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G = Dic6.D10order 480 = 25·3·5

2nd non-split extension by Dic6 of D10 acting via D10/C5=C22

Series: Derived Chief Lower central Upper central

 Derived series C1 — C60 — Dic6.D10
 Chief series C1 — C5 — C15 — C30 — C60 — C3×D20 — D20⋊S3 — Dic6.D10
 Lower central C15 — C30 — C60 — Dic6.D10
 Upper central C1 — C2 — C4 — C8

Generators and relations for Dic6.D10
G = < a,b,c,d | a20=c6=1, b2=d2=a10, bab-1=cac-1=a-1, dad-1=a9, cbc-1=a15b, bd=db, dcd-1=c-1 >

Subgroups: 716 in 124 conjugacy classes, 38 normal (all characteristic)
C1, C2, C2 [×3], C3, C4, C4 [×3], C22 [×3], C5, S3 [×2], C6, C6, C8, C8, C2×C4 [×3], D4 [×4], Q8 [×2], D5 [×2], C10, C10, Dic3 [×2], C12, C12, D6 [×2], C2×C6, C15, C2×C8, D8, SD16 [×2], Q16, C4○D4 [×2], Dic5 [×2], C20, C20, D10 [×2], C2×C10, C3⋊C8, C24, Dic6, C4×S3 [×2], D12, D12, C2×Dic3, C3⋊D4, C3×D4, C3×Q8, C5×S3, C3×D5, D15, C30, C4○D8, C52C8, C40, Dic10, C4×D5 [×2], D20, D20, C2×Dic5, C5⋊D4, C5×D4, C5×Q8, S3×C8, C24⋊C2, D4⋊S3, C3⋊Q16, C3×SD16, D42S3, Q83S3, C5×Dic3, C3×Dic5, Dic15, C60, C6×D5, S3×C10, D30, C8×D5, C40⋊C2, D4⋊D5, C5⋊Q16, C5×SD16, D42D5, Q82D5, Q8.7D6, C153C8, C120, D5×Dic3, S3×Dic5, C3⋊D20, C5⋊D12, C3×Dic10, C3×D20, C5×Dic6, C5×D12, C4×D15, SD163D5, C15⋊D8, C15⋊Q16, C3×C40⋊C2, C5×C24⋊C2, C8×D15, D20⋊S3, D12⋊D5, Dic6.D10
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], C22×S3, C4○D8, C22×D5, S3×D4, S3×D5, D4×D5, Q8.7D6, C2×S3×D5, SD163D5, C20⋊D6, Dic6.D10

Smallest permutation representation of Dic6.D10
On 240 points
Generators in S240
(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)
(1 202 11 212)(2 201 12 211)(3 220 13 210)(4 219 14 209)(5 218 15 208)(6 217 16 207)(7 216 17 206)(8 215 18 205)(9 214 19 204)(10 213 20 203)(21 55 31 45)(22 54 32 44)(23 53 33 43)(24 52 34 42)(25 51 35 41)(26 50 36 60)(27 49 37 59)(28 48 38 58)(29 47 39 57)(30 46 40 56)(61 182 71 192)(62 181 72 191)(63 200 73 190)(64 199 74 189)(65 198 75 188)(66 197 76 187)(67 196 77 186)(68 195 78 185)(69 194 79 184)(70 193 80 183)(81 110 91 120)(82 109 92 119)(83 108 93 118)(84 107 94 117)(85 106 95 116)(86 105 96 115)(87 104 97 114)(88 103 98 113)(89 102 99 112)(90 101 100 111)(121 224 131 234)(122 223 132 233)(123 222 133 232)(124 221 134 231)(125 240 135 230)(126 239 136 229)(127 238 137 228)(128 237 138 227)(129 236 139 226)(130 235 140 225)(141 172 151 162)(142 171 152 161)(143 170 153 180)(144 169 154 179)(145 168 155 178)(146 167 156 177)(147 166 157 176)(148 165 158 175)(149 164 159 174)(150 163 160 173)
(1 179 181 41 102 133)(2 178 182 60 103 132)(3 177 183 59 104 131)(4 176 184 58 105 130)(5 175 185 57 106 129)(6 174 186 56 107 128)(7 173 187 55 108 127)(8 172 188 54 109 126)(9 171 189 53 110 125)(10 170 190 52 111 124)(11 169 191 51 112 123)(12 168 192 50 113 122)(13 167 193 49 114 121)(14 166 194 48 115 140)(15 165 195 47 116 139)(16 164 196 46 117 138)(17 163 197 45 118 137)(18 162 198 44 119 136)(19 161 199 43 120 135)(20 180 200 42 101 134)(21 88 228 211 160 61)(22 87 229 210 141 80)(23 86 230 209 142 79)(24 85 231 208 143 78)(25 84 232 207 144 77)(26 83 233 206 145 76)(27 82 234 205 146 75)(28 81 235 204 147 74)(29 100 236 203 148 73)(30 99 237 202 149 72)(31 98 238 201 150 71)(32 97 239 220 151 70)(33 96 240 219 152 69)(34 95 221 218 153 68)(35 94 222 217 154 67)(36 93 223 216 155 66)(37 92 224 215 156 65)(38 91 225 214 157 64)(39 90 226 213 158 63)(40 89 227 212 159 62)
(1 196 11 186)(2 185 12 195)(3 194 13 184)(4 183 14 193)(5 192 15 182)(6 181 16 191)(7 190 17 200)(8 199 18 189)(9 188 19 198)(10 197 20 187)(21 231 31 221)(22 240 32 230)(23 229 33 239)(24 238 34 228)(25 227 35 237)(26 236 36 226)(27 225 37 235)(28 234 38 224)(29 223 39 233)(30 232 40 222)(41 138 51 128)(42 127 52 137)(43 136 53 126)(44 125 54 135)(45 134 55 124)(46 123 56 133)(47 132 57 122)(48 121 58 131)(49 130 59 140)(50 139 60 129)(61 208 71 218)(62 217 72 207)(63 206 73 216)(64 215 74 205)(65 204 75 214)(66 213 76 203)(67 202 77 212)(68 211 78 201)(69 220 79 210)(70 209 80 219)(81 82 91 92)(83 100 93 90)(84 89 94 99)(85 98 95 88)(86 87 96 97)(101 108 111 118)(102 117 112 107)(103 106 113 116)(104 115 114 105)(109 120 119 110)(141 152 151 142)(143 150 153 160)(144 159 154 149)(145 148 155 158)(146 157 156 147)(161 162 171 172)(163 180 173 170)(164 169 174 179)(165 178 175 168)(166 167 176 177)

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

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

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

51 conjugacy classes

 class 1 2A 2B 2C 2D 3 4A 4B 4C 4D 4E 5A 5B 6A 6B 8A 8B 8C 8D 10A 10B 10C 10D 12A 12B 15A 15B 20A 20B 20C 20D 24A 24B 30A 30B 40A 40B 40C 40D 60A 60B 60C 60D 120A ··· 120H order 1 2 2 2 2 3 4 4 4 4 4 5 5 6 6 8 8 8 8 10 10 10 10 12 12 15 15 20 20 20 20 24 24 30 30 40 40 40 40 60 60 60 60 120 ··· 120 size 1 1 12 20 30 2 2 12 15 15 20 2 2 2 40 2 2 30 30 2 2 24 24 4 40 4 4 4 4 24 24 4 4 4 4 4 4 4 4 4 4 4 4 4 ··· 4

51 irreducible representations

 dim 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 type + + + + + + + + + + + + + + + + + + + + + + image C1 C2 C2 C2 C2 C2 C2 C2 S3 D4 D4 D5 D6 D6 D6 D10 D10 D10 C4○D8 S3×D4 S3×D5 D4×D5 Q8.7D6 C2×S3×D5 SD16⋊3D5 C20⋊D6 Dic6.D10 kernel Dic6.D10 C15⋊D8 C15⋊Q16 C3×C40⋊C2 C5×C24⋊C2 C8×D15 D20⋊S3 D12⋊D5 C40⋊C2 Dic15 D30 C24⋊C2 C40 Dic10 D20 C24 Dic6 D12 C15 C10 C8 C6 C5 C4 C3 C2 C1 # reps 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 2 2 4 1 2 2 2 2 4 4 8

Matrix representation of Dic6.D10 in GL6(𝔽241)

 0 1 0 0 0 0 240 189 0 0 0 0 0 0 64 0 0 0 0 0 16 177 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 1 0 0 0 0 0 189 240 0 0 0 0 0 0 77 107 0 0 0 0 109 164 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 240 0 0 0 0 0 52 1 0 0 0 0 0 0 141 77 0 0 0 0 180 100 0 0 0 0 0 0 240 49 0 0 0 0 177 2
,
 1 0 0 0 0 0 189 240 0 0 0 0 0 0 177 0 0 0 0 0 0 177 0 0 0 0 0 0 1 192 0 0 0 0 0 240

G:=sub<GL(6,GF(241))| [0,240,0,0,0,0,1,189,0,0,0,0,0,0,64,16,0,0,0,0,0,177,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,189,0,0,0,0,0,240,0,0,0,0,0,0,77,109,0,0,0,0,107,164,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[240,52,0,0,0,0,0,1,0,0,0,0,0,0,141,180,0,0,0,0,77,100,0,0,0,0,0,0,240,177,0,0,0,0,49,2],[1,189,0,0,0,0,0,240,0,0,0,0,0,0,177,0,0,0,0,0,0,177,0,0,0,0,0,0,1,0,0,0,0,0,192,240] >;

Dic6.D10 in GAP, Magma, Sage, TeX

{\rm Dic}_6.D_{10}
% in TeX

G:=Group("Dic6.D10");
// GroupNames label

G:=SmallGroup(480,352);
// by ID

G=gap.SmallGroup(480,352);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,120,254,135,58,675,346,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^20=c^6=1,b^2=d^2=a^10,b*a*b^-1=c*a*c^-1=a^-1,d*a*d^-1=a^9,c*b*c^-1=a^15*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations

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