 √2 0 0 0 ζ3210-ζ326 ζ3214-ζ322 -ζ3214+ζ322 -ζ3210+ζ326 -√2 √2 ζ3213-ζ323 ζ329-ζ327 ζ3231-ζ3217 -ζ3231+ζ3217 -ζ3227+ζ3221 ζ3227-ζ3221 -ζ3213+ζ323 -ζ329+ζ327 ζ3214-ζ322 -ζ3210+ζ326 -ζ3214+ζ322 ζ3210-ζ326 symplectic lifted from Q64, Schur index 2 ρ19 2 -2 2 0 0 0 -2 -√2 √2 0 0 0 -ζ3210+ζ326 -ζ3214+ζ322 ζ3214-ζ322 ζ3210-ζ326 -√2 √2 -ζ3227+ζ3221 -ζ3231+ζ3217 ζ329-ζ327 -ζ329+ζ327 -ζ3213+ζ323 ζ3213-ζ323 ζ3227-ζ3221 ζ3231-ζ3217 -ζ3214+ζ322 ζ3210-ζ326 ζ3214-ζ322 -ζ3210+ζ326 symplectic lifted from Q64, Schur index 2 ρ20 2 -2 2 0 0 0 -2 -√2 √2 0 0 0 -ζ3210+ζ326 -ζ3214+ζ322 ζ3214-ζ322 ζ3210-ζ326 -√2 √2 ζ3227-ζ3221 ζ3231-ζ3217 -ζ329+ζ327 ζ329-ζ327 ζ3213-ζ323 -ζ3213+ζ323 -ζ3227+ζ3221 -ζ3231+ζ3217 -ζ3214+ζ322 ζ3210-ζ326 ζ3214-ζ322 -ζ3210+ζ326 symplectic lifted from Q64, Schur index 2 ρ21 2 -2 2 0 0 0 -2 -√2 √2 0 0 0 ζ3210-ζ326 ζ3214-ζ322 -ζ3214+ζ322 -ζ3210+ζ326 -√2 √2 -ζ3213+ζ323 -ζ329+ζ327 -ζ3231+ζ3217 ζ3231-ζ3217 ζ3227-ζ3221 -ζ3227+ζ3221 ζ3213-ζ323 ζ329-ζ327 ζ3214-ζ322 -ζ3210+ζ326 -ζ3214+ζ322 ζ3210-ζ326 symplectic lifted from Q64, Schur index 2 ρ22 2 2 -1 2 0 0 -1 2 2 -1 -√-3 √-3 -2 -2 -2 -2 -1 -1 0 0 0 0 0 0 0 0 1 1 1 1 complex lifted from C3⋊D4 ρ23 2 2 -1 2 0 0 -1 2 2 -1 √-3 -√-3 -2 -2 -2 -2 -1 -1 0 0 0 0 0 0 0 0 1 1 1 1 complex lifted from C3⋊D4 ρ24 4 4 -2 4 0 0 -2 -4 -4 -2 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 orthogonal lifted from D4⋊S3, Schur index 2 ρ25 4 4 -2 -4 0 0 -2 0 0 2 0 0 2√2 -2√2 -2√2 2√2 0 0 0 0 0 0 0 0 0 0 √2 -√2 √2 -√2 orthogonal lifted from C3⋊D16, Schur index 2 ρ26 4 4 -2 -4 0 0 -2 0 0 2 0 0 -2√2 2√2 2√2 -2√2 0 0 0 0 0 0 0 0 0 0 -√2 √2 -√2 √2 orthogonal lifted from C3⋊D16, Schur index 2 ρ27 4 -4 -2 0 0 0 2 -2√2 2√2 0 0 0 2ζ165-2ζ163 -2ζ1615+2ζ169 2ζ1615-2ζ169 -2ζ165+2ζ163 √2 -√2 0 0 0 0 0 0 0 0 -ζ167+ζ16 ζ165-ζ163 ζ167-ζ16 -ζ165+ζ163 symplectic faithful, Schur index 2 ρ28 4 -4 -2 0 0 0 2 2√2 -2√2 0 0 0 -2ζ1615+2ζ169 -2ζ165+2ζ163 2ζ165-2ζ163 2ζ1615-2ζ169 -√2 √2 0 0 0 0 0 0 0 0 ζ165-ζ163 ζ167-ζ16 -ζ165+ζ163 -ζ167+ζ16 symplectic faithful, Schur index 2 ρ29 4 -4 -2 0 0 0 2 -2√2 2√2 0 0 0 -2ζ165+2ζ163 2ζ1615-2ζ169 -2ζ1615+2ζ169 2ζ165-2ζ163 √2 -√2 0 0 0 0 0 0 0 0 ζ167-ζ16 -ζ165+ζ163 -ζ167+ζ16 ζ165-ζ163 symplectic faithful, Schur index 2 ρ30 4 -4 -2 0 0 0 2 2√2 -2√2 0 0 0 2ζ1615-2ζ169 2ζ165-2ζ163 -2ζ165+2ζ163 -2ζ1615+2ζ169 -√2 √2 0 0 0 0 0 0 0 0 -ζ165+ζ163 -ζ167+ζ16 ζ165-ζ163 ζ167-ζ16 symplectic faithful, Schur index 2

Smallest permutation representation of C3⋊Q64
Regular action on 192 points
Generators in S192
```(1 184 39)(2 40 185)(3 186 41)(4 42 187)(5 188 43)(6 44 189)(7 190 45)(8 46 191)(9 192 47)(10 48 161)(11 162 49)(12 50 163)(13 164 51)(14 52 165)(15 166 53)(16 54 167)(17 168 55)(18 56 169)(19 170 57)(20 58 171)(21 172 59)(22 60 173)(23 174 61)(24 62 175)(25 176 63)(26 64 177)(27 178 33)(28 34 179)(29 180 35)(30 36 181)(31 182 37)(32 38 183)(65 155 98)(66 99 156)(67 157 100)(68 101 158)(69 159 102)(70 103 160)(71 129 104)(72 105 130)(73 131 106)(74 107 132)(75 133 108)(76 109 134)(77 135 110)(78 111 136)(79 137 112)(80 113 138)(81 139 114)(82 115 140)(83 141 116)(84 117 142)(85 143 118)(86 119 144)(87 145 120)(88 121 146)(89 147 122)(90 123 148)(91 149 124)(92 125 150)(93 151 126)(94 127 152)(95 153 128)(96 97 154)
(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 86 17 70)(2 85 18 69)(3 84 19 68)(4 83 20 67)(5 82 21 66)(6 81 22 65)(7 80 23 96)(8 79 24 95)(9 78 25 94)(10 77 26 93)(11 76 27 92)(12 75 28 91)(13 74 29 90)(14 73 30 89)(15 72 31 88)(16 71 32 87)(33 150 49 134)(34 149 50 133)(35 148 51 132)(36 147 52 131)(37 146 53 130)(38 145 54 129)(39 144 55 160)(40 143 56 159)(41 142 57 158)(42 141 58 157)(43 140 59 156)(44 139 60 155)(45 138 61 154)(46 137 62 153)(47 136 63 152)(48 135 64 151)(97 190 113 174)(98 189 114 173)(99 188 115 172)(100 187 116 171)(101 186 117 170)(102 185 118 169)(103 184 119 168)(104 183 120 167)(105 182 121 166)(106 181 122 165)(107 180 123 164)(108 179 124 163)(109 178 125 162)(110 177 126 161)(111 176 127 192)(112 175 128 191)```

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

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

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

Matrix representation of C3⋊Q64 in GL4(𝔽97) generated by

 1 0 0 0 0 1 0 0 0 0 0 1 0 0 96 96
,
 27 57 0 0 40 27 0 0 0 0 47 80 0 0 33 50
,
 13 86 0 0 86 84 0 0 0 0 56 15 0 0 82 41
`G:=sub<GL(4,GF(97))| [1,0,0,0,0,1,0,0,0,0,0,96,0,0,1,96],[27,40,0,0,57,27,0,0,0,0,47,33,0,0,80,50],[13,86,0,0,86,84,0,0,0,0,56,82,0,0,15,41] >;`

C3⋊Q64 in GAP, Magma, Sage, TeX

`C_3\rtimes Q_{64}`
`% in TeX`

`G:=Group("C3:Q64");`
`// GroupNames label`

`G:=SmallGroup(192,81);`
`// by ID`

`G=gap.SmallGroup(192,81);`
`# by ID`

`G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,224,85,232,254,135,142,675,346,192,1684,851,102,6278]);`
`// Polycyclic`

`G:=Group<a,b,c|a^3=b^32=1,c^2=b^16,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=b^-1>;`
`// generators/relations`

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