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G = D20.29D6order 480 = 25·3·5

12nd non-split extension by D20 of D6 acting via D6/S3=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D20.29D6, C30.32C24, C60.56C23, C1552- 1+4, Dic6.30D10, D30.39C23, Dic15.19C23, Dic30.20C22, (S3×Q8)⋊4D5, (Q8×D15)⋊4C2, C54(Q8○D12), Q82D57S3, (D5×Dic6)⋊6C2, (C4×D5).16D6, (C5×Q8).41D6, Q8.26(S3×D5), D205S36C2, D20⋊S36C2, C15⋊Q8.5C22, (C4×S3).16D10, (C3×Q8).24D10, C6.32(C23×D5), D6.D105C2, C20.56(C22×S3), C10.32(S3×C23), (C6×D5).14C23, D6.28(C22×D5), C12.56(C22×D5), C15⋊D4.3C22, C5⋊D12.5C22, C3⋊D20.3C22, (S3×C10).31C23, (S3×C20).19C22, C33(Q8.10D10), (C3×D20).19C22, (C4×D15).19C22, (D5×C12).19C22, D10.17(C22×S3), (Q8×C15).19C22, (D5×Dic3).4C22, Dic3.17(C22×D5), Dic5.44(C22×S3), (C5×Dic3).18C23, (C3×Dic5).47C23, (C5×Dic6).20C22, (C5×S3×Q8)⋊4C2, C4.56(C2×S3×D5), C2.35(C22×S3×D5), (C3×Q82D5)⋊4C2, SmallGroup(480,1104)

Series: Derived Chief Lower central Upper central

C1C30 — D20.29D6
C1C5C15C30C6×D5D5×Dic3D5×Dic6 — D20.29D6
C15C30 — D20.29D6
C1C2Q8

Generators and relations for D20.29D6
 G = < a,b,c,d | a20=b2=1, c6=d2=a10, bab=a-1, cac-1=a11, ad=da, cbc-1=a10b, bd=db, dcd-1=a10c5 >

Subgroups: 1340 in 292 conjugacy classes, 108 normal (24 characteristic)
C1, C2, C2 [×5], C3, C4 [×3], C4 [×7], C22 [×5], C5, S3 [×2], C6, C6 [×3], C2×C4 [×15], D4 [×10], Q8, Q8 [×9], D5 [×4], C10, C10, Dic3 [×3], Dic3 [×3], C12 [×3], C12, D6, D6, C2×C6 [×3], C15, C2×Q8 [×5], C4○D4 [×10], Dic5, Dic5 [×3], C20 [×3], C20 [×3], D10 [×3], D10, C2×C10, Dic6 [×3], Dic6 [×6], C4×S3 [×3], C4×S3 [×3], D12, C2×Dic3 [×6], C3⋊D4 [×6], C2×C12 [×3], C3×D4 [×3], C3×Q8, C5×S3, C3×D5 [×3], D15, C30, 2- 1+4, Dic10 [×6], C4×D5 [×3], C4×D5 [×9], D20 [×3], D20 [×3], C5⋊D4 [×4], C2×C20 [×3], C5×Q8, C5×Q8 [×3], C2×Dic6 [×3], C4○D12 [×3], D42S3 [×6], S3×Q8, S3×Q8, C3×C4○D4, C5×Dic3 [×3], C3×Dic5, Dic15 [×3], C60 [×3], C6×D5 [×3], S3×C10, D30, C4○D20 [×6], Q8×D5 [×4], Q82D5, Q82D5 [×3], Q8×C10, Q8○D12, D5×Dic3 [×6], C15⋊D4 [×3], C3⋊D20 [×3], C5⋊D12, C15⋊Q8 [×3], D5×C12 [×3], C3×D20 [×3], C5×Dic6 [×3], S3×C20 [×3], Dic30 [×3], C4×D15 [×3], Q8×C15, Q8.10D10, D5×Dic6 [×3], D205S3 [×3], D20⋊S3 [×3], D6.D10 [×3], C3×Q82D5, C5×S3×Q8, Q8×D15, D20.29D6
Quotients: C1, C2 [×15], C22 [×35], S3, C23 [×15], D5, D6 [×7], C24, D10 [×7], C22×S3 [×7], 2- 1+4, C22×D5 [×7], S3×C23, S3×D5, C23×D5, Q8○D12, C2×S3×D5 [×3], Q8.10D10, C22×S3×D5, D20.29D6

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

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

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

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

57 conjugacy classes

class 1 2A2B2C2D2E2F 3 4A4B4C4D4E4F4G4H4I4J5A5B6A6B6C6D10A10B10C10D10E10F12A12B12C12D12E15A15B20A···20F20G···20L30A30B60A···60F
order1222222344444444445566661010101010101212121212151520···2020···20303060···60
size116101010302222666103030302222020202266664441010444···412···12448···8

57 irreducible representations

dim1111111122222222444448
type++++++++++++++++-+-+-
imageC1C2C2C2C2C2C2C2S3D5D6D6D6D10D10D102- 1+4S3×D5Q8○D12C2×S3×D5Q8.10D10D20.29D6
kernelD20.29D6D5×Dic6D205S3D20⋊S3D6.D10C3×Q82D5C5×S3×Q8Q8×D15Q82D5S3×Q8C4×D5D20C5×Q8Dic6C4×S3C3×Q8C15Q8C5C4C3C1
# reps1333311112331662122642

Matrix representation of D20.29D6 in GL8(𝔽61)

060000000
144000000
000600000
001440000
000039303813
000053312325
0000510031
000048513052
,
3529150000
482646520000
524626480000
1592350000
000047301315
00002814259
000048551731
000048543044
,
10100000
01010000
600000000
060000000
0000470025
00000473636
000033140
0000580014
,
23548260000
26483520000
465259260000
91535130000
000054392542
00001471744
000043561522
000043483946

G:=sub<GL(8,GF(61))| [0,1,0,0,0,0,0,0,60,44,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,60,44,0,0,0,0,0,0,0,0,39,53,51,48,0,0,0,0,30,31,0,51,0,0,0,0,38,23,0,30,0,0,0,0,13,25,31,52],[35,48,52,15,0,0,0,0,2,26,46,9,0,0,0,0,9,46,26,2,0,0,0,0,15,52,48,35,0,0,0,0,0,0,0,0,47,28,48,48,0,0,0,0,30,14,55,54,0,0,0,0,13,2,17,30,0,0,0,0,15,59,31,44],[1,0,60,0,0,0,0,0,0,1,0,60,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,47,0,3,58,0,0,0,0,0,47,3,0,0,0,0,0,0,36,14,0,0,0,0,0,25,36,0,14],[2,26,46,9,0,0,0,0,35,48,52,15,0,0,0,0,48,35,59,35,0,0,0,0,26,2,26,13,0,0,0,0,0,0,0,0,54,14,43,43,0,0,0,0,39,7,56,48,0,0,0,0,25,17,15,39,0,0,0,0,42,44,22,46] >;

D20.29D6 in GAP, Magma, Sage, TeX

D_{20}._{29}D_6
% in TeX

G:=Group("D20.29D6");
// GroupNames label

G:=SmallGroup(480,1104);
// by ID

G=gap.SmallGroup(480,1104);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,120,219,100,675,185,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^20=b^2=1,c^6=d^2=a^10,b*a*b=a^-1,c*a*c^-1=a^11,a*d=d*a,c*b*c^-1=a^10*b,b*d=d*b,d*c*d^-1=a^10*c^5>;
// generators/relations

׿
×
𝔽