direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C3×C20.47D4, C12.64D20, C60.218D4, C20.47(C3×D4), C4.12(C3×D20), (C6×Dic5).2C4, C22.5(D5×C12), C4.Dic5.3C6, (C2×C12).212D10, C15⋊8(C4.10D4), (C2×Dic10).7C6, (C2×Dic5).1C12, M4(2).2(C3×D5), (C3×M4(2)).2D5, (C5×M4(2)).2C6, C12.115(C5⋊D4), C30.88(C22⋊C4), (C2×C60).277C22, (C6×Dic10).18C2, (C15×M4(2)).2C2, C6.41(D10⋊C4), (C2×C4).2(C6×D5), (C2×C6).39(C4×D5), C4.22(C3×C5⋊D4), C5⋊2(C3×C4.10D4), (C2×C20).13(C2×C6), (C2×C10).23(C2×C12), (C2×C30).120(C2×C4), C10.20(C3×C22⋊C4), (C3×C4.Dic5).7C2, C2.10(C3×D10⋊C4), SmallGroup(480,102)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3×C20.47D4
G = < a,b,c,d | a3=b20=1, c4=d2=b10, ab=ba, ac=ca, ad=da, cbc-1=dbd-1=b-1, dcd-1=b5c3 >
Subgroups: 224 in 76 conjugacy classes, 38 normal (34 characteristic)
C1, C2, C2, C3, C4 [×2], C4 [×2], C22, C5, C6, C6, C8 [×2], C2×C4, C2×C4 [×2], Q8 [×2], C10, C10, C12 [×2], C12 [×2], C2×C6, C15, M4(2), M4(2), C2×Q8, Dic5 [×2], C20 [×2], C2×C10, C24 [×2], C2×C12, C2×C12 [×2], C3×Q8 [×2], C30, C30, C4.10D4, C5⋊2C8, C40, Dic10 [×2], C2×Dic5 [×2], C2×C20, C3×M4(2), C3×M4(2), C6×Q8, C3×Dic5 [×2], C60 [×2], C2×C30, C4.Dic5, C5×M4(2), C2×Dic10, C3×C4.10D4, C3×C5⋊2C8, C120, C3×Dic10 [×2], C6×Dic5 [×2], C2×C60, C20.47D4, C3×C4.Dic5, C15×M4(2), C6×Dic10, C3×C20.47D4
Quotients: C1, C2 [×3], C3, C4 [×2], C22, C6 [×3], C2×C4, D4 [×2], D5, C12 [×2], C2×C6, C22⋊C4, D10, C2×C12, C3×D4 [×2], C3×D5, C4.10D4, C4×D5, D20, C5⋊D4, C3×C22⋊C4, C6×D5, D10⋊C4, C3×C4.10D4, D5×C12, C3×D20, C3×C5⋊D4, C20.47D4, C3×D10⋊C4, C3×C20.47D4
►On 240 points
Generators in S240
(1 47 32)(2 48 33)(3 49 34)(4 50 35)(5 51 36)(6 52 37)(7 53 38)(8 54 39)(9 55 40)(10 56 21)(11 57 22)(12 58 23)(13 59 24)(14 60 25)(15 41 26)(16 42 27)(17 43 28)(18 44 29)(19 45 30)(20 46 31)(61 119 81)(62 120 82)(63 101 83)(64 102 84)(65 103 85)(66 104 86)(67 105 87)(68 106 88)(69 107 89)(70 108 90)(71 109 91)(72 110 92)(73 111 93)(74 112 94)(75 113 95)(76 114 96)(77 115 97)(78 116 98)(79 117 99)(80 118 100)(121 171 146)(122 172 147)(123 173 148)(124 174 149)(125 175 150)(126 176 151)(127 177 152)(128 178 153)(129 179 154)(130 180 155)(131 161 156)(132 162 157)(133 163 158)(134 164 159)(135 165 160)(136 166 141)(137 167 142)(138 168 143)(139 169 144)(140 170 145)(181 236 216)(182 237 217)(183 238 218)(184 239 219)(185 240 220)(186 221 201)(187 222 202)(188 223 203)(189 224 204)(190 225 205)(191 226 206)(192 227 207)(193 228 208)(194 229 209)(195 230 210)(196 231 211)(197 232 212)(198 233 213)(199 234 214)(200 235 215)
(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)
(1 191 6 186 11 181 16 196)(2 190 7 185 12 200 17 195)(3 189 8 184 13 199 18 194)(4 188 9 183 14 198 19 193)(5 187 10 182 15 197 20 192)(21 217 26 212 31 207 36 202)(22 216 27 211 32 206 37 201)(23 215 28 210 33 205 38 220)(24 214 29 209 34 204 39 219)(25 213 30 208 35 203 40 218)(41 232 46 227 51 222 56 237)(42 231 47 226 52 221 57 236)(43 230 48 225 53 240 58 235)(44 229 49 224 54 239 59 234)(45 228 50 223 55 238 60 233)(61 129 76 134 71 139 66 124)(62 128 77 133 72 138 67 123)(63 127 78 132 73 137 68 122)(64 126 79 131 74 136 69 121)(65 125 80 130 75 135 70 140)(81 154 96 159 91 144 86 149)(82 153 97 158 92 143 87 148)(83 152 98 157 93 142 88 147)(84 151 99 156 94 141 89 146)(85 150 100 155 95 160 90 145)(101 177 116 162 111 167 106 172)(102 176 117 161 112 166 107 171)(103 175 118 180 113 165 108 170)(104 174 119 179 114 164 109 169)(105 173 120 178 115 163 110 168)
(1 121 11 131)(2 140 12 130)(3 139 13 129)(4 138 14 128)(5 137 15 127)(6 136 16 126)(7 135 17 125)(8 134 18 124)(9 133 19 123)(10 132 20 122)(21 157 31 147)(22 156 32 146)(23 155 33 145)(24 154 34 144)(25 153 35 143)(26 152 36 142)(27 151 37 141)(28 150 38 160)(29 149 39 159)(30 148 40 158)(41 177 51 167)(42 176 52 166)(43 175 53 165)(44 174 54 164)(45 173 55 163)(46 172 56 162)(47 171 57 161)(48 170 58 180)(49 169 59 179)(50 168 60 178)(61 194 71 184)(62 193 72 183)(63 192 73 182)(64 191 74 181)(65 190 75 200)(66 189 76 199)(67 188 77 198)(68 187 78 197)(69 186 79 196)(70 185 80 195)(81 209 91 219)(82 208 92 218)(83 207 93 217)(84 206 94 216)(85 205 95 215)(86 204 96 214)(87 203 97 213)(88 202 98 212)(89 201 99 211)(90 220 100 210)(101 227 111 237)(102 226 112 236)(103 225 113 235)(104 224 114 234)(105 223 115 233)(106 222 116 232)(107 221 117 231)(108 240 118 230)(109 239 119 229)(110 238 120 228)
G:=sub<Sym(240)| (1,47,32)(2,48,33)(3,49,34)(4,50,35)(5,51,36)(6,52,37)(7,53,38)(8,54,39)(9,55,40)(10,56,21)(11,57,22)(12,58,23)(13,59,24)(14,60,25)(15,41,26)(16,42,27)(17,43,28)(18,44,29)(19,45,30)(20,46,31)(61,119,81)(62,120,82)(63,101,83)(64,102,84)(65,103,85)(66,104,86)(67,105,87)(68,106,88)(69,107,89)(70,108,90)(71,109,91)(72,110,92)(73,111,93)(74,112,94)(75,113,95)(76,114,96)(77,115,97)(78,116,98)(79,117,99)(80,118,100)(121,171,146)(122,172,147)(123,173,148)(124,174,149)(125,175,150)(126,176,151)(127,177,152)(128,178,153)(129,179,154)(130,180,155)(131,161,156)(132,162,157)(133,163,158)(134,164,159)(135,165,160)(136,166,141)(137,167,142)(138,168,143)(139,169,144)(140,170,145)(181,236,216)(182,237,217)(183,238,218)(184,239,219)(185,240,220)(186,221,201)(187,222,202)(188,223,203)(189,224,204)(190,225,205)(191,226,206)(192,227,207)(193,228,208)(194,229,209)(195,230,210)(196,231,211)(197,232,212)(198,233,213)(199,234,214)(200,235,215), (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), (1,191,6,186,11,181,16,196)(2,190,7,185,12,200,17,195)(3,189,8,184,13,199,18,194)(4,188,9,183,14,198,19,193)(5,187,10,182,15,197,20,192)(21,217,26,212,31,207,36,202)(22,216,27,211,32,206,37,201)(23,215,28,210,33,205,38,220)(24,214,29,209,34,204,39,219)(25,213,30,208,35,203,40,218)(41,232,46,227,51,222,56,237)(42,231,47,226,52,221,57,236)(43,230,48,225,53,240,58,235)(44,229,49,224,54,239,59,234)(45,228,50,223,55,238,60,233)(61,129,76,134,71,139,66,124)(62,128,77,133,72,138,67,123)(63,127,78,132,73,137,68,122)(64,126,79,131,74,136,69,121)(65,125,80,130,75,135,70,140)(81,154,96,159,91,144,86,149)(82,153,97,158,92,143,87,148)(83,152,98,157,93,142,88,147)(84,151,99,156,94,141,89,146)(85,150,100,155,95,160,90,145)(101,177,116,162,111,167,106,172)(102,176,117,161,112,166,107,171)(103,175,118,180,113,165,108,170)(104,174,119,179,114,164,109,169)(105,173,120,178,115,163,110,168), (1,121,11,131)(2,140,12,130)(3,139,13,129)(4,138,14,128)(5,137,15,127)(6,136,16,126)(7,135,17,125)(8,134,18,124)(9,133,19,123)(10,132,20,122)(21,157,31,147)(22,156,32,146)(23,155,33,145)(24,154,34,144)(25,153,35,143)(26,152,36,142)(27,151,37,141)(28,150,38,160)(29,149,39,159)(30,148,40,158)(41,177,51,167)(42,176,52,166)(43,175,53,165)(44,174,54,164)(45,173,55,163)(46,172,56,162)(47,171,57,161)(48,170,58,180)(49,169,59,179)(50,168,60,178)(61,194,71,184)(62,193,72,183)(63,192,73,182)(64,191,74,181)(65,190,75,200)(66,189,76,199)(67,188,77,198)(68,187,78,197)(69,186,79,196)(70,185,80,195)(81,209,91,219)(82,208,92,218)(83,207,93,217)(84,206,94,216)(85,205,95,215)(86,204,96,214)(87,203,97,213)(88,202,98,212)(89,201,99,211)(90,220,100,210)(101,227,111,237)(102,226,112,236)(103,225,113,235)(104,224,114,234)(105,223,115,233)(106,222,116,232)(107,221,117,231)(108,240,118,230)(109,239,119,229)(110,238,120,228)>;
G:=Group( (1,47,32)(2,48,33)(3,49,34)(4,50,35)(5,51,36)(6,52,37)(7,53,38)(8,54,39)(9,55,40)(10,56,21)(11,57,22)(12,58,23)(13,59,24)(14,60,25)(15,41,26)(16,42,27)(17,43,28)(18,44,29)(19,45,30)(20,46,31)(61,119,81)(62,120,82)(63,101,83)(64,102,84)(65,103,85)(66,104,86)(67,105,87)(68,106,88)(69,107,89)(70,108,90)(71,109,91)(72,110,92)(73,111,93)(74,112,94)(75,113,95)(76,114,96)(77,115,97)(78,116,98)(79,117,99)(80,118,100)(121,171,146)(122,172,147)(123,173,148)(124,174,149)(125,175,150)(126,176,151)(127,177,152)(128,178,153)(129,179,154)(130,180,155)(131,161,156)(132,162,157)(133,163,158)(134,164,159)(135,165,160)(136,166,141)(137,167,142)(138,168,143)(139,169,144)(140,170,145)(181,236,216)(182,237,217)(183,238,218)(184,239,219)(185,240,220)(186,221,201)(187,222,202)(188,223,203)(189,224,204)(190,225,205)(191,226,206)(192,227,207)(193,228,208)(194,229,209)(195,230,210)(196,231,211)(197,232,212)(198,233,213)(199,234,214)(200,235,215), (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), (1,191,6,186,11,181,16,196)(2,190,7,185,12,200,17,195)(3,189,8,184,13,199,18,194)(4,188,9,183,14,198,19,193)(5,187,10,182,15,197,20,192)(21,217,26,212,31,207,36,202)(22,216,27,211,32,206,37,201)(23,215,28,210,33,205,38,220)(24,214,29,209,34,204,39,219)(25,213,30,208,35,203,40,218)(41,232,46,227,51,222,56,237)(42,231,47,226,52,221,57,236)(43,230,48,225,53,240,58,235)(44,229,49,224,54,239,59,234)(45,228,50,223,55,238,60,233)(61,129,76,134,71,139,66,124)(62,128,77,133,72,138,67,123)(63,127,78,132,73,137,68,122)(64,126,79,131,74,136,69,121)(65,125,80,130,75,135,70,140)(81,154,96,159,91,144,86,149)(82,153,97,158,92,143,87,148)(83,152,98,157,93,142,88,147)(84,151,99,156,94,141,89,146)(85,150,100,155,95,160,90,145)(101,177,116,162,111,167,106,172)(102,176,117,161,112,166,107,171)(103,175,118,180,113,165,108,170)(104,174,119,179,114,164,109,169)(105,173,120,178,115,163,110,168), (1,121,11,131)(2,140,12,130)(3,139,13,129)(4,138,14,128)(5,137,15,127)(6,136,16,126)(7,135,17,125)(8,134,18,124)(9,133,19,123)(10,132,20,122)(21,157,31,147)(22,156,32,146)(23,155,33,145)(24,154,34,144)(25,153,35,143)(26,152,36,142)(27,151,37,141)(28,150,38,160)(29,149,39,159)(30,148,40,158)(41,177,51,167)(42,176,52,166)(43,175,53,165)(44,174,54,164)(45,173,55,163)(46,172,56,162)(47,171,57,161)(48,170,58,180)(49,169,59,179)(50,168,60,178)(61,194,71,184)(62,193,72,183)(63,192,73,182)(64,191,74,181)(65,190,75,200)(66,189,76,199)(67,188,77,198)(68,187,78,197)(69,186,79,196)(70,185,80,195)(81,209,91,219)(82,208,92,218)(83,207,93,217)(84,206,94,216)(85,205,95,215)(86,204,96,214)(87,203,97,213)(88,202,98,212)(89,201,99,211)(90,220,100,210)(101,227,111,237)(102,226,112,236)(103,225,113,235)(104,224,114,234)(105,223,115,233)(106,222,116,232)(107,221,117,231)(108,240,118,230)(109,239,119,229)(110,238,120,228) );
G=PermutationGroup([(1,47,32),(2,48,33),(3,49,34),(4,50,35),(5,51,36),(6,52,37),(7,53,38),(8,54,39),(9,55,40),(10,56,21),(11,57,22),(12,58,23),(13,59,24),(14,60,25),(15,41,26),(16,42,27),(17,43,28),(18,44,29),(19,45,30),(20,46,31),(61,119,81),(62,120,82),(63,101,83),(64,102,84),(65,103,85),(66,104,86),(67,105,87),(68,106,88),(69,107,89),(70,108,90),(71,109,91),(72,110,92),(73,111,93),(74,112,94),(75,113,95),(76,114,96),(77,115,97),(78,116,98),(79,117,99),(80,118,100),(121,171,146),(122,172,147),(123,173,148),(124,174,149),(125,175,150),(126,176,151),(127,177,152),(128,178,153),(129,179,154),(130,180,155),(131,161,156),(132,162,157),(133,163,158),(134,164,159),(135,165,160),(136,166,141),(137,167,142),(138,168,143),(139,169,144),(140,170,145),(181,236,216),(182,237,217),(183,238,218),(184,239,219),(185,240,220),(186,221,201),(187,222,202),(188,223,203),(189,224,204),(190,225,205),(191,226,206),(192,227,207),(193,228,208),(194,229,209),(195,230,210),(196,231,211),(197,232,212),(198,233,213),(199,234,214),(200,235,215)], [(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)], [(1,191,6,186,11,181,16,196),(2,190,7,185,12,200,17,195),(3,189,8,184,13,199,18,194),(4,188,9,183,14,198,19,193),(5,187,10,182,15,197,20,192),(21,217,26,212,31,207,36,202),(22,216,27,211,32,206,37,201),(23,215,28,210,33,205,38,220),(24,214,29,209,34,204,39,219),(25,213,30,208,35,203,40,218),(41,232,46,227,51,222,56,237),(42,231,47,226,52,221,57,236),(43,230,48,225,53,240,58,235),(44,229,49,224,54,239,59,234),(45,228,50,223,55,238,60,233),(61,129,76,134,71,139,66,124),(62,128,77,133,72,138,67,123),(63,127,78,132,73,137,68,122),(64,126,79,131,74,136,69,121),(65,125,80,130,75,135,70,140),(81,154,96,159,91,144,86,149),(82,153,97,158,92,143,87,148),(83,152,98,157,93,142,88,147),(84,151,99,156,94,141,89,146),(85,150,100,155,95,160,90,145),(101,177,116,162,111,167,106,172),(102,176,117,161,112,166,107,171),(103,175,118,180,113,165,108,170),(104,174,119,179,114,164,109,169),(105,173,120,178,115,163,110,168)], [(1,121,11,131),(2,140,12,130),(3,139,13,129),(4,138,14,128),(5,137,15,127),(6,136,16,126),(7,135,17,125),(8,134,18,124),(9,133,19,123),(10,132,20,122),(21,157,31,147),(22,156,32,146),(23,155,33,145),(24,154,34,144),(25,153,35,143),(26,152,36,142),(27,151,37,141),(28,150,38,160),(29,149,39,159),(30,148,40,158),(41,177,51,167),(42,176,52,166),(43,175,53,165),(44,174,54,164),(45,173,55,163),(46,172,56,162),(47,171,57,161),(48,170,58,180),(49,169,59,179),(50,168,60,178),(61,194,71,184),(62,193,72,183),(63,192,73,182),(64,191,74,181),(65,190,75,200),(66,189,76,199),(67,188,77,198),(68,187,78,197),(69,186,79,196),(70,185,80,195),(81,209,91,219),(82,208,92,218),(83,207,93,217),(84,206,94,216),(85,205,95,215),(86,204,96,214),(87,203,97,213),(88,202,98,212),(89,201,99,211),(90,220,100,210),(101,227,111,237),(102,226,112,236),(103,225,113,235),(104,224,114,234),(105,223,115,233),(106,222,116,232),(107,221,117,231),(108,240,118,230),(109,239,119,229),(110,238,120,228)])
93 conjugacy classes
| class | 1 | 2A | 2B | 3A | 3B | 4A | 4B | 4C | 4D | 5A | 5B | 6A | 6B | 6C | 6D | 8A | 8B | 8C | 8D | 10A | 10B | 10C | 10D | 12A | 12B | 12C | 12D | 12E | 12F | 12G | 12H | 15A | 15B | 15C | 15D | 20A | 20B | 20C | 20D | 20E | 20F | 24A | 24B | 24C | 24D | 24E | 24F | 24G | 24H | 30A | 30B | 30C | 30D | 30E | 30F | 30G | 30H | 40A | ··· | 40H | 60A | ··· | 60H | 60I | 60J | 60K | 60L | 120A | ··· | 120P |
| order | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 6 | 8 | 8 | 8 | 8 | 10 | 10 | 10 | 10 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 15 | 15 | 15 | 15 | 20 | 20 | 20 | 20 | 20 | 20 | 24 | 24 | 24 | 24 | 24 | 24 | 24 | 24 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 40 | ··· | 40 | 60 | ··· | 60 | 60 | 60 | 60 | 60 | 120 | ··· | 120 |
| size | 1 | 1 | 2 | 1 | 1 | 2 | 2 | 20 | 20 | 2 | 2 | 1 | 1 | 2 | 2 | 4 | 4 | 20 | 20 | 2 | 2 | 4 | 4 | 2 | 2 | 2 | 2 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 20 | 20 | 20 | 20 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 |
93 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | - | ||||||||||||||||
| image | C1 | C2 | C2 | C2 | C3 | C4 | C6 | C6 | C6 | C12 | D4 | D5 | D10 | C3×D4 | C3×D5 | D20 | C5⋊D4 | C4×D5 | C6×D5 | C3×D20 | C3×C5⋊D4 | D5×C12 | C4.10D4 | C3×C4.10D4 | C20.47D4 | C3×C20.47D4 |
| kernel | C3×C20.47D4 | C3×C4.Dic5 | C15×M4(2) | C6×Dic10 | C20.47D4 | C6×Dic5 | C4.Dic5 | C5×M4(2) | C2×Dic10 | C2×Dic5 | C60 | C3×M4(2) | C2×C12 | C20 | M4(2) | C12 | C12 | C2×C6 | C2×C4 | C4 | C4 | C22 | C15 | C5 | C3 | C1 |
| # reps | 1 | 1 | 1 | 1 | 2 | 4 | 2 | 2 | 2 | 8 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 1 | 2 | 4 | 8 |
Matrix representation of C3×C20.47D4 ►in GL4(𝔽241) generated by
| 15 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 |
| 0 | 0 | 15 | 0 |
| 0 | 0 | 0 | 15 |
| 238 | 197 | 0 | 0 |
| 44 | 163 | 0 | 0 |
| 0 | 0 | 41 | 197 |
| 0 | 0 | 163 | 119 |
| 60 | 148 | 196 | 203 |
| 75 | 181 | 225 | 83 |
| 47 | 36 | 135 | 181 |
| 70 | 230 | 119 | 106 |
| 60 | 148 | 0 | 0 |
| 75 | 181 | 0 | 0 |
| 0 | 0 | 106 | 60 |
| 0 | 0 | 122 | 135 |
G:=sub<GL(4,GF(241))| [15,0,0,0,0,15,0,0,0,0,15,0,0,0,0,15],[238,44,0,0,197,163,0,0,0,0,41,163,0,0,197,119],[60,75,47,70,148,181,36,230,196,225,135,119,203,83,181,106],[60,75,0,0,148,181,0,0,0,0,106,122,0,0,60,135] >;
C3×C20.47D4 in GAP, Magma, Sage, TeX
C_3\times C_{20}._{47}D_4 % in TeX
G:=Group("C3xC20.47D4"); // GroupNames label
G:=SmallGroup(480,102);
// by ID
G=gap.SmallGroup(480,102);
# by ID
G:=PCGroup([7,-2,-2,-3,-2,-2,-2,-5,336,365,92,1683,136,1271,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^20=1,c^4=d^2=b^10,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d^-1=b^-1,d*c*d^-1=b^5*c^3>;
// generators/relations