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G = D20.13D6order 480 = 25·3·5

13rd non-split extension by D20 of D6 acting via D6/C3=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D20.13D6, C60.32C23, Dic6.26D10, Dic30.9C22, C3⋊C8.7D10, C3⋊Q161D5, (D5×Dic6)⋊3C2, C157Q162C2, (C6×D5).13D4, (C4×D5).10D6, C6.149(D4×D5), (C5×Q8).19D6, Q8.15(S3×D5), C37(Q16⋊D5), C30.D46C2, C6.D206C2, C30.194(C2×D4), C53(Q8.14D6), Q82D5.3S3, (C3×Q8).19D10, C20.32D66C2, C1516(C8.C22), C20.32(C22×S3), C153C8.8C22, (C3×Dic5).71D4, C12.32(C22×D5), (Q8×C15).2C22, D10.20(C3⋊D4), (D5×C12).12C22, (C3×D20).12C22, (C5×Dic6).9C22, Dic5.34(C3⋊D4), C4.32(C2×S3×D5), (C5×C3⋊Q16)⋊2C2, C2.31(D5×C3⋊D4), (C5×C3⋊C8).8C22, C10.52(C2×C3⋊D4), (C3×Q82D5).1C2, SmallGroup(480,584)

Series: Derived Chief Lower central Upper central

C1C60 — D20.13D6
C1C5C15C30C60D5×C12D5×Dic6 — D20.13D6
C15C30C60 — D20.13D6
C1C2C4Q8

Generators and relations for D20.13D6
 G = < a,b,c,d | a20=b2=c6=1, d2=a10, bab=dad-1=a-1, cac-1=a9, cbc-1=a18b, dbd-1=a3b, dcd-1=c-1 >

Subgroups: 604 in 120 conjugacy classes, 40 normal (all characteristic)
C1, C2, C2 [×2], C3, C4, C4 [×4], C22 [×2], C5, C6, C6 [×2], C8 [×2], C2×C4 [×3], D4 [×2], Q8, Q8 [×3], D5 [×2], C10, Dic3 [×2], C12, C12 [×2], C2×C6 [×2], C15, M4(2), SD16 [×2], Q16 [×2], C2×Q8, C4○D4, Dic5, Dic5, C20, C20 [×2], D10, D10, C3⋊C8, C3⋊C8, Dic6, Dic6 [×2], C2×Dic3, C2×C12 [×2], C3×D4 [×2], C3×Q8, C3×D5 [×2], C30, C8.C22, C52C8, C40, Dic10 [×2], C4×D5, C4×D5 [×2], D20, D20, C5×Q8, C5×Q8, C4.Dic3, D4.S3 [×2], C3⋊Q16, C3⋊Q16, C2×Dic6, C3×C4○D4, C5×Dic3, C3×Dic5, Dic15, C60, C60, C6×D5, C6×D5, C8⋊D5, C40⋊C2, Q8⋊D5, C5⋊Q16, C5×Q16, Q8×D5, Q82D5, Q8.14D6, C5×C3⋊C8, C153C8, D5×Dic3, C15⋊Q8, D5×C12, D5×C12, C3×D20, C3×D20, C5×Dic6, Dic30, Q8×C15, Q16⋊D5, C20.32D6, C30.D4, C6.D20, C5×C3⋊Q16, C157Q16, D5×Dic6, C3×Q82D5, D20.13D6
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], C3⋊D4 [×2], C22×S3, C8.C22, C22×D5, C2×C3⋊D4, S3×D5, D4×D5, Q8.14D6, C2×S3×D5, Q16⋊D5, D5×C3⋊D4, D20.13D6

Smallest permutation representation of D20.13D6
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 21)(2 40)(3 39)(4 38)(5 37)(6 36)(7 35)(8 34)(9 33)(10 32)(11 31)(12 30)(13 29)(14 28)(15 27)(16 26)(17 25)(18 24)(19 23)(20 22)(41 212)(42 211)(43 210)(44 209)(45 208)(46 207)(47 206)(48 205)(49 204)(50 203)(51 202)(52 201)(53 220)(54 219)(55 218)(56 217)(57 216)(58 215)(59 214)(60 213)(61 86)(62 85)(63 84)(64 83)(65 82)(66 81)(67 100)(68 99)(69 98)(70 97)(71 96)(72 95)(73 94)(74 93)(75 92)(76 91)(77 90)(78 89)(79 88)(80 87)(101 195)(102 194)(103 193)(104 192)(105 191)(106 190)(107 189)(108 188)(109 187)(110 186)(111 185)(112 184)(113 183)(114 182)(115 181)(116 200)(117 199)(118 198)(119 197)(120 196)(121 235)(122 234)(123 233)(124 232)(125 231)(126 230)(127 229)(128 228)(129 227)(130 226)(131 225)(132 224)(133 223)(134 222)(135 221)(136 240)(137 239)(138 238)(139 237)(140 236)(141 177)(142 176)(143 175)(144 174)(145 173)(146 172)(147 171)(148 170)(149 169)(150 168)(151 167)(152 166)(153 165)(154 164)(155 163)(156 162)(157 161)(158 180)(159 179)(160 178)
(1 143 139)(2 152 140 10 144 128)(3 141 121 19 145 137)(4 150 122 8 146 126)(5 159 123 17 147 135)(6 148 124)(7 157 125 15 149 133)(9 155 127 13 151 131)(11 153 129)(12 142 130 20 154 138)(14 160 132 18 156 136)(16 158 134)(21 177 237 23 175 239)(22 166 238 32 176 228)(24 164 240 30 178 226)(25 173 221 39 179 235)(26 162 222 28 180 224)(27 171 223 37 161 233)(29 169 225 35 163 231)(31 167 227 33 165 229)(34 174 230 40 168 236)(36 172 232 38 170 234)(41 106 88 53 114 100)(42 115 89)(43 104 90 51 116 98)(44 113 91 60 117 87)(45 102 92 49 118 96)(46 111 93 58 119 85)(47 120 94)(48 109 95 56 101 83)(50 107 97 54 103 81)(52 105 99)(55 112 82 59 108 86)(57 110 84)(61 220 184 67 214 190)(62 209 185 76 215 199)(63 218 186 65 216 188)(64 207 187 74 217 197)(66 205 189 72 219 195)(68 203 191 70 201 193)(69 212 192 79 202 182)(71 210 194 77 204 200)(73 208 196 75 206 198)(78 213 181 80 211 183)
(1 42 11 52)(2 41 12 51)(3 60 13 50)(4 59 14 49)(5 58 15 48)(6 57 16 47)(7 56 17 46)(8 55 18 45)(9 54 19 44)(10 53 20 43)(21 208 31 218)(22 207 32 217)(23 206 33 216)(24 205 34 215)(25 204 35 214)(26 203 36 213)(27 202 37 212)(28 201 38 211)(29 220 39 210)(30 219 40 209)(61 179 71 169)(62 178 72 168)(63 177 73 167)(64 176 74 166)(65 175 75 165)(66 174 76 164)(67 173 77 163)(68 172 78 162)(69 171 79 161)(70 170 80 180)(81 141 91 151)(82 160 92 150)(83 159 93 149)(84 158 94 148)(85 157 95 147)(86 156 96 146)(87 155 97 145)(88 154 98 144)(89 153 99 143)(90 152 100 142)(101 123 111 133)(102 122 112 132)(103 121 113 131)(104 140 114 130)(105 139 115 129)(106 138 116 128)(107 137 117 127)(108 136 118 126)(109 135 119 125)(110 134 120 124)(181 224 191 234)(182 223 192 233)(183 222 193 232)(184 221 194 231)(185 240 195 230)(186 239 196 229)(187 238 197 228)(188 237 198 227)(189 236 199 226)(190 235 200 225)

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

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

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

45 conjugacy classes

class 1 2A2B2C 3 4A4B4C4D4E5A5B6A6B6C6D8A8B10A10B12A12B12C12D12E15A15B20A20B20C20D20E20F30A30B40A40B40C40D60A···60F
order12223444445566668810101212121212151520202020202030304040404060···60
size1110202241012602222020201260224441010444488242444121212128···8

45 irreducible representations

dim1111111122222222222244444448
type++++++++++++++++++-++-+-
imageC1C2C2C2C2C2C2C2S3D4D4D5D6D6D6D10D10D10C3⋊D4C3⋊D4C8.C22S3×D5D4×D5Q8.14D6C2×S3×D5Q16⋊D5D5×C3⋊D4D20.13D6
kernelD20.13D6C20.32D6C30.D4C6.D20C5×C3⋊Q16C157Q16D5×Dic6C3×Q82D5Q82D5C3×Dic5C6×D5C3⋊Q16C4×D5D20C5×Q8C3⋊C8Dic6C3×Q8Dic5D10C15Q8C6C5C4C3C2C1
# reps1111111111121112222212222442

Matrix representation of D20.13D6 in GL8(𝔽241)

190240000000
10000000
001902400000
00100000
000051240883
00001911150238
0000341601901
0000478150240
,
017101400000
171014000000
01010700000
10107000000
000015421840138
000017487161201
0000581768723
000012518367154
,
002401900000
00010000
1512401900000
0240010000
0000515200
000019119000
0000005152
000000191190
,
10190921130000
014001490000
1932031401510000
04801010000
00007095204208
00001961714137
00009256171146
00001131494570

G:=sub<GL(8,GF(241))| [190,1,0,0,0,0,0,0,240,0,0,0,0,0,0,0,0,0,190,1,0,0,0,0,0,0,240,0,0,0,0,0,0,0,0,0,51,191,34,47,0,0,0,0,240,1,160,81,0,0,0,0,88,150,190,50,0,0,0,0,3,238,1,240],[0,171,0,101,0,0,0,0,171,0,101,0,0,0,0,0,0,140,0,70,0,0,0,0,140,0,70,0,0,0,0,0,0,0,0,0,154,174,58,125,0,0,0,0,218,87,176,183,0,0,0,0,40,161,87,67,0,0,0,0,138,201,23,154],[0,0,1,0,0,0,0,0,0,0,51,240,0,0,0,0,240,0,240,0,0,0,0,0,190,1,190,1,0,0,0,0,0,0,0,0,51,191,0,0,0,0,0,0,52,190,0,0,0,0,0,0,0,0,51,191,0,0,0,0,0,0,52,190],[101,0,193,0,0,0,0,0,90,140,203,48,0,0,0,0,92,0,140,0,0,0,0,0,113,149,151,101,0,0,0,0,0,0,0,0,70,196,92,113,0,0,0,0,95,171,56,149,0,0,0,0,204,41,171,45,0,0,0,0,208,37,146,70] >;

D20.13D6 in GAP, Magma, Sage, TeX

D_{20}._{13}D_6
% in TeX

G:=Group("D20.13D6");
// GroupNames label

G:=SmallGroup(480,584);
// by ID

G=gap.SmallGroup(480,584);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,120,422,135,100,346,185,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^20=b^2=c^6=1,d^2=a^10,b*a*b=d*a*d^-1=a^-1,c*a*c^-1=a^9,c*b*c^-1=a^18*b,d*b*d^-1=a^3*b,d*c*d^-1=c^-1>;
// generators/relations

׿
×
𝔽