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G = D20.2Dic3order 480 = 25·3·5

The non-split extension by D20 of Dic3 acting via Dic3/C6=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D20.2Dic3, C60.177C23, Dic10.2Dic3, C3⋊C8.25D10, C1512(C8○D4), C4○D20.3S3, (C3×D20).4C4, (C4×D5).59D6, (C2×C20).78D6, C12.20(C4×D5), C4.Dic35D5, C4.9(D5×Dic3), C60.129(C2×C4), (C2×C12).79D10, C54(D4.Dic3), C5⋊D4.2Dic3, C35(D20.2C4), C30.99(C22×C4), D10.4(C2×Dic3), (C3×Dic10).4C4, C20.32(C2×Dic3), C20.32D614C2, C22.2(D5×Dic3), (C2×C60).213C22, C20.174(C22×S3), C153C8.48C22, Dic5.4(C2×Dic3), (D5×C12).59C22, C12.174(C22×D5), C10.17(C22×Dic3), (D5×C3⋊C8)⋊13C2, C6.80(C2×C4×D5), C4.147(C2×S3×D5), (C2×C6).8(C4×D5), C2.6(C2×D5×Dic3), (C6×D5).6(C2×C4), (C2×C153C8)⋊18C2, (C3×C5⋊D4).4C4, (C2×C30).96(C2×C4), (C3×C4○D20).6C2, (C2×C4).193(S3×D5), (C5×C3⋊C8).25C22, (C5×C4.Dic3)⋊11C2, (C3×Dic5).6(C2×C4), (C2×C10).25(C2×Dic3), SmallGroup(480,360)

Series: Derived Chief Lower central Upper central

C1C30 — D20.2Dic3
C1C5C15C30C60D5×C12D5×C3⋊C8 — D20.2Dic3
C15C30 — D20.2Dic3
C1C4C2×C4

Generators and relations for D20.2Dic3
 G = < a,b,c,d | a20=b2=1, c6=a10, d2=a10c3, bab=a-1, ac=ca, dad-1=a11, bc=cb, dbd-1=a10b, dcd-1=c5 >

Subgroups: 428 in 124 conjugacy classes, 60 normal (36 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 [×3], C4.Dic3, C4.Dic3 [×2], C3×C4○D4, C3×Dic5 [×2], C60 [×2], C6×D5 [×2], C2×C30, C8×D5 [×2], C8⋊D5 [×2], C2×C52C8, C5×M4(2), C4○D20, D4.Dic3, C5×C3⋊C8 [×2], C153C8 [×2], C3×Dic10, D5×C12 [×2], C3×D20, C3×C5⋊D4 [×2], C2×C60, D20.2C4, D5×C3⋊C8 [×2], C20.32D6 [×2], C5×C4.Dic3, C2×C153C8, C3×C4○D20, D20.2Dic3
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, D20.2C4, C2×D5×Dic3, D20.2Dic3

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

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

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

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

66 conjugacy classes

class 1 2A2B2C2D 3 4A4B4C4D4E5A5B6A6B6C6D8A8B8C8D8E8F8G8H8I8J10A10B10C10D12A12B12C12D12E15A15B20A20B20C20D20E20F30A···30F40A···40H60A···60H
order122223444445566668888888888101010101212121212151520202020202030···3040···4060···60
size11210102112101022242020666615151515303022442242020442222444···412···124···4

66 irreducible representations

dim1111111112222222222224444444
type++++++++-+--++++-+-
imageC1C2C2C2C2C2C4C4C4S3D5Dic3D6Dic3Dic3D6D10D10C8○D4C4×D5C4×D5S3×D5D4.Dic3D5×Dic3C2×S3×D5D5×Dic3D20.2C4D20.2Dic3
kernelD20.2Dic3D5×C3⋊C8C20.32D6C5×C4.Dic3C2×C153C8C3×C4○D20C3×Dic10C3×D20C3×C5⋊D4C4○D20C4.Dic3Dic10C4×D5D20C5⋊D4C2×C20C3⋊C8C2×C12C15C12C2×C6C2×C4C5C4C4C22C3C1
# reps1221112241212121424442222248

Matrix representation of D20.2Dic3 in GL6(𝔽241)

24000000
02400000
0019024000
001000
000011235
0000181230
,
24000000
02400000
0024019000
000100
000011235
000020230
,
24010000
24000000
001000
000100
00001770
00000177
,
26690000
952150000
00240000
00024000
00002110
000013130

G:=sub<GL(6,GF(241))| [240,0,0,0,0,0,0,240,0,0,0,0,0,0,190,1,0,0,0,0,240,0,0,0,0,0,0,0,11,181,0,0,0,0,235,230],[240,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,190,1,0,0,0,0,0,0,11,20,0,0,0,0,235,230],[240,240,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,177,0,0,0,0,0,0,177],[26,95,0,0,0,0,69,215,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,0,211,131,0,0,0,0,0,30] >;

D20.2Dic3 in GAP, Magma, Sage, TeX

D_{20}._2{\rm Dic}_3
% in TeX

G:=Group("D20.2Dic3");
// GroupNames label

G:=SmallGroup(480,360);
// by ID

G=gap.SmallGroup(480,360);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,64,422,219,80,1356,18822]);
// 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,d*a*d^-1=a^11,b*c=c*b,d*b*d^-1=a^10*b,d*c*d^-1=c^5>;
// generators/relations

׿
×
𝔽