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## G = C5×D6⋊C8order 480 = 25·3·5

### Direct product of C5 and D6⋊C8

Series: Derived Chief Lower central Upper central

 Derived series C1 — C6 — C5×D6⋊C8
 Chief series C1 — C3 — C6 — C2×C6 — C2×C12 — C2×C60 — S3×C2×C20 — C5×D6⋊C8
 Lower central C3 — C6 — C5×D6⋊C8
 Upper central C1 — C2×C20 — C2×C40

Generators and relations for C5×D6⋊C8
G = < a,b,c,d | a5=b6=c2=d8=1, ab=ba, ac=ca, ad=da, cbc=b-1, bd=db, dcd-1=b3c >

Subgroups: 228 in 100 conjugacy classes, 50 normal (46 characteristic)
C1, C2 [×3], C2 [×2], C3, C4 [×2], C4, C22, C22 [×4], C5, S3 [×2], C6 [×3], C8 [×2], C2×C4, C2×C4 [×3], C23, C10 [×3], C10 [×2], Dic3, C12 [×2], D6 [×2], D6 [×2], C2×C6, C15, C2×C8, C2×C8, C22×C4, C20 [×2], C20, C2×C10, C2×C10 [×4], C3⋊C8, C24, C4×S3 [×2], C2×Dic3, C2×C12, C22×S3, C5×S3 [×2], C30 [×3], C22⋊C8, C40 [×2], C2×C20, C2×C20 [×3], C22×C10, C2×C3⋊C8, C2×C24, S3×C2×C4, C5×Dic3, C60 [×2], S3×C10 [×2], S3×C10 [×2], C2×C30, C2×C40, C2×C40, C22×C20, D6⋊C8, C5×C3⋊C8, C120, S3×C20 [×2], C10×Dic3, C2×C60, S3×C2×C10, C5×C22⋊C8, C10×C3⋊C8, C2×C120, S3×C2×C20, C5×D6⋊C8
Quotients: C1, C2 [×3], C4 [×2], C22, C5, S3, C8 [×2], C2×C4, D4 [×2], C10 [×3], D6, C22⋊C4, C2×C8, M4(2), C20 [×2], C2×C10, C4×S3, D12, C3⋊D4, C5×S3, C22⋊C8, C40 [×2], C2×C20, C5×D4 [×2], S3×C8, C8⋊S3, D6⋊C4, S3×C10, C5×C22⋊C4, C2×C40, C5×M4(2), D6⋊C8, S3×C20, C5×D12, C5×C3⋊D4, C5×C22⋊C8, S3×C40, C5×C8⋊S3, C5×D6⋊C4, C5×D6⋊C8

Smallest permutation representation of C5×D6⋊C8
On 240 points
Generators in S240
(1 15 119 219 95)(2 16 120 220 96)(3 9 113 221 89)(4 10 114 222 90)(5 11 115 223 91)(6 12 116 224 92)(7 13 117 217 93)(8 14 118 218 94)(17 44 152 170 29)(18 45 145 171 30)(19 46 146 172 31)(20 47 147 173 32)(21 48 148 174 25)(22 41 149 175 26)(23 42 150 176 27)(24 43 151 169 28)(33 141 189 57 165)(34 142 190 58 166)(35 143 191 59 167)(36 144 192 60 168)(37 137 185 61 161)(38 138 186 62 162)(39 139 187 63 163)(40 140 188 64 164)(49 153 71 193 177)(50 154 72 194 178)(51 155 65 195 179)(52 156 66 196 180)(53 157 67 197 181)(54 158 68 198 182)(55 159 69 199 183)(56 160 70 200 184)(73 121 225 97 201)(74 122 226 98 202)(75 123 227 99 203)(76 124 228 100 204)(77 125 229 101 205)(78 126 230 102 206)(79 127 231 103 207)(80 128 232 104 208)(81 133 237 105 213)(82 134 238 106 214)(83 135 239 107 215)(84 136 240 108 216)(85 129 233 109 209)(86 130 234 110 210)(87 131 235 111 211)(88 132 236 112 212)
(1 83 173 155 139 77)(2 84 174 156 140 78)(3 85 175 157 141 79)(4 86 176 158 142 80)(5 87 169 159 143 73)(6 88 170 160 144 74)(7 81 171 153 137 75)(8 82 172 154 138 76)(9 129 26 67 189 127)(10 130 27 68 190 128)(11 131 28 69 191 121)(12 132 29 70 192 122)(13 133 30 71 185 123)(14 134 31 72 186 124)(15 135 32 65 187 125)(16 136 25 66 188 126)(17 200 60 226 116 236)(18 193 61 227 117 237)(19 194 62 228 118 238)(20 195 63 229 119 239)(21 196 64 230 120 240)(22 197 57 231 113 233)(23 198 58 232 114 234)(24 199 59 225 115 235)(33 207 89 209 149 53)(34 208 90 210 150 54)(35 201 91 211 151 55)(36 202 92 212 152 56)(37 203 93 213 145 49)(38 204 94 214 146 50)(39 205 95 215 147 51)(40 206 96 216 148 52)(41 181 165 103 221 109)(42 182 166 104 222 110)(43 183 167 97 223 111)(44 184 168 98 224 112)(45 177 161 99 217 105)(46 178 162 100 218 106)(47 179 163 101 219 107)(48 180 164 102 220 108)
(1 77)(2 174)(3 79)(4 176)(5 73)(6 170)(7 75)(8 172)(9 127)(10 27)(11 121)(12 29)(13 123)(14 31)(15 125)(16 25)(17 116)(18 193)(19 118)(20 195)(21 120)(22 197)(23 114)(24 199)(26 67)(28 69)(30 71)(32 65)(33 209)(35 211)(37 213)(39 215)(41 181)(42 222)(43 183)(44 224)(45 177)(46 218)(47 179)(48 220)(49 145)(50 204)(51 147)(52 206)(53 149)(54 208)(55 151)(56 202)(57 233)(59 235)(61 237)(63 239)(66 126)(68 128)(70 122)(72 124)(74 160)(76 154)(78 156)(80 158)(81 137)(83 139)(85 141)(87 143)(89 207)(90 150)(91 201)(92 152)(93 203)(94 146)(95 205)(96 148)(97 223)(98 184)(99 217)(100 178)(101 219)(102 180)(103 221)(104 182)(105 161)(107 163)(109 165)(111 167)(113 231)(115 225)(117 227)(119 229)(129 189)(131 191)(133 185)(135 187)(153 171)(155 173)(157 175)(159 169)(194 228)(196 230)(198 232)(200 226)
(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)(193 194 195 196 197 198 199 200)(201 202 203 204 205 206 207 208)(209 210 211 212 213 214 215 216)(217 218 219 220 221 222 223 224)(225 226 227 228 229 230 231 232)(233 234 235 236 237 238 239 240)

G:=sub<Sym(240)| (1,15,119,219,95)(2,16,120,220,96)(3,9,113,221,89)(4,10,114,222,90)(5,11,115,223,91)(6,12,116,224,92)(7,13,117,217,93)(8,14,118,218,94)(17,44,152,170,29)(18,45,145,171,30)(19,46,146,172,31)(20,47,147,173,32)(21,48,148,174,25)(22,41,149,175,26)(23,42,150,176,27)(24,43,151,169,28)(33,141,189,57,165)(34,142,190,58,166)(35,143,191,59,167)(36,144,192,60,168)(37,137,185,61,161)(38,138,186,62,162)(39,139,187,63,163)(40,140,188,64,164)(49,153,71,193,177)(50,154,72,194,178)(51,155,65,195,179)(52,156,66,196,180)(53,157,67,197,181)(54,158,68,198,182)(55,159,69,199,183)(56,160,70,200,184)(73,121,225,97,201)(74,122,226,98,202)(75,123,227,99,203)(76,124,228,100,204)(77,125,229,101,205)(78,126,230,102,206)(79,127,231,103,207)(80,128,232,104,208)(81,133,237,105,213)(82,134,238,106,214)(83,135,239,107,215)(84,136,240,108,216)(85,129,233,109,209)(86,130,234,110,210)(87,131,235,111,211)(88,132,236,112,212), (1,83,173,155,139,77)(2,84,174,156,140,78)(3,85,175,157,141,79)(4,86,176,158,142,80)(5,87,169,159,143,73)(6,88,170,160,144,74)(7,81,171,153,137,75)(8,82,172,154,138,76)(9,129,26,67,189,127)(10,130,27,68,190,128)(11,131,28,69,191,121)(12,132,29,70,192,122)(13,133,30,71,185,123)(14,134,31,72,186,124)(15,135,32,65,187,125)(16,136,25,66,188,126)(17,200,60,226,116,236)(18,193,61,227,117,237)(19,194,62,228,118,238)(20,195,63,229,119,239)(21,196,64,230,120,240)(22,197,57,231,113,233)(23,198,58,232,114,234)(24,199,59,225,115,235)(33,207,89,209,149,53)(34,208,90,210,150,54)(35,201,91,211,151,55)(36,202,92,212,152,56)(37,203,93,213,145,49)(38,204,94,214,146,50)(39,205,95,215,147,51)(40,206,96,216,148,52)(41,181,165,103,221,109)(42,182,166,104,222,110)(43,183,167,97,223,111)(44,184,168,98,224,112)(45,177,161,99,217,105)(46,178,162,100,218,106)(47,179,163,101,219,107)(48,180,164,102,220,108), (1,77)(2,174)(3,79)(4,176)(5,73)(6,170)(7,75)(8,172)(9,127)(10,27)(11,121)(12,29)(13,123)(14,31)(15,125)(16,25)(17,116)(18,193)(19,118)(20,195)(21,120)(22,197)(23,114)(24,199)(26,67)(28,69)(30,71)(32,65)(33,209)(35,211)(37,213)(39,215)(41,181)(42,222)(43,183)(44,224)(45,177)(46,218)(47,179)(48,220)(49,145)(50,204)(51,147)(52,206)(53,149)(54,208)(55,151)(56,202)(57,233)(59,235)(61,237)(63,239)(66,126)(68,128)(70,122)(72,124)(74,160)(76,154)(78,156)(80,158)(81,137)(83,139)(85,141)(87,143)(89,207)(90,150)(91,201)(92,152)(93,203)(94,146)(95,205)(96,148)(97,223)(98,184)(99,217)(100,178)(101,219)(102,180)(103,221)(104,182)(105,161)(107,163)(109,165)(111,167)(113,231)(115,225)(117,227)(119,229)(129,189)(131,191)(133,185)(135,187)(153,171)(155,173)(157,175)(159,169)(194,228)(196,230)(198,232)(200,226), (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)(193,194,195,196,197,198,199,200)(201,202,203,204,205,206,207,208)(209,210,211,212,213,214,215,216)(217,218,219,220,221,222,223,224)(225,226,227,228,229,230,231,232)(233,234,235,236,237,238,239,240)>;

G:=Group( (1,15,119,219,95)(2,16,120,220,96)(3,9,113,221,89)(4,10,114,222,90)(5,11,115,223,91)(6,12,116,224,92)(7,13,117,217,93)(8,14,118,218,94)(17,44,152,170,29)(18,45,145,171,30)(19,46,146,172,31)(20,47,147,173,32)(21,48,148,174,25)(22,41,149,175,26)(23,42,150,176,27)(24,43,151,169,28)(33,141,189,57,165)(34,142,190,58,166)(35,143,191,59,167)(36,144,192,60,168)(37,137,185,61,161)(38,138,186,62,162)(39,139,187,63,163)(40,140,188,64,164)(49,153,71,193,177)(50,154,72,194,178)(51,155,65,195,179)(52,156,66,196,180)(53,157,67,197,181)(54,158,68,198,182)(55,159,69,199,183)(56,160,70,200,184)(73,121,225,97,201)(74,122,226,98,202)(75,123,227,99,203)(76,124,228,100,204)(77,125,229,101,205)(78,126,230,102,206)(79,127,231,103,207)(80,128,232,104,208)(81,133,237,105,213)(82,134,238,106,214)(83,135,239,107,215)(84,136,240,108,216)(85,129,233,109,209)(86,130,234,110,210)(87,131,235,111,211)(88,132,236,112,212), (1,83,173,155,139,77)(2,84,174,156,140,78)(3,85,175,157,141,79)(4,86,176,158,142,80)(5,87,169,159,143,73)(6,88,170,160,144,74)(7,81,171,153,137,75)(8,82,172,154,138,76)(9,129,26,67,189,127)(10,130,27,68,190,128)(11,131,28,69,191,121)(12,132,29,70,192,122)(13,133,30,71,185,123)(14,134,31,72,186,124)(15,135,32,65,187,125)(16,136,25,66,188,126)(17,200,60,226,116,236)(18,193,61,227,117,237)(19,194,62,228,118,238)(20,195,63,229,119,239)(21,196,64,230,120,240)(22,197,57,231,113,233)(23,198,58,232,114,234)(24,199,59,225,115,235)(33,207,89,209,149,53)(34,208,90,210,150,54)(35,201,91,211,151,55)(36,202,92,212,152,56)(37,203,93,213,145,49)(38,204,94,214,146,50)(39,205,95,215,147,51)(40,206,96,216,148,52)(41,181,165,103,221,109)(42,182,166,104,222,110)(43,183,167,97,223,111)(44,184,168,98,224,112)(45,177,161,99,217,105)(46,178,162,100,218,106)(47,179,163,101,219,107)(48,180,164,102,220,108), (1,77)(2,174)(3,79)(4,176)(5,73)(6,170)(7,75)(8,172)(9,127)(10,27)(11,121)(12,29)(13,123)(14,31)(15,125)(16,25)(17,116)(18,193)(19,118)(20,195)(21,120)(22,197)(23,114)(24,199)(26,67)(28,69)(30,71)(32,65)(33,209)(35,211)(37,213)(39,215)(41,181)(42,222)(43,183)(44,224)(45,177)(46,218)(47,179)(48,220)(49,145)(50,204)(51,147)(52,206)(53,149)(54,208)(55,151)(56,202)(57,233)(59,235)(61,237)(63,239)(66,126)(68,128)(70,122)(72,124)(74,160)(76,154)(78,156)(80,158)(81,137)(83,139)(85,141)(87,143)(89,207)(90,150)(91,201)(92,152)(93,203)(94,146)(95,205)(96,148)(97,223)(98,184)(99,217)(100,178)(101,219)(102,180)(103,221)(104,182)(105,161)(107,163)(109,165)(111,167)(113,231)(115,225)(117,227)(119,229)(129,189)(131,191)(133,185)(135,187)(153,171)(155,173)(157,175)(159,169)(194,228)(196,230)(198,232)(200,226), (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)(193,194,195,196,197,198,199,200)(201,202,203,204,205,206,207,208)(209,210,211,212,213,214,215,216)(217,218,219,220,221,222,223,224)(225,226,227,228,229,230,231,232)(233,234,235,236,237,238,239,240) );

G=PermutationGroup([(1,15,119,219,95),(2,16,120,220,96),(3,9,113,221,89),(4,10,114,222,90),(5,11,115,223,91),(6,12,116,224,92),(7,13,117,217,93),(8,14,118,218,94),(17,44,152,170,29),(18,45,145,171,30),(19,46,146,172,31),(20,47,147,173,32),(21,48,148,174,25),(22,41,149,175,26),(23,42,150,176,27),(24,43,151,169,28),(33,141,189,57,165),(34,142,190,58,166),(35,143,191,59,167),(36,144,192,60,168),(37,137,185,61,161),(38,138,186,62,162),(39,139,187,63,163),(40,140,188,64,164),(49,153,71,193,177),(50,154,72,194,178),(51,155,65,195,179),(52,156,66,196,180),(53,157,67,197,181),(54,158,68,198,182),(55,159,69,199,183),(56,160,70,200,184),(73,121,225,97,201),(74,122,226,98,202),(75,123,227,99,203),(76,124,228,100,204),(77,125,229,101,205),(78,126,230,102,206),(79,127,231,103,207),(80,128,232,104,208),(81,133,237,105,213),(82,134,238,106,214),(83,135,239,107,215),(84,136,240,108,216),(85,129,233,109,209),(86,130,234,110,210),(87,131,235,111,211),(88,132,236,112,212)], [(1,83,173,155,139,77),(2,84,174,156,140,78),(3,85,175,157,141,79),(4,86,176,158,142,80),(5,87,169,159,143,73),(6,88,170,160,144,74),(7,81,171,153,137,75),(8,82,172,154,138,76),(9,129,26,67,189,127),(10,130,27,68,190,128),(11,131,28,69,191,121),(12,132,29,70,192,122),(13,133,30,71,185,123),(14,134,31,72,186,124),(15,135,32,65,187,125),(16,136,25,66,188,126),(17,200,60,226,116,236),(18,193,61,227,117,237),(19,194,62,228,118,238),(20,195,63,229,119,239),(21,196,64,230,120,240),(22,197,57,231,113,233),(23,198,58,232,114,234),(24,199,59,225,115,235),(33,207,89,209,149,53),(34,208,90,210,150,54),(35,201,91,211,151,55),(36,202,92,212,152,56),(37,203,93,213,145,49),(38,204,94,214,146,50),(39,205,95,215,147,51),(40,206,96,216,148,52),(41,181,165,103,221,109),(42,182,166,104,222,110),(43,183,167,97,223,111),(44,184,168,98,224,112),(45,177,161,99,217,105),(46,178,162,100,218,106),(47,179,163,101,219,107),(48,180,164,102,220,108)], [(1,77),(2,174),(3,79),(4,176),(5,73),(6,170),(7,75),(8,172),(9,127),(10,27),(11,121),(12,29),(13,123),(14,31),(15,125),(16,25),(17,116),(18,193),(19,118),(20,195),(21,120),(22,197),(23,114),(24,199),(26,67),(28,69),(30,71),(32,65),(33,209),(35,211),(37,213),(39,215),(41,181),(42,222),(43,183),(44,224),(45,177),(46,218),(47,179),(48,220),(49,145),(50,204),(51,147),(52,206),(53,149),(54,208),(55,151),(56,202),(57,233),(59,235),(61,237),(63,239),(66,126),(68,128),(70,122),(72,124),(74,160),(76,154),(78,156),(80,158),(81,137),(83,139),(85,141),(87,143),(89,207),(90,150),(91,201),(92,152),(93,203),(94,146),(95,205),(96,148),(97,223),(98,184),(99,217),(100,178),(101,219),(102,180),(103,221),(104,182),(105,161),(107,163),(109,165),(111,167),(113,231),(115,225),(117,227),(119,229),(129,189),(131,191),(133,185),(135,187),(153,171),(155,173),(157,175),(159,169),(194,228),(196,230),(198,232),(200,226)], [(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),(193,194,195,196,197,198,199,200),(201,202,203,204,205,206,207,208),(209,210,211,212,213,214,215,216),(217,218,219,220,221,222,223,224),(225,226,227,228,229,230,231,232),(233,234,235,236,237,238,239,240)])

180 conjugacy classes

 class 1 2A 2B 2C 2D 2E 3 4A 4B 4C 4D 4E 4F 5A 5B 5C 5D 6A 6B 6C 8A 8B 8C 8D 8E 8F 8G 8H 10A ··· 10L 10M ··· 10T 12A 12B 12C 12D 15A 15B 15C 15D 20A ··· 20P 20Q ··· 20X 24A ··· 24H 30A ··· 30L 40A ··· 40P 40Q ··· 40AF 60A ··· 60P 120A ··· 120AF order 1 2 2 2 2 2 3 4 4 4 4 4 4 5 5 5 5 6 6 6 8 8 8 8 8 8 8 8 10 ··· 10 10 ··· 10 12 12 12 12 15 15 15 15 20 ··· 20 20 ··· 20 24 ··· 24 30 ··· 30 40 ··· 40 40 ··· 40 60 ··· 60 120 ··· 120 size 1 1 1 1 6 6 2 1 1 1 1 6 6 1 1 1 1 2 2 2 2 2 2 2 6 6 6 6 1 ··· 1 6 ··· 6 2 2 2 2 2 2 2 2 1 ··· 1 6 ··· 6 2 ··· 2 2 ··· 2 2 ··· 2 6 ··· 6 2 ··· 2 2 ··· 2

180 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 type + + + + + + + + image C1 C2 C2 C2 C4 C4 C5 C8 C10 C10 C10 C20 C20 C40 S3 D4 D6 M4(2) D12 C3⋊D4 C4×S3 C5×S3 C5×D4 S3×C8 C8⋊S3 S3×C10 C5×M4(2) C5×D12 C5×C3⋊D4 S3×C20 S3×C40 C5×C8⋊S3 kernel C5×D6⋊C8 C10×C3⋊C8 C2×C120 S3×C2×C20 C10×Dic3 S3×C2×C10 D6⋊C8 S3×C10 C2×C3⋊C8 C2×C24 S3×C2×C4 C2×Dic3 C22×S3 D6 C2×C40 C60 C2×C20 C30 C20 C20 C2×C10 C2×C8 C12 C10 C10 C2×C4 C6 C4 C4 C22 C2 C2 # reps 1 1 1 1 2 2 4 8 4 4 4 8 8 32 1 2 1 2 2 2 2 4 8 4 4 4 8 8 8 8 16 16

Matrix representation of C5×D6⋊C8 in GL4(𝔽241) generated by

 205 0 0 0 0 205 0 0 0 0 91 0 0 0 0 91
,
 0 1 0 0 240 240 0 0 0 0 0 240 0 0 1 1
,
 0 1 0 0 1 0 0 0 0 0 0 240 0 0 240 0
,
 30 0 0 0 0 30 0 0 0 0 172 103 0 0 138 69
G:=sub<GL(4,GF(241))| [205,0,0,0,0,205,0,0,0,0,91,0,0,0,0,91],[0,240,0,0,1,240,0,0,0,0,0,1,0,0,240,1],[0,1,0,0,1,0,0,0,0,0,0,240,0,0,240,0],[30,0,0,0,0,30,0,0,0,0,172,138,0,0,103,69] >;

C5×D6⋊C8 in GAP, Magma, Sage, TeX

C_5\times D_6\rtimes C_8
% in TeX

G:=Group("C5xD6:C8");
// GroupNames label

G:=SmallGroup(480,139);
// by ID

G=gap.SmallGroup(480,139);
# by ID

G:=PCGroup([7,-2,-2,-5,-2,-2,-2,-3,589,148,136,15686]);
// Polycyclic

G:=Group<a,b,c,d|a^5=b^6=c^2=d^8=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c=b^-1,b*d=d*b,d*c*d^-1=b^3*c>;
// generators/relations

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