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G = C3×C20.53D4order 480 = 25·3·5

Direct product of C3 and C20.53D4

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

Aliases: C3×C20.53D4, C60.231D4, (C2×C30).9Q8, C52C8.1C12, C4.13(D5×C12), C20.53(C3×D4), C12.83(C4×D5), C30.51(C4⋊C4), C20.26(C2×C12), C60.160(C2×C4), (C2×C6).4Dic10, C1514(C8.C4), C4.Dic5.2C6, (C2×C12).352D10, (C3×M4(2)).1D5, M4(2).1(C3×D5), (C5×M4(2)).1C6, C12.121(C5⋊D4), (C2×C60).275C22, (C15×M4(2)).1C2, C22.1(C3×Dic10), C6.18(C10.D4), (C2×C10).(C3×Q8), C54(C3×C8.C4), C10.15(C3×C4⋊C4), (C2×C52C8).4C6, (C3×C52C8).4C4, (C2×C4).31(C6×D5), C4.28(C3×C5⋊D4), (C6×C52C8).16C2, (C2×C20).11(C2×C6), C2.5(C3×C10.D4), (C3×C4.Dic5).6C2, SmallGroup(480,100)

Series: Derived Chief Lower central Upper central

C1C20 — C3×C20.53D4
C1C5C10C20C2×C20C2×C60C6×C52C8 — C3×C20.53D4
C5C10C20 — C3×C20.53D4
C1C12C2×C12C3×M4(2)

Generators and relations for C3×C20.53D4
 G = < a,b,c,d | a3=b20=1, c4=b10, d2=b5, ab=ba, ac=ca, ad=da, cbc-1=dbd-1=b9, dcd-1=b10c3 >

Subgroups: 128 in 60 conjugacy classes, 38 normal (all characteristic)
C1, C2, C2, C3, C4 [×2], C22, C5, C6, C6, C8 [×4], C2×C4, C10, C10, C12 [×2], C2×C6, C15, C2×C8, M4(2), M4(2), C20 [×2], C2×C10, C24 [×4], C2×C12, C30, C30, C8.C4, C52C8 [×2], C52C8, C40, C2×C20, C2×C24, C3×M4(2), C3×M4(2), C60 [×2], C2×C30, C2×C52C8, C4.Dic5, C5×M4(2), C3×C8.C4, C3×C52C8 [×2], C3×C52C8, C120, C2×C60, C20.53D4, C6×C52C8, C3×C4.Dic5, C15×M4(2), C3×C20.53D4
Quotients: C1, C2 [×3], C3, C4 [×2], C22, C6 [×3], C2×C4, D4, Q8, D5, C12 [×2], C2×C6, C4⋊C4, D10, C2×C12, C3×D4, C3×Q8, C3×D5, C8.C4, Dic10, C4×D5, C5⋊D4, C3×C4⋊C4, C6×D5, C10.D4, C3×C8.C4, C3×Dic10, D5×C12, C3×C5⋊D4, C20.53D4, C3×C10.D4, C3×C20.53D4

Smallest permutation representation of C3×C20.53D4
On 240 points
Generators in S240
(1 60 32)(2 41 33)(3 42 34)(4 43 35)(5 44 36)(6 45 37)(7 46 38)(8 47 39)(9 48 40)(10 49 21)(11 50 22)(12 51 23)(13 52 24)(14 53 25)(15 54 26)(16 55 27)(17 56 28)(18 57 29)(19 58 30)(20 59 31)(61 112 95)(62 113 96)(63 114 97)(64 115 98)(65 116 99)(66 117 100)(67 118 81)(68 119 82)(69 120 83)(70 101 84)(71 102 85)(72 103 86)(73 104 87)(74 105 88)(75 106 89)(76 107 90)(77 108 91)(78 109 92)(79 110 93)(80 111 94)(121 161 151)(122 162 152)(123 163 153)(124 164 154)(125 165 155)(126 166 156)(127 167 157)(128 168 158)(129 169 159)(130 170 160)(131 171 141)(132 172 142)(133 173 143)(134 174 144)(135 175 145)(136 176 146)(137 177 147)(138 178 148)(139 179 149)(140 180 150)(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)
(1 136 16 131 11 126 6 121)(2 125 17 140 12 135 7 130)(3 134 18 129 13 124 8 139)(4 123 19 138 14 133 9 128)(5 132 20 127 15 122 10 137)(21 147 36 142 31 157 26 152)(22 156 37 151 32 146 27 141)(23 145 38 160 33 155 28 150)(24 154 39 149 34 144 29 159)(25 143 40 158 35 153 30 148)(41 165 56 180 51 175 46 170)(42 174 57 169 52 164 47 179)(43 163 58 178 53 173 48 168)(44 172 59 167 54 162 49 177)(45 161 60 176 55 171 50 166)(61 183 66 188 71 193 76 198)(62 192 67 197 72 182 77 187)(63 181 68 186 73 191 78 196)(64 190 69 195 74 200 79 185)(65 199 70 184 75 189 80 194)(81 212 86 217 91 202 96 207)(82 201 87 206 92 211 97 216)(83 210 88 215 93 220 98 205)(84 219 89 204 94 209 99 214)(85 208 90 213 95 218 100 203)(101 239 106 224 111 229 116 234)(102 228 107 233 112 238 117 223)(103 237 108 222 113 227 118 232)(104 226 109 231 114 236 119 221)(105 235 110 240 115 225 120 230)
(1 191 6 196 11 181 16 186)(2 200 7 185 12 190 17 195)(3 189 8 194 13 199 18 184)(4 198 9 183 14 188 19 193)(5 187 10 192 15 197 20 182)(21 207 26 212 31 217 36 202)(22 216 27 201 32 206 37 211)(23 205 28 210 33 215 38 220)(24 214 29 219 34 204 39 209)(25 203 30 208 35 213 40 218)(41 235 46 240 51 225 56 230)(42 224 47 229 52 234 57 239)(43 233 48 238 53 223 58 228)(44 222 49 227 54 232 59 237)(45 231 50 236 55 221 60 226)(61 133 66 138 71 123 76 128)(62 122 67 127 72 132 77 137)(63 131 68 136 73 121 78 126)(64 140 69 125 74 130 79 135)(65 129 70 134 75 139 80 124)(81 157 86 142 91 147 96 152)(82 146 87 151 92 156 97 141)(83 155 88 160 93 145 98 150)(84 144 89 149 94 154 99 159)(85 153 90 158 95 143 100 148)(101 174 106 179 111 164 116 169)(102 163 107 168 112 173 117 178)(103 172 108 177 113 162 118 167)(104 161 109 166 114 171 119 176)(105 170 110 175 115 180 120 165)

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

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

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

102 conjugacy classes

class 1 2A2B3A3B4A4B4C5A5B6A6B6C6D8A8B8C8D8E8F8G8H10A10B10C10D12A12B12C12D12E12F15A15B15C15D20A20B20C20D20E20F24A24B24C24D24E···24L24M24N24O24P30A30B30C30D30E30F30G30H40A···40H60A···60H60I60J60K60L120A···120P
order122334445566668888888810101010121212121212151515152020202020202424242424···2424242424303030303030303040···4060···6060606060120···120
size112111122211224410101010202022441111222222222244444410···1020202020222244444···42···244444···4

102 irreducible representations

dim1111111111222222222222222244
type+++++-++-
imageC1C2C2C2C3C4C6C6C6C12D4Q8D5D10C3×D4C3×Q8C3×D5C8.C4C4×D5C5⋊D4Dic10C6×D5C3×C8.C4D5×C12C3×C5⋊D4C3×Dic10C20.53D4C3×C20.53D4
kernelC3×C20.53D4C6×C52C8C3×C4.Dic5C15×M4(2)C20.53D4C3×C52C8C2×C52C8C4.Dic5C5×M4(2)C52C8C60C2×C30C3×M4(2)C2×C12C20C2×C10M4(2)C15C12C12C2×C6C2×C4C5C4C4C22C3C1
# reps1111242228112222444444888848

Matrix representation of C3×C20.53D4 in GL4(𝔽241) generated by

1000
0100
002250
000225
,
51100
240000
001770
000177
,
1929800
1874900
0080
00136211
,
1929800
1874900
009067
0058151
G:=sub<GL(4,GF(241))| [1,0,0,0,0,1,0,0,0,0,225,0,0,0,0,225],[51,240,0,0,1,0,0,0,0,0,177,0,0,0,0,177],[192,187,0,0,98,49,0,0,0,0,8,136,0,0,0,211],[192,187,0,0,98,49,0,0,0,0,90,58,0,0,67,151] >;

C3×C20.53D4 in GAP, Magma, Sage, TeX

C_3\times C_{20}._{53}D_4
% in TeX

G:=Group("C3xC20.53D4");
// GroupNames label

G:=SmallGroup(480,100);
// by ID

G=gap.SmallGroup(480,100);
# by ID

G:=PCGroup([7,-2,-2,-3,-2,-2,-2,-5,168,365,92,136,1271,102,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^3=b^20=1,c^4=b^10,d^2=b^5,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^3>;
// generators/relations

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