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G = C2×C20.32D6order 480 = 25·3·5

Direct product of C2 and C20.32D6

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C2×C20.32D6, C305M4(2), C60.186C23, C3⋊C829D10, C63(C8⋊D5), (C4×D5).85D6, (D5×C12).5C4, C12.79(C4×D5), C60.150(C2×C4), (C2×C20).330D6, C1518(C2×M4(2)), (C4×D5).3Dic3, C4.23(D5×Dic3), C153C844C22, (C2×C12).334D10, C103(C4.Dic3), (C6×Dic5).11C4, D10.9(C2×Dic3), C20.49(C2×Dic3), (C2×C60).232C22, C30.108(C22×C4), C20.183(C22×S3), (C2×Dic5).7Dic3, C12.183(C22×D5), (C22×D5).5Dic3, C22.14(D5×Dic3), Dic5.12(C2×Dic3), (D5×C12).103C22, C10.18(C22×Dic3), (C2×C3⋊C8)⋊11D5, C34(C2×C8⋊D5), (C10×C3⋊C8)⋊13C2, (D5×C2×C6).8C4, C6.81(C2×C4×D5), (C2×C4×D5).10S3, (D5×C2×C12).9C2, C4.156(C2×S3×D5), C54(C2×C4.Dic3), C2.7(C2×D5×Dic3), (C5×C3⋊C8)⋊36C22, (C2×C6).52(C4×D5), (C2×C153C8)⋊25C2, (C6×D5).49(C2×C4), (C2×C4).235(S3×D5), (C2×C30).105(C2×C4), (C3×Dic5).57(C2×C4), (C2×C10).36(C2×Dic3), SmallGroup(480,369)

Series: Derived Chief Lower central Upper central

C1C30 — C2×C20.32D6
C1C5C15C30C60D5×C12C20.32D6 — C2×C20.32D6
C15C30 — C2×C20.32D6
C1C2×C4

Generators and relations for C2×C20.32D6
 G = < a,b,c,d | a2=b20=c6=1, d2=b15, ab=ba, ac=ca, ad=da, cbc-1=dbd-1=b9, dcd-1=b10c-1 >

Subgroups: 476 in 136 conjugacy classes, 68 normal (34 characteristic)
C1, C2, C2 [×2], C2 [×2], C3, C4 [×2], C4 [×2], C22, C22 [×4], C5, C6, C6 [×2], C6 [×2], C8 [×4], C2×C4, C2×C4 [×5], C23, D5 [×2], C10, C10 [×2], C12 [×2], C12 [×2], C2×C6, C2×C6 [×4], C15, C2×C8 [×2], M4(2) [×4], C22×C4, Dic5 [×2], C20 [×2], D10 [×2], D10 [×2], C2×C10, C3⋊C8 [×2], C3⋊C8 [×2], C2×C12, C2×C12 [×5], C22×C6, C3×D5 [×2], C30, C30 [×2], C2×M4(2), C52C8 [×2], C40 [×2], C4×D5 [×4], C2×Dic5, C2×C20, C22×D5, C2×C3⋊C8, C2×C3⋊C8, C4.Dic3 [×4], C22×C12, C3×Dic5 [×2], C60 [×2], C6×D5 [×2], C6×D5 [×2], C2×C30, C8⋊D5 [×4], C2×C52C8, C2×C40, C2×C4×D5, C2×C4.Dic3, C5×C3⋊C8 [×2], C153C8 [×2], D5×C12 [×4], C6×Dic5, C2×C60, D5×C2×C6, C2×C8⋊D5, C20.32D6 [×4], C10×C3⋊C8, C2×C153C8, D5×C2×C12, C2×C20.32D6
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], S3, C2×C4 [×6], C23, D5, Dic3 [×4], D6 [×3], M4(2) [×2], C22×C4, D10 [×3], C2×Dic3 [×6], C22×S3, C2×M4(2), C4×D5 [×2], C22×D5, C4.Dic3 [×2], C22×Dic3, S3×D5, C8⋊D5 [×2], C2×C4×D5, C2×C4.Dic3, D5×Dic3 [×2], C2×S3×D5, C2×C8⋊D5, C20.32D6 [×2], C2×D5×Dic3, C2×C20.32D6

Smallest permutation representation of C2×C20.32D6
On 240 points
Generators in S240
(1 38)(2 39)(3 40)(4 21)(5 22)(6 23)(7 24)(8 25)(9 26)(10 27)(11 28)(12 29)(13 30)(14 31)(15 32)(16 33)(17 34)(18 35)(19 36)(20 37)(41 85)(42 86)(43 87)(44 88)(45 89)(46 90)(47 91)(48 92)(49 93)(50 94)(51 95)(52 96)(53 97)(54 98)(55 99)(56 100)(57 81)(58 82)(59 83)(60 84)(61 231)(62 232)(63 233)(64 234)(65 235)(66 236)(67 237)(68 238)(69 239)(70 240)(71 221)(72 222)(73 223)(74 224)(75 225)(76 226)(77 227)(78 228)(79 229)(80 230)(101 214)(102 215)(103 216)(104 217)(105 218)(106 219)(107 220)(108 201)(109 202)(110 203)(111 204)(112 205)(113 206)(114 207)(115 208)(116 209)(117 210)(118 211)(119 212)(120 213)(121 191)(122 192)(123 193)(124 194)(125 195)(126 196)(127 197)(128 198)(129 199)(130 200)(131 181)(132 182)(133 183)(134 184)(135 185)(136 186)(137 187)(138 188)(139 189)(140 190)(141 174)(142 175)(143 176)(144 177)(145 178)(146 179)(147 180)(148 161)(149 162)(150 163)(151 164)(152 165)(153 166)(154 167)(155 168)(156 169)(157 170)(158 171)(159 172)(160 173)
(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)
(1 186 68 38 136 238)(2 195 69 27 137 227)(3 184 70 36 138 236)(4 193 71 25 139 225)(5 182 72 34 140 234)(6 191 73 23 121 223)(7 200 74 32 122 232)(8 189 75 21 123 221)(9 198 76 30 124 230)(10 187 77 39 125 239)(11 196 78 28 126 228)(12 185 79 37 127 237)(13 194 80 26 128 226)(14 183 61 35 129 235)(15 192 62 24 130 224)(16 181 63 33 131 233)(17 190 64 22 132 222)(18 199 65 31 133 231)(19 188 66 40 134 240)(20 197 67 29 135 229)(41 112 157 83 207 168)(42 101 158 92 208 177)(43 110 159 81 209 166)(44 119 160 90 210 175)(45 108 141 99 211 164)(46 117 142 88 212 173)(47 106 143 97 213 162)(48 115 144 86 214 171)(49 104 145 95 215 180)(50 113 146 84 216 169)(51 102 147 93 217 178)(52 111 148 82 218 167)(53 120 149 91 219 176)(54 109 150 100 220 165)(55 118 151 89 201 174)(56 107 152 98 202 163)(57 116 153 87 203 172)(58 105 154 96 204 161)(59 114 155 85 205 170)(60 103 156 94 206 179)
(1 169 16 164 11 179 6 174)(2 178 17 173 12 168 7 163)(3 167 18 162 13 177 8 172)(4 176 19 171 14 166 9 161)(5 165 20 180 15 175 10 170)(21 143 36 158 31 153 26 148)(22 152 37 147 32 142 27 157)(23 141 38 156 33 151 28 146)(24 150 39 145 34 160 29 155)(25 159 40 154 35 149 30 144)(41 222 56 237 51 232 46 227)(42 231 57 226 52 221 47 236)(43 240 58 235 53 230 48 225)(44 229 59 224 54 239 49 234)(45 238 60 233 55 228 50 223)(61 81 76 96 71 91 66 86)(62 90 77 85 72 100 67 95)(63 99 78 94 73 89 68 84)(64 88 79 83 74 98 69 93)(65 97 80 92 75 87 70 82)(101 123 116 138 111 133 106 128)(102 132 117 127 112 122 107 137)(103 121 118 136 113 131 108 126)(104 130 119 125 114 140 109 135)(105 139 120 134 115 129 110 124)(181 201 196 216 191 211 186 206)(182 210 197 205 192 220 187 215)(183 219 198 214 193 209 188 204)(184 208 199 203 194 218 189 213)(185 217 200 212 195 207 190 202)

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

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

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

84 conjugacy classes

class 1 2A2B2C2D2E 3 4A4B4C4D4E4F5A5B6A6B6C6D6E6F6G8A8B8C8D8E8F8G8H10A···10F12A12B12C12D12E12F12G12H15A15B20A···20H30A···30F40A···40P60A···60H
order12222234444445566666668888888810···101212121212121212151520···2030···3040···4060···60
size1111101021111101022222101010106666303030302···2222210101010442···24···46···64···4

84 irreducible representations

dim111111112222222222222244444
type+++++++-+-+-+++-+-
imageC1C2C2C2C2C4C4C4S3D5Dic3D6Dic3D6Dic3M4(2)D10D10C4×D5C4×D5C4.Dic3C8⋊D5S3×D5D5×Dic3C2×S3×D5D5×Dic3C20.32D6
kernelC2×C20.32D6C20.32D6C10×C3⋊C8C2×C153C8D5×C2×C12D5×C12C6×Dic5D5×C2×C6C2×C4×D5C2×C3⋊C8C4×D5C4×D5C2×Dic5C2×C20C22×D5C30C3⋊C8C2×C12C12C2×C6C10C6C2×C4C4C4C22C2
# reps1411142212221114424481622228

Matrix representation of C2×C20.32D6 in GL4(𝔽241) generated by

240000
024000
0010
0001
,
177000
017700
0017764
00223195
,
226000
21722500
001891
0018952
,
1014100
1023100
00196115
009545
G:=sub<GL(4,GF(241))| [240,0,0,0,0,240,0,0,0,0,1,0,0,0,0,1],[177,0,0,0,0,177,0,0,0,0,177,223,0,0,64,195],[226,217,0,0,0,225,0,0,0,0,189,189,0,0,1,52],[10,10,0,0,141,231,0,0,0,0,196,95,0,0,115,45] >;

C2×C20.32D6 in GAP, Magma, Sage, TeX

C_2\times C_{20}._{32}D_6
% in TeX

G:=Group("C2xC20.32D6");
// GroupNames label

G:=SmallGroup(480,369);
// by ID

G=gap.SmallGroup(480,369);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,253,64,80,1356,18822]);
// Polycyclic

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

׿
×
𝔽