Copied to
clipboard

## G = D20.3Dic3order 480 = 25·3·5

### The non-split extension by D20 of Dic3 acting through Inn(D20)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C30 — D20.3Dic3
 Chief series C1 — C5 — C15 — C30 — C60 — D5×C12 — D5×C3⋊C8 — D20.3Dic3
 Lower central C15 — C30 — D20.3Dic3
 Upper central C1 — C4 — C2×C4

Generators and relations for D20.3Dic3
G = < a,b,c,d | a20=b2=1, c6=a10, d2=a10c3, bab=a-1, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c5 >

Subgroups: 428 in 124 conjugacy classes, 60 normal (38 characteristic)
C1, C2, C2 [×3], C3, C4 [×2], C4 [×2], C22, C22 [×2], C5, C6, C6 [×3], C8 [×4], C2×C4, C2×C4 [×2], D4 [×3], Q8, D5 [×2], C10, C10, C12 [×2], C12 [×2], C2×C6, C2×C6 [×2], C15, C2×C8 [×3], M4(2) [×3], C4○D4, Dic5 [×2], C20 [×2], D10 [×2], C2×C10, C3⋊C8 [×2], C3⋊C8 [×2], C2×C12, C2×C12 [×2], C3×D4 [×3], C3×Q8, C3×D5 [×2], C30, C30, C8○D4, C52C8 [×2], C40 [×2], Dic10, C4×D5 [×2], D20, C5⋊D4 [×2], C2×C20, C2×C3⋊C8, C2×C3⋊C8 [×2], C4.Dic3 [×3], C3×C4○D4, C3×Dic5 [×2], C60 [×2], C6×D5 [×2], C2×C30, C8×D5 [×2], C8⋊D5 [×2], C4.Dic5, C2×C40, C4○D20, D4.Dic3, C5×C3⋊C8 [×2], C153C8 [×2], C3×Dic10, D5×C12 [×2], C3×D20, C3×C5⋊D4 [×2], C2×C60, D20.3C4, D5×C3⋊C8 [×2], C20.32D6 [×2], C10×C3⋊C8, C60.7C4, C3×C4○D20, D20.3Dic3
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], S3, C2×C4 [×6], C23, D5, Dic3 [×4], D6 [×3], C22×C4, D10 [×3], C2×Dic3 [×6], C22×S3, C8○D4, C4×D5 [×2], C22×D5, C22×Dic3, S3×D5, C2×C4×D5, D4.Dic3, D5×Dic3 [×2], C2×S3×D5, D20.3C4, C2×D5×Dic3, D20.3Dic3

Smallest permutation representation of D20.3Dic3
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 20)(2 19)(3 18)(4 17)(5 16)(6 15)(7 14)(8 13)(9 12)(10 11)(21 32)(22 31)(23 30)(24 29)(25 28)(26 27)(33 40)(34 39)(35 38)(36 37)(41 50)(42 49)(43 48)(44 47)(45 46)(51 60)(52 59)(53 58)(54 57)(55 56)(61 78)(62 77)(63 76)(64 75)(65 74)(66 73)(67 72)(68 71)(69 70)(79 80)(81 86)(82 85)(83 84)(87 100)(88 99)(89 98)(90 97)(91 96)(92 95)(93 94)(101 120)(102 119)(103 118)(104 117)(105 116)(106 115)(107 114)(108 113)(109 112)(110 111)(121 138)(122 137)(123 136)(124 135)(125 134)(126 133)(127 132)(128 131)(129 130)(139 140)(141 142)(143 160)(144 159)(145 158)(146 157)(147 156)(148 155)(149 154)(150 153)(151 152)(161 180)(162 179)(163 178)(164 177)(165 176)(166 175)(167 174)(168 173)(169 172)(170 171)(181 196)(182 195)(183 194)(184 193)(185 192)(186 191)(187 190)(188 189)(197 200)(198 199)(201 202)(203 220)(204 219)(205 218)(206 217)(207 216)(208 215)(209 214)(210 213)(211 212)(221 226)(222 225)(223 224)(227 240)(228 239)(229 238)(230 237)(231 236)(232 235)(233 234)
(1 37 101 224 161 130 11 27 111 234 171 140)(2 38 102 225 162 131 12 28 112 235 172 121)(3 39 103 226 163 132 13 29 113 236 173 122)(4 40 104 227 164 133 14 30 114 237 174 123)(5 21 105 228 165 134 15 31 115 238 175 124)(6 22 106 229 166 135 16 32 116 239 176 125)(7 23 107 230 167 136 17 33 117 240 177 126)(8 24 108 231 168 137 18 34 118 221 178 127)(9 25 109 232 169 138 19 35 119 222 179 128)(10 26 110 233 170 139 20 36 120 223 180 129)(41 99 194 157 65 207 51 89 184 147 75 217)(42 100 195 158 66 208 52 90 185 148 76 218)(43 81 196 159 67 209 53 91 186 149 77 219)(44 82 197 160 68 210 54 92 187 150 78 220)(45 83 198 141 69 211 55 93 188 151 79 201)(46 84 199 142 70 212 56 94 189 152 80 202)(47 85 200 143 71 213 57 95 190 153 61 203)(48 86 181 144 72 214 58 96 191 154 62 204)(49 87 182 145 73 215 59 97 192 155 63 205)(50 88 183 146 74 216 60 98 193 156 64 206)
(1 94 234 70 11 84 224 80)(2 95 235 71 12 85 225 61)(3 96 236 72 13 86 226 62)(4 97 237 73 14 87 227 63)(5 98 238 74 15 88 228 64)(6 99 239 75 16 89 229 65)(7 100 240 76 17 90 230 66)(8 81 221 77 18 91 231 67)(9 82 222 78 19 92 232 68)(10 83 223 79 20 93 233 69)(21 50 175 156 31 60 165 146)(22 51 176 157 32 41 166 147)(23 52 177 158 33 42 167 148)(24 53 178 159 34 43 168 149)(25 54 179 160 35 44 169 150)(26 55 180 141 36 45 170 151)(27 56 161 142 37 46 171 152)(28 57 162 143 38 47 172 153)(29 58 163 144 39 48 173 154)(30 59 164 145 40 49 174 155)(101 212 140 199 111 202 130 189)(102 213 121 200 112 203 131 190)(103 214 122 181 113 204 132 191)(104 215 123 182 114 205 133 192)(105 216 124 183 115 206 134 193)(106 217 125 184 116 207 135 194)(107 218 126 185 117 208 136 195)(108 219 127 186 118 209 137 196)(109 220 128 187 119 210 138 197)(110 201 129 188 120 211 139 198)

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

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

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

78 conjugacy classes

 class 1 2A 2B 2C 2D 3 4A 4B 4C 4D 4E 5A 5B 6A 6B 6C 6D 8A 8B 8C 8D 8E 8F 8G 8H 8I 8J 10A ··· 10F 12A 12B 12C 12D 12E 15A 15B 20A ··· 20H 30A ··· 30F 40A ··· 40P 60A ··· 60H order 1 2 2 2 2 3 4 4 4 4 4 5 5 6 6 6 6 8 8 8 8 8 8 8 8 8 8 10 ··· 10 12 12 12 12 12 15 15 20 ··· 20 30 ··· 30 40 ··· 40 60 ··· 60 size 1 1 2 10 10 2 1 1 2 10 10 2 2 2 4 20 20 3 3 3 3 6 6 30 30 30 30 2 ··· 2 2 2 4 20 20 4 4 2 ··· 2 4 ··· 4 6 ··· 6 4 ··· 4

78 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 type + + + + + + + + - + - - + + + + - + - image C1 C2 C2 C2 C2 C2 C4 C4 C4 S3 D5 Dic3 D6 Dic3 Dic3 D6 D10 D10 C8○D4 C4×D5 C4×D5 D20.3C4 S3×D5 D4.Dic3 D5×Dic3 C2×S3×D5 D5×Dic3 D20.3Dic3 kernel D20.3Dic3 D5×C3⋊C8 C20.32D6 C10×C3⋊C8 C60.7C4 C3×C4○D20 C3×Dic10 C3×D20 C3×C5⋊D4 C4○D20 C2×C3⋊C8 Dic10 C4×D5 D20 C5⋊D4 C2×C20 C3⋊C8 C2×C12 C15 C12 C2×C6 C3 C2×C4 C5 C4 C4 C22 C1 # reps 1 2 2 1 1 1 2 2 4 1 2 1 2 1 2 1 4 2 4 4 4 16 2 2 2 2 2 8

Matrix representation of D20.3Dic3 in GL4(𝔽241) generated by

 156 200 0 0 41 119 0 0 0 0 1 0 0 0 0 1
,
 156 200 0 0 41 85 0 0 0 0 1 0 0 0 0 1
,
 177 0 0 0 0 177 0 0 0 0 1 5 0 0 144 239
,
 30 0 0 0 0 30 0 0 0 0 150 151 0 0 92 91
G:=sub<GL(4,GF(241))| [156,41,0,0,200,119,0,0,0,0,1,0,0,0,0,1],[156,41,0,0,200,85,0,0,0,0,1,0,0,0,0,1],[177,0,0,0,0,177,0,0,0,0,1,144,0,0,5,239],[30,0,0,0,0,30,0,0,0,0,150,92,0,0,151,91] >;

D20.3Dic3 in GAP, Magma, Sage, TeX

D_{20}._3{\rm Dic}_3
% in TeX

G:=Group("D20.3Dic3");
// GroupNames label

G:=SmallGroup(480,359);
// by ID

G=gap.SmallGroup(480,359);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,64,422,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^20=b^2=1,c^6=a^10,d^2=a^10*c^3,b*a*b=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^5>;
// generators/relations

׿
×
𝔽