direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C3×C20.10D4, C60.120D4, (C6×Q8).7D5, (C2×C60).23C4, C20.10(C3×D4), (Q8×C10).6C6, (Q8×C30).7C2, (C2×C20).12C12, (C2×C12).1Dic5, C4.Dic5.4C6, (C2×C12).214D10, C12.94(C5⋊D4), C22.4(C6×Dic5), C15⋊11(C4.10D4), (C2×C60).282C22, C6.26(C23.D5), C30.114(C22⋊C4), (C2×C4).4(C6×D5), (C2×C4).(C3×Dic5), C5⋊3(C3×C4.10D4), C4.15(C3×C5⋊D4), (C2×Q8).4(C3×D5), (C2×C20).18(C2×C6), (C2×C10).51(C2×C12), (C2×C30).187(C2×C4), C2.7(C3×C23.D5), C10.28(C3×C22⋊C4), (C2×C6).22(C2×Dic5), (C3×C4.Dic5).8C2, SmallGroup(480,114)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3×C20.10D4
G = < a,b,c,d | a3=b20=1, c4=b10, d2=b5, ab=ba, ac=ca, ad=da, cbc-1=b-1, dbd-1=b9, dcd-1=b5c3 >
Subgroups: 160 in 76 conjugacy classes, 42 normal (22 characteristic)
C1, C2, C2, C3, C4, C4, C22, C5, C6, C6, C8, C2×C4, C2×C4, Q8, C10, C10, C12, C12, C2×C6, C15, M4(2), C2×Q8, C20, C20, C2×C10, C24, C2×C12, C2×C12, C3×Q8, C30, C30, C4.10D4, C5⋊2C8, C2×C20, C2×C20, C5×Q8, C3×M4(2), C6×Q8, C60, C60, C2×C30, C4.Dic5, Q8×C10, C3×C4.10D4, C3×C5⋊2C8, C2×C60, C2×C60, Q8×C15, C20.10D4, C3×C4.Dic5, Q8×C30, C3×C20.10D4
Quotients: C1, C2, C3, C4, C22, C6, C2×C4, D4, D5, C12, C2×C6, C22⋊C4, Dic5, D10, C2×C12, C3×D4, C3×D5, C4.10D4, C2×Dic5, C5⋊D4, C3×C22⋊C4, C3×Dic5, C6×D5, C23.D5, C3×C4.10D4, C6×Dic5, C3×C5⋊D4, C20.10D4, C3×C23.D5, C3×C20.10D4
►On 240 points
Generators in S240
(1 41 24)(2 42 25)(3 43 26)(4 44 27)(5 45 28)(6 46 29)(7 47 30)(8 48 31)(9 49 32)(10 50 33)(11 51 34)(12 52 35)(13 53 36)(14 54 37)(15 55 38)(16 56 39)(17 57 40)(18 58 21)(19 59 22)(20 60 23)(61 120 86)(62 101 87)(63 102 88)(64 103 89)(65 104 90)(66 105 91)(67 106 92)(68 107 93)(69 108 94)(70 109 95)(71 110 96)(72 111 97)(73 112 98)(74 113 99)(75 114 100)(76 115 81)(77 116 82)(78 117 83)(79 118 84)(80 119 85)(121 161 156)(122 162 157)(123 163 158)(124 164 159)(125 165 160)(126 166 141)(127 167 142)(128 168 143)(129 169 144)(130 170 145)(131 171 146)(132 172 147)(133 173 148)(134 174 149)(135 175 150)(136 176 151)(137 177 152)(138 178 153)(139 179 154)(140 180 155)(181 231 211)(182 232 212)(183 233 213)(184 234 214)(185 235 215)(186 236 216)(187 237 217)(188 238 218)(189 239 219)(190 240 220)(191 221 201)(192 222 202)(193 223 203)(194 224 204)(195 225 205)(196 226 206)(197 227 207)(198 228 208)(199 229 209)(200 230 210)
(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)
(1 196 16 181 11 186 6 191)(2 195 17 200 12 185 7 190)(3 194 18 199 13 184 8 189)(4 193 19 198 14 183 9 188)(5 192 20 197 15 182 10 187)(21 209 36 214 31 219 26 204)(22 208 37 213 32 218 27 203)(23 207 38 212 33 217 28 202)(24 206 39 211 34 216 29 201)(25 205 40 210 35 215 30 220)(41 226 56 231 51 236 46 221)(42 225 57 230 52 235 47 240)(43 224 58 229 53 234 48 239)(44 223 59 228 54 233 49 238)(45 222 60 227 55 232 50 237)(61 140 76 125 71 130 66 135)(62 139 77 124 72 129 67 134)(63 138 78 123 73 128 68 133)(64 137 79 122 74 127 69 132)(65 136 80 121 75 126 70 131)(81 160 96 145 91 150 86 155)(82 159 97 144 92 149 87 154)(83 158 98 143 93 148 88 153)(84 157 99 142 94 147 89 152)(85 156 100 141 95 146 90 151)(101 179 116 164 111 169 106 174)(102 178 117 163 112 168 107 173)(103 177 118 162 113 167 108 172)(104 176 119 161 114 166 109 171)(105 175 120 180 115 165 110 170)
(1 136 6 121 11 126 16 131)(2 125 7 130 12 135 17 140)(3 134 8 139 13 124 18 129)(4 123 9 128 14 133 19 138)(5 132 10 137 15 122 20 127)(21 144 26 149 31 154 36 159)(22 153 27 158 32 143 37 148)(23 142 28 147 33 152 38 157)(24 151 29 156 34 141 39 146)(25 160 30 145 35 150 40 155)(41 176 46 161 51 166 56 171)(42 165 47 170 52 175 57 180)(43 174 48 179 53 164 58 169)(44 163 49 168 54 173 59 178)(45 172 50 177 55 162 60 167)(61 190 66 195 71 200 76 185)(62 199 67 184 72 189 77 194)(63 188 68 193 73 198 78 183)(64 197 69 182 74 187 79 192)(65 186 70 191 75 196 80 181)(81 215 86 220 91 205 96 210)(82 204 87 209 92 214 97 219)(83 213 88 218 93 203 98 208)(84 202 89 207 94 212 99 217)(85 211 90 216 95 201 100 206)(101 229 106 234 111 239 116 224)(102 238 107 223 112 228 117 233)(103 227 108 232 113 237 118 222)(104 236 109 221 114 226 119 231)(105 225 110 230 115 235 120 240)
G:=sub<Sym(240)| (1,41,24)(2,42,25)(3,43,26)(4,44,27)(5,45,28)(6,46,29)(7,47,30)(8,48,31)(9,49,32)(10,50,33)(11,51,34)(12,52,35)(13,53,36)(14,54,37)(15,55,38)(16,56,39)(17,57,40)(18,58,21)(19,59,22)(20,60,23)(61,120,86)(62,101,87)(63,102,88)(64,103,89)(65,104,90)(66,105,91)(67,106,92)(68,107,93)(69,108,94)(70,109,95)(71,110,96)(72,111,97)(73,112,98)(74,113,99)(75,114,100)(76,115,81)(77,116,82)(78,117,83)(79,118,84)(80,119,85)(121,161,156)(122,162,157)(123,163,158)(124,164,159)(125,165,160)(126,166,141)(127,167,142)(128,168,143)(129,169,144)(130,170,145)(131,171,146)(132,172,147)(133,173,148)(134,174,149)(135,175,150)(136,176,151)(137,177,152)(138,178,153)(139,179,154)(140,180,155)(181,231,211)(182,232,212)(183,233,213)(184,234,214)(185,235,215)(186,236,216)(187,237,217)(188,238,218)(189,239,219)(190,240,220)(191,221,201)(192,222,202)(193,223,203)(194,224,204)(195,225,205)(196,226,206)(197,227,207)(198,228,208)(199,229,209)(200,230,210), (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), (1,196,16,181,11,186,6,191)(2,195,17,200,12,185,7,190)(3,194,18,199,13,184,8,189)(4,193,19,198,14,183,9,188)(5,192,20,197,15,182,10,187)(21,209,36,214,31,219,26,204)(22,208,37,213,32,218,27,203)(23,207,38,212,33,217,28,202)(24,206,39,211,34,216,29,201)(25,205,40,210,35,215,30,220)(41,226,56,231,51,236,46,221)(42,225,57,230,52,235,47,240)(43,224,58,229,53,234,48,239)(44,223,59,228,54,233,49,238)(45,222,60,227,55,232,50,237)(61,140,76,125,71,130,66,135)(62,139,77,124,72,129,67,134)(63,138,78,123,73,128,68,133)(64,137,79,122,74,127,69,132)(65,136,80,121,75,126,70,131)(81,160,96,145,91,150,86,155)(82,159,97,144,92,149,87,154)(83,158,98,143,93,148,88,153)(84,157,99,142,94,147,89,152)(85,156,100,141,95,146,90,151)(101,179,116,164,111,169,106,174)(102,178,117,163,112,168,107,173)(103,177,118,162,113,167,108,172)(104,176,119,161,114,166,109,171)(105,175,120,180,115,165,110,170), (1,136,6,121,11,126,16,131)(2,125,7,130,12,135,17,140)(3,134,8,139,13,124,18,129)(4,123,9,128,14,133,19,138)(5,132,10,137,15,122,20,127)(21,144,26,149,31,154,36,159)(22,153,27,158,32,143,37,148)(23,142,28,147,33,152,38,157)(24,151,29,156,34,141,39,146)(25,160,30,145,35,150,40,155)(41,176,46,161,51,166,56,171)(42,165,47,170,52,175,57,180)(43,174,48,179,53,164,58,169)(44,163,49,168,54,173,59,178)(45,172,50,177,55,162,60,167)(61,190,66,195,71,200,76,185)(62,199,67,184,72,189,77,194)(63,188,68,193,73,198,78,183)(64,197,69,182,74,187,79,192)(65,186,70,191,75,196,80,181)(81,215,86,220,91,205,96,210)(82,204,87,209,92,214,97,219)(83,213,88,218,93,203,98,208)(84,202,89,207,94,212,99,217)(85,211,90,216,95,201,100,206)(101,229,106,234,111,239,116,224)(102,238,107,223,112,228,117,233)(103,227,108,232,113,237,118,222)(104,236,109,221,114,226,119,231)(105,225,110,230,115,235,120,240)>;
G:=Group( (1,41,24)(2,42,25)(3,43,26)(4,44,27)(5,45,28)(6,46,29)(7,47,30)(8,48,31)(9,49,32)(10,50,33)(11,51,34)(12,52,35)(13,53,36)(14,54,37)(15,55,38)(16,56,39)(17,57,40)(18,58,21)(19,59,22)(20,60,23)(61,120,86)(62,101,87)(63,102,88)(64,103,89)(65,104,90)(66,105,91)(67,106,92)(68,107,93)(69,108,94)(70,109,95)(71,110,96)(72,111,97)(73,112,98)(74,113,99)(75,114,100)(76,115,81)(77,116,82)(78,117,83)(79,118,84)(80,119,85)(121,161,156)(122,162,157)(123,163,158)(124,164,159)(125,165,160)(126,166,141)(127,167,142)(128,168,143)(129,169,144)(130,170,145)(131,171,146)(132,172,147)(133,173,148)(134,174,149)(135,175,150)(136,176,151)(137,177,152)(138,178,153)(139,179,154)(140,180,155)(181,231,211)(182,232,212)(183,233,213)(184,234,214)(185,235,215)(186,236,216)(187,237,217)(188,238,218)(189,239,219)(190,240,220)(191,221,201)(192,222,202)(193,223,203)(194,224,204)(195,225,205)(196,226,206)(197,227,207)(198,228,208)(199,229,209)(200,230,210), (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), (1,196,16,181,11,186,6,191)(2,195,17,200,12,185,7,190)(3,194,18,199,13,184,8,189)(4,193,19,198,14,183,9,188)(5,192,20,197,15,182,10,187)(21,209,36,214,31,219,26,204)(22,208,37,213,32,218,27,203)(23,207,38,212,33,217,28,202)(24,206,39,211,34,216,29,201)(25,205,40,210,35,215,30,220)(41,226,56,231,51,236,46,221)(42,225,57,230,52,235,47,240)(43,224,58,229,53,234,48,239)(44,223,59,228,54,233,49,238)(45,222,60,227,55,232,50,237)(61,140,76,125,71,130,66,135)(62,139,77,124,72,129,67,134)(63,138,78,123,73,128,68,133)(64,137,79,122,74,127,69,132)(65,136,80,121,75,126,70,131)(81,160,96,145,91,150,86,155)(82,159,97,144,92,149,87,154)(83,158,98,143,93,148,88,153)(84,157,99,142,94,147,89,152)(85,156,100,141,95,146,90,151)(101,179,116,164,111,169,106,174)(102,178,117,163,112,168,107,173)(103,177,118,162,113,167,108,172)(104,176,119,161,114,166,109,171)(105,175,120,180,115,165,110,170), (1,136,6,121,11,126,16,131)(2,125,7,130,12,135,17,140)(3,134,8,139,13,124,18,129)(4,123,9,128,14,133,19,138)(5,132,10,137,15,122,20,127)(21,144,26,149,31,154,36,159)(22,153,27,158,32,143,37,148)(23,142,28,147,33,152,38,157)(24,151,29,156,34,141,39,146)(25,160,30,145,35,150,40,155)(41,176,46,161,51,166,56,171)(42,165,47,170,52,175,57,180)(43,174,48,179,53,164,58,169)(44,163,49,168,54,173,59,178)(45,172,50,177,55,162,60,167)(61,190,66,195,71,200,76,185)(62,199,67,184,72,189,77,194)(63,188,68,193,73,198,78,183)(64,197,69,182,74,187,79,192)(65,186,70,191,75,196,80,181)(81,215,86,220,91,205,96,210)(82,204,87,209,92,214,97,219)(83,213,88,218,93,203,98,208)(84,202,89,207,94,212,99,217)(85,211,90,216,95,201,100,206)(101,229,106,234,111,239,116,224)(102,238,107,223,112,228,117,233)(103,227,108,232,113,237,118,222)(104,236,109,221,114,226,119,231)(105,225,110,230,115,235,120,240) );
G=PermutationGroup([[(1,41,24),(2,42,25),(3,43,26),(4,44,27),(5,45,28),(6,46,29),(7,47,30),(8,48,31),(9,49,32),(10,50,33),(11,51,34),(12,52,35),(13,53,36),(14,54,37),(15,55,38),(16,56,39),(17,57,40),(18,58,21),(19,59,22),(20,60,23),(61,120,86),(62,101,87),(63,102,88),(64,103,89),(65,104,90),(66,105,91),(67,106,92),(68,107,93),(69,108,94),(70,109,95),(71,110,96),(72,111,97),(73,112,98),(74,113,99),(75,114,100),(76,115,81),(77,116,82),(78,117,83),(79,118,84),(80,119,85),(121,161,156),(122,162,157),(123,163,158),(124,164,159),(125,165,160),(126,166,141),(127,167,142),(128,168,143),(129,169,144),(130,170,145),(131,171,146),(132,172,147),(133,173,148),(134,174,149),(135,175,150),(136,176,151),(137,177,152),(138,178,153),(139,179,154),(140,180,155),(181,231,211),(182,232,212),(183,233,213),(184,234,214),(185,235,215),(186,236,216),(187,237,217),(188,238,218),(189,239,219),(190,240,220),(191,221,201),(192,222,202),(193,223,203),(194,224,204),(195,225,205),(196,226,206),(197,227,207),(198,228,208),(199,229,209),(200,230,210)], [(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)], [(1,196,16,181,11,186,6,191),(2,195,17,200,12,185,7,190),(3,194,18,199,13,184,8,189),(4,193,19,198,14,183,9,188),(5,192,20,197,15,182,10,187),(21,209,36,214,31,219,26,204),(22,208,37,213,32,218,27,203),(23,207,38,212,33,217,28,202),(24,206,39,211,34,216,29,201),(25,205,40,210,35,215,30,220),(41,226,56,231,51,236,46,221),(42,225,57,230,52,235,47,240),(43,224,58,229,53,234,48,239),(44,223,59,228,54,233,49,238),(45,222,60,227,55,232,50,237),(61,140,76,125,71,130,66,135),(62,139,77,124,72,129,67,134),(63,138,78,123,73,128,68,133),(64,137,79,122,74,127,69,132),(65,136,80,121,75,126,70,131),(81,160,96,145,91,150,86,155),(82,159,97,144,92,149,87,154),(83,158,98,143,93,148,88,153),(84,157,99,142,94,147,89,152),(85,156,100,141,95,146,90,151),(101,179,116,164,111,169,106,174),(102,178,117,163,112,168,107,173),(103,177,118,162,113,167,108,172),(104,176,119,161,114,166,109,171),(105,175,120,180,115,165,110,170)], [(1,136,6,121,11,126,16,131),(2,125,7,130,12,135,17,140),(3,134,8,139,13,124,18,129),(4,123,9,128,14,133,19,138),(5,132,10,137,15,122,20,127),(21,144,26,149,31,154,36,159),(22,153,27,158,32,143,37,148),(23,142,28,147,33,152,38,157),(24,151,29,156,34,141,39,146),(25,160,30,145,35,150,40,155),(41,176,46,161,51,166,56,171),(42,165,47,170,52,175,57,180),(43,174,48,179,53,164,58,169),(44,163,49,168,54,173,59,178),(45,172,50,177,55,162,60,167),(61,190,66,195,71,200,76,185),(62,199,67,184,72,189,77,194),(63,188,68,193,73,198,78,183),(64,197,69,182,74,187,79,192),(65,186,70,191,75,196,80,181),(81,215,86,220,91,205,96,210),(82,204,87,209,92,214,97,219),(83,213,88,218,93,203,98,208),(84,202,89,207,94,212,99,217),(85,211,90,216,95,201,100,206),(101,229,106,234,111,239,116,224),(102,238,107,223,112,228,117,233),(103,227,108,232,113,237,118,222),(104,236,109,221,114,226,119,231),(105,225,110,230,115,235,120,240)]])
93 conjugacy classes
| class | 1 | 2A | 2B | 3A | 3B | 4A | 4B | 4C | 4D | 5A | 5B | 6A | 6B | 6C | 6D | 8A | 8B | 8C | 8D | 10A | ··· | 10F | 12A | 12B | 12C | 12D | 12E | 12F | 12G | 12H | 15A | 15B | 15C | 15D | 20A | ··· | 20L | 24A | ··· | 24H | 30A | ··· | 30L | 60A | ··· | 60X |
| order | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 6 | 8 | 8 | 8 | 8 | 10 | ··· | 10 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 15 | 15 | 15 | 15 | 20 | ··· | 20 | 24 | ··· | 24 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 2 | 1 | 1 | 2 | 2 | 4 | 4 | 2 | 2 | 1 | 1 | 2 | 2 | 20 | 20 | 20 | 20 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 20 | ··· | 20 | 2 | ··· | 2 | 4 | ··· | 4 |
93 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | - | + | - | ||||||||||||||
| image | C1 | C2 | C2 | C3 | C4 | C6 | C6 | C12 | D4 | D5 | Dic5 | D10 | C3×D4 | C3×D5 | C5⋊D4 | C3×Dic5 | C6×D5 | C3×C5⋊D4 | C4.10D4 | C3×C4.10D4 | C20.10D4 | C3×C20.10D4 |
| kernel | C3×C20.10D4 | C3×C4.Dic5 | Q8×C30 | C20.10D4 | C2×C60 | C4.Dic5 | Q8×C10 | C2×C20 | C60 | C6×Q8 | C2×C12 | C2×C12 | C20 | C2×Q8 | C12 | C2×C4 | C2×C4 | C4 | C15 | C5 | C3 | C1 |
| # reps | 1 | 2 | 1 | 2 | 4 | 4 | 2 | 8 | 2 | 2 | 4 | 2 | 4 | 4 | 8 | 8 | 4 | 16 | 1 | 2 | 4 | 8 |
Matrix representation of C3×C20.10D4 ►in GL6(𝔽241)
| 15 | 0 | 0 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 98 | 117 | 0 | 0 | 0 | 0 |
| 0 | 91 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 240 | 0 | 0 | 0 |
| 0 | 0 | 153 | 0 | 0 | 1 |
| 0 | 0 | 0 | 88 | 240 | 0 |
| 21 | 219 | 0 | 0 | 0 | 0 |
| 42 | 220 | 0 | 0 | 0 | 0 |
| 0 | 0 | 53 | 25 | 183 | 214 |
| 0 | 0 | 223 | 154 | 214 | 58 |
| 0 | 0 | 170 | 106 | 188 | 18 |
| 0 | 0 | 106 | 205 | 216 | 87 |
| 220 | 240 | 0 | 0 | 0 | 0 |
| 199 | 21 | 0 | 0 | 0 | 0 |
| 0 | 0 | 152 | 88 | 239 | 0 |
| 0 | 0 | 88 | 152 | 0 | 239 |
| 0 | 0 | 0 | 0 | 89 | 153 |
| 0 | 0 | 1 | 0 | 153 | 89 |
G:=sub<GL(6,GF(241))| [15,0,0,0,0,0,0,15,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[98,0,0,0,0,0,117,91,0,0,0,0,0,0,0,240,153,0,0,0,1,0,0,88,0,0,0,0,0,240,0,0,0,0,1,0],[21,42,0,0,0,0,219,220,0,0,0,0,0,0,53,223,170,106,0,0,25,154,106,205,0,0,183,214,188,216,0,0,214,58,18,87],[220,199,0,0,0,0,240,21,0,0,0,0,0,0,152,88,0,1,0,0,88,152,0,0,0,0,239,0,89,153,0,0,0,239,153,89] >;
C3×C20.10D4 in GAP, Magma, Sage, TeX
C_3\times C_{20}._{10}D_4 % in TeX
G:=Group("C3xC20.10D4"); // GroupNames label
G:=SmallGroup(480,114);
// by ID
G=gap.SmallGroup(480,114);
# by ID
G:=PCGroup([7,-2,-2,-3,-2,-2,-2,-5,84,365,344,850,136,2524,18822]);
// 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=b^-1,d*b*d^-1=b^9,d*c*d^-1=b^5*c^3>;
// generators/relations