metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic3⋊C4⋊10D5, (C4×Dic15)⋊8C2, (C2×C20).182D6, C6.Dic10⋊6C2, C30.Q8⋊7C2, C15⋊8(C42⋊2C2), D10⋊C4.5S3, C30.32(C4○D4), C6.24(C4○D20), (C2×C12).181D10, (C2×C30).56C23, (C2×Dic5).14D6, (C22×D5).10D6, C5⋊3(C23.8D6), C10.28(C4○D12), C6.66(D4⋊2D5), (C2×C60).159C22, C6.26(Q8⋊2D5), (C2×Dic3).14D10, D10⋊Dic3.8C2, C10.66(D4⋊2S3), C2.10(D20⋊S3), (C6×Dic5).33C22, C2.17(D6.D10), C2.12(C30.C23), (C10×Dic3).33C22, (C2×Dic15).186C22, C3⋊6(C4⋊C4⋊D5), (D5×C2×C6).8C22, (C2×C4).172(S3×D5), C22.143(C2×S3×D5), (C5×Dic3⋊C4)⋊10C2, (C2×C6).68(C22×D5), (C3×D10⋊C4).5C2, (C2×C10).68(C22×S3), SmallGroup(480,442)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C4×Dic15)⋊C2
G = < a,b,c,d | a4=b30=d2=1, c2=b15, ab=ba, ac=ca, dad=a-1b15, cbc-1=b-1, dbd=b19, dcd=a2c >
Subgroups: 556 in 120 conjugacy classes, 44 normal (all characteristic)
C1, C2, C2, C3, C4, C22, C22, C5, C6, C6, C2×C4, C2×C4, C23, D5, C10, Dic3, C12, C2×C6, C2×C6, C15, C42, C22⋊C4, C4⋊C4, Dic5, C20, D10, C2×C10, C2×Dic3, C2×Dic3, C2×C12, C2×C12, C22×C6, C3×D5, C30, C42⋊2C2, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C22×D5, C4×Dic3, Dic3⋊C4, Dic3⋊C4, C4⋊Dic3, C6.D4, C3×C22⋊C4, C5×Dic3, C3×Dic5, Dic15, C60, C6×D5, C2×C30, C4×Dic5, C10.D4, C4⋊Dic5, D10⋊C4, D10⋊C4, C5×C4⋊C4, C23.8D6, C6×Dic5, C10×Dic3, C2×Dic15, C2×C60, D5×C2×C6, C4⋊C4⋊D5, D10⋊Dic3, C30.Q8, C6.Dic10, C3×D10⋊C4, C5×Dic3⋊C4, C4×Dic15, (C4×Dic15)⋊C2
Quotients: C1, C2, C22, S3, C23, D5, D6, C4○D4, D10, C22×S3, C42⋊2C2, C22×D5, C4○D12, D4⋊2S3, S3×D5, C4○D20, D4⋊2D5, Q8⋊2D5, C23.8D6, C2×S3×D5, C4⋊C4⋊D5, D20⋊S3, D6.D10, C30.C23, (C4×Dic15)⋊C2
►On 240 points
Generators in S240
(1 153 189 47)(2 154 190 48)(3 155 191 49)(4 156 192 50)(5 157 193 51)(6 158 194 52)(7 159 195 53)(8 160 196 54)(9 161 197 55)(10 162 198 56)(11 163 199 57)(12 164 200 58)(13 165 201 59)(14 166 202 60)(15 167 203 31)(16 168 204 32)(17 169 205 33)(18 170 206 34)(19 171 207 35)(20 172 208 36)(21 173 209 37)(22 174 210 38)(23 175 181 39)(24 176 182 40)(25 177 183 41)(26 178 184 42)(27 179 185 43)(28 180 186 44)(29 151 187 45)(30 152 188 46)(61 140 212 113)(62 141 213 114)(63 142 214 115)(64 143 215 116)(65 144 216 117)(66 145 217 118)(67 146 218 119)(68 147 219 120)(69 148 220 91)(70 149 221 92)(71 150 222 93)(72 121 223 94)(73 122 224 95)(74 123 225 96)(75 124 226 97)(76 125 227 98)(77 126 228 99)(78 127 229 100)(79 128 230 101)(80 129 231 102)(81 130 232 103)(82 131 233 104)(83 132 234 105)(84 133 235 106)(85 134 236 107)(86 135 237 108)(87 136 238 109)(88 137 239 110)(89 138 240 111)(90 139 211 112)
(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)
(1 216 16 231)(2 215 17 230)(3 214 18 229)(4 213 19 228)(5 212 20 227)(6 211 21 226)(7 240 22 225)(8 239 23 224)(9 238 24 223)(10 237 25 222)(11 236 26 221)(12 235 27 220)(13 234 28 219)(14 233 29 218)(15 232 30 217)(31 130 46 145)(32 129 47 144)(33 128 48 143)(34 127 49 142)(35 126 50 141)(36 125 51 140)(37 124 52 139)(38 123 53 138)(39 122 54 137)(40 121 55 136)(41 150 56 135)(42 149 57 134)(43 148 58 133)(44 147 59 132)(45 146 60 131)(61 208 76 193)(62 207 77 192)(63 206 78 191)(64 205 79 190)(65 204 80 189)(66 203 81 188)(67 202 82 187)(68 201 83 186)(69 200 84 185)(70 199 85 184)(71 198 86 183)(72 197 87 182)(73 196 88 181)(74 195 89 210)(75 194 90 209)(91 164 106 179)(92 163 107 178)(93 162 108 177)(94 161 109 176)(95 160 110 175)(96 159 111 174)(97 158 112 173)(98 157 113 172)(99 156 114 171)(100 155 115 170)(101 154 116 169)(102 153 117 168)(103 152 118 167)(104 151 119 166)(105 180 120 165)
(2 20)(3 9)(4 28)(5 17)(7 25)(8 14)(10 22)(12 30)(13 19)(15 27)(18 24)(23 29)(31 164)(32 153)(33 172)(34 161)(35 180)(36 169)(37 158)(38 177)(39 166)(40 155)(41 174)(42 163)(43 152)(44 171)(45 160)(46 179)(47 168)(48 157)(49 176)(50 165)(51 154)(52 173)(53 162)(54 151)(55 170)(56 159)(57 178)(58 167)(59 156)(60 175)(61 230)(62 219)(63 238)(64 227)(65 216)(66 235)(67 224)(68 213)(69 232)(70 221)(71 240)(72 229)(73 218)(74 237)(75 226)(76 215)(77 234)(78 223)(79 212)(80 231)(81 220)(82 239)(83 228)(84 217)(85 236)(86 225)(87 214)(88 233)(89 222)(90 211)(91 118)(92 107)(93 96)(94 115)(95 104)(97 112)(98 101)(99 120)(100 109)(102 117)(103 106)(105 114)(108 111)(110 119)(113 116)(121 142)(122 131)(123 150)(124 139)(125 128)(126 147)(127 136)(129 144)(130 133)(132 141)(134 149)(135 138)(137 146)(140 143)(145 148)(181 187)(182 206)(183 195)(185 203)(186 192)(188 200)(190 208)(191 197)(193 205)(196 202)(198 210)(201 207)
G:=sub<Sym(240)| (1,153,189,47)(2,154,190,48)(3,155,191,49)(4,156,192,50)(5,157,193,51)(6,158,194,52)(7,159,195,53)(8,160,196,54)(9,161,197,55)(10,162,198,56)(11,163,199,57)(12,164,200,58)(13,165,201,59)(14,166,202,60)(15,167,203,31)(16,168,204,32)(17,169,205,33)(18,170,206,34)(19,171,207,35)(20,172,208,36)(21,173,209,37)(22,174,210,38)(23,175,181,39)(24,176,182,40)(25,177,183,41)(26,178,184,42)(27,179,185,43)(28,180,186,44)(29,151,187,45)(30,152,188,46)(61,140,212,113)(62,141,213,114)(63,142,214,115)(64,143,215,116)(65,144,216,117)(66,145,217,118)(67,146,218,119)(68,147,219,120)(69,148,220,91)(70,149,221,92)(71,150,222,93)(72,121,223,94)(73,122,224,95)(74,123,225,96)(75,124,226,97)(76,125,227,98)(77,126,228,99)(78,127,229,100)(79,128,230,101)(80,129,231,102)(81,130,232,103)(82,131,233,104)(83,132,234,105)(84,133,235,106)(85,134,236,107)(86,135,237,108)(87,136,238,109)(88,137,239,110)(89,138,240,111)(90,139,211,112), (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), (1,216,16,231)(2,215,17,230)(3,214,18,229)(4,213,19,228)(5,212,20,227)(6,211,21,226)(7,240,22,225)(8,239,23,224)(9,238,24,223)(10,237,25,222)(11,236,26,221)(12,235,27,220)(13,234,28,219)(14,233,29,218)(15,232,30,217)(31,130,46,145)(32,129,47,144)(33,128,48,143)(34,127,49,142)(35,126,50,141)(36,125,51,140)(37,124,52,139)(38,123,53,138)(39,122,54,137)(40,121,55,136)(41,150,56,135)(42,149,57,134)(43,148,58,133)(44,147,59,132)(45,146,60,131)(61,208,76,193)(62,207,77,192)(63,206,78,191)(64,205,79,190)(65,204,80,189)(66,203,81,188)(67,202,82,187)(68,201,83,186)(69,200,84,185)(70,199,85,184)(71,198,86,183)(72,197,87,182)(73,196,88,181)(74,195,89,210)(75,194,90,209)(91,164,106,179)(92,163,107,178)(93,162,108,177)(94,161,109,176)(95,160,110,175)(96,159,111,174)(97,158,112,173)(98,157,113,172)(99,156,114,171)(100,155,115,170)(101,154,116,169)(102,153,117,168)(103,152,118,167)(104,151,119,166)(105,180,120,165), (2,20)(3,9)(4,28)(5,17)(7,25)(8,14)(10,22)(12,30)(13,19)(15,27)(18,24)(23,29)(31,164)(32,153)(33,172)(34,161)(35,180)(36,169)(37,158)(38,177)(39,166)(40,155)(41,174)(42,163)(43,152)(44,171)(45,160)(46,179)(47,168)(48,157)(49,176)(50,165)(51,154)(52,173)(53,162)(54,151)(55,170)(56,159)(57,178)(58,167)(59,156)(60,175)(61,230)(62,219)(63,238)(64,227)(65,216)(66,235)(67,224)(68,213)(69,232)(70,221)(71,240)(72,229)(73,218)(74,237)(75,226)(76,215)(77,234)(78,223)(79,212)(80,231)(81,220)(82,239)(83,228)(84,217)(85,236)(86,225)(87,214)(88,233)(89,222)(90,211)(91,118)(92,107)(93,96)(94,115)(95,104)(97,112)(98,101)(99,120)(100,109)(102,117)(103,106)(105,114)(108,111)(110,119)(113,116)(121,142)(122,131)(123,150)(124,139)(125,128)(126,147)(127,136)(129,144)(130,133)(132,141)(134,149)(135,138)(137,146)(140,143)(145,148)(181,187)(182,206)(183,195)(185,203)(186,192)(188,200)(190,208)(191,197)(193,205)(196,202)(198,210)(201,207)>;
G:=Group( (1,153,189,47)(2,154,190,48)(3,155,191,49)(4,156,192,50)(5,157,193,51)(6,158,194,52)(7,159,195,53)(8,160,196,54)(9,161,197,55)(10,162,198,56)(11,163,199,57)(12,164,200,58)(13,165,201,59)(14,166,202,60)(15,167,203,31)(16,168,204,32)(17,169,205,33)(18,170,206,34)(19,171,207,35)(20,172,208,36)(21,173,209,37)(22,174,210,38)(23,175,181,39)(24,176,182,40)(25,177,183,41)(26,178,184,42)(27,179,185,43)(28,180,186,44)(29,151,187,45)(30,152,188,46)(61,140,212,113)(62,141,213,114)(63,142,214,115)(64,143,215,116)(65,144,216,117)(66,145,217,118)(67,146,218,119)(68,147,219,120)(69,148,220,91)(70,149,221,92)(71,150,222,93)(72,121,223,94)(73,122,224,95)(74,123,225,96)(75,124,226,97)(76,125,227,98)(77,126,228,99)(78,127,229,100)(79,128,230,101)(80,129,231,102)(81,130,232,103)(82,131,233,104)(83,132,234,105)(84,133,235,106)(85,134,236,107)(86,135,237,108)(87,136,238,109)(88,137,239,110)(89,138,240,111)(90,139,211,112), (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), (1,216,16,231)(2,215,17,230)(3,214,18,229)(4,213,19,228)(5,212,20,227)(6,211,21,226)(7,240,22,225)(8,239,23,224)(9,238,24,223)(10,237,25,222)(11,236,26,221)(12,235,27,220)(13,234,28,219)(14,233,29,218)(15,232,30,217)(31,130,46,145)(32,129,47,144)(33,128,48,143)(34,127,49,142)(35,126,50,141)(36,125,51,140)(37,124,52,139)(38,123,53,138)(39,122,54,137)(40,121,55,136)(41,150,56,135)(42,149,57,134)(43,148,58,133)(44,147,59,132)(45,146,60,131)(61,208,76,193)(62,207,77,192)(63,206,78,191)(64,205,79,190)(65,204,80,189)(66,203,81,188)(67,202,82,187)(68,201,83,186)(69,200,84,185)(70,199,85,184)(71,198,86,183)(72,197,87,182)(73,196,88,181)(74,195,89,210)(75,194,90,209)(91,164,106,179)(92,163,107,178)(93,162,108,177)(94,161,109,176)(95,160,110,175)(96,159,111,174)(97,158,112,173)(98,157,113,172)(99,156,114,171)(100,155,115,170)(101,154,116,169)(102,153,117,168)(103,152,118,167)(104,151,119,166)(105,180,120,165), (2,20)(3,9)(4,28)(5,17)(7,25)(8,14)(10,22)(12,30)(13,19)(15,27)(18,24)(23,29)(31,164)(32,153)(33,172)(34,161)(35,180)(36,169)(37,158)(38,177)(39,166)(40,155)(41,174)(42,163)(43,152)(44,171)(45,160)(46,179)(47,168)(48,157)(49,176)(50,165)(51,154)(52,173)(53,162)(54,151)(55,170)(56,159)(57,178)(58,167)(59,156)(60,175)(61,230)(62,219)(63,238)(64,227)(65,216)(66,235)(67,224)(68,213)(69,232)(70,221)(71,240)(72,229)(73,218)(74,237)(75,226)(76,215)(77,234)(78,223)(79,212)(80,231)(81,220)(82,239)(83,228)(84,217)(85,236)(86,225)(87,214)(88,233)(89,222)(90,211)(91,118)(92,107)(93,96)(94,115)(95,104)(97,112)(98,101)(99,120)(100,109)(102,117)(103,106)(105,114)(108,111)(110,119)(113,116)(121,142)(122,131)(123,150)(124,139)(125,128)(126,147)(127,136)(129,144)(130,133)(132,141)(134,149)(135,138)(137,146)(140,143)(145,148)(181,187)(182,206)(183,195)(185,203)(186,192)(188,200)(190,208)(191,197)(193,205)(196,202)(198,210)(201,207) );
G=PermutationGroup([[(1,153,189,47),(2,154,190,48),(3,155,191,49),(4,156,192,50),(5,157,193,51),(6,158,194,52),(7,159,195,53),(8,160,196,54),(9,161,197,55),(10,162,198,56),(11,163,199,57),(12,164,200,58),(13,165,201,59),(14,166,202,60),(15,167,203,31),(16,168,204,32),(17,169,205,33),(18,170,206,34),(19,171,207,35),(20,172,208,36),(21,173,209,37),(22,174,210,38),(23,175,181,39),(24,176,182,40),(25,177,183,41),(26,178,184,42),(27,179,185,43),(28,180,186,44),(29,151,187,45),(30,152,188,46),(61,140,212,113),(62,141,213,114),(63,142,214,115),(64,143,215,116),(65,144,216,117),(66,145,217,118),(67,146,218,119),(68,147,219,120),(69,148,220,91),(70,149,221,92),(71,150,222,93),(72,121,223,94),(73,122,224,95),(74,123,225,96),(75,124,226,97),(76,125,227,98),(77,126,228,99),(78,127,229,100),(79,128,230,101),(80,129,231,102),(81,130,232,103),(82,131,233,104),(83,132,234,105),(84,133,235,106),(85,134,236,107),(86,135,237,108),(87,136,238,109),(88,137,239,110),(89,138,240,111),(90,139,211,112)], [(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)], [(1,216,16,231),(2,215,17,230),(3,214,18,229),(4,213,19,228),(5,212,20,227),(6,211,21,226),(7,240,22,225),(8,239,23,224),(9,238,24,223),(10,237,25,222),(11,236,26,221),(12,235,27,220),(13,234,28,219),(14,233,29,218),(15,232,30,217),(31,130,46,145),(32,129,47,144),(33,128,48,143),(34,127,49,142),(35,126,50,141),(36,125,51,140),(37,124,52,139),(38,123,53,138),(39,122,54,137),(40,121,55,136),(41,150,56,135),(42,149,57,134),(43,148,58,133),(44,147,59,132),(45,146,60,131),(61,208,76,193),(62,207,77,192),(63,206,78,191),(64,205,79,190),(65,204,80,189),(66,203,81,188),(67,202,82,187),(68,201,83,186),(69,200,84,185),(70,199,85,184),(71,198,86,183),(72,197,87,182),(73,196,88,181),(74,195,89,210),(75,194,90,209),(91,164,106,179),(92,163,107,178),(93,162,108,177),(94,161,109,176),(95,160,110,175),(96,159,111,174),(97,158,112,173),(98,157,113,172),(99,156,114,171),(100,155,115,170),(101,154,116,169),(102,153,117,168),(103,152,118,167),(104,151,119,166),(105,180,120,165)], [(2,20),(3,9),(4,28),(5,17),(7,25),(8,14),(10,22),(12,30),(13,19),(15,27),(18,24),(23,29),(31,164),(32,153),(33,172),(34,161),(35,180),(36,169),(37,158),(38,177),(39,166),(40,155),(41,174),(42,163),(43,152),(44,171),(45,160),(46,179),(47,168),(48,157),(49,176),(50,165),(51,154),(52,173),(53,162),(54,151),(55,170),(56,159),(57,178),(58,167),(59,156),(60,175),(61,230),(62,219),(63,238),(64,227),(65,216),(66,235),(67,224),(68,213),(69,232),(70,221),(71,240),(72,229),(73,218),(74,237),(75,226),(76,215),(77,234),(78,223),(79,212),(80,231),(81,220),(82,239),(83,228),(84,217),(85,236),(86,225),(87,214),(88,233),(89,222),(90,211),(91,118),(92,107),(93,96),(94,115),(95,104),(97,112),(98,101),(99,120),(100,109),(102,117),(103,106),(105,114),(108,111),(110,119),(113,116),(121,142),(122,131),(123,150),(124,139),(125,128),(126,147),(127,136),(129,144),(130,133),(132,141),(134,149),(135,138),(137,146),(140,143),(145,148),(181,187),(182,206),(183,195),(185,203),(186,192),(188,200),(190,208),(191,197),(193,205),(196,202),(198,210),(201,207)]])
60 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 5A | 5B | 6A | 6B | 6C | 6D | 6E | 10A | ··· | 10F | 12A | 12B | 12C | 12D | 15A | 15B | 20A | 20B | 20C | 20D | 20E | ··· | 20L | 30A | ··· | 30F | 60A | ··· | 60H |
| order | 1 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 6 | 6 | 10 | ··· | 10 | 12 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 20 | 20 | ··· | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 20 | 2 | 2 | 2 | 12 | 12 | 20 | 30 | 30 | 30 | 30 | 2 | 2 | 2 | 2 | 2 | 20 | 20 | 2 | ··· | 2 | 4 | 4 | 20 | 20 | 4 | 4 | 4 | 4 | 4 | 4 | 12 | ··· | 12 | 4 | ··· | 4 | 4 | ··· | 4 |
60 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | + | + | - | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | S3 | D5 | D6 | D6 | D6 | C4○D4 | D10 | D10 | C4○D12 | C4○D20 | D4⋊2S3 | S3×D5 | D4⋊2D5 | Q8⋊2D5 | C2×S3×D5 | D20⋊S3 | D6.D10 | C30.C23 |
| kernel | (C4×Dic15)⋊C2 | D10⋊Dic3 | C30.Q8 | C6.Dic10 | C3×D10⋊C4 | C5×Dic3⋊C4 | C4×Dic15 | D10⋊C4 | Dic3⋊C4 | C2×Dic5 | C2×C20 | C22×D5 | C30 | C2×Dic3 | C2×C12 | C10 | C6 | C10 | C2×C4 | C6 | C6 | C22 | C2 | C2 | C2 |
| # reps | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 6 | 4 | 2 | 4 | 8 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
Matrix representation of (C4×Dic15)⋊C2 ►in GL6(𝔽61)
| 11 | 0 | 0 | 0 | 0 | 0 |
| 0 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 8 | 0 | 0 |
| 0 | 0 | 15 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 0 |
| 0 | 0 | 0 | 0 | 0 | 11 |
| 43 | 1 | 0 | 0 | 0 | 0 |
| 42 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 14 | 39 |
| 0 | 0 | 0 | 0 | 0 | 48 |
| 8 | 14 | 0 | 0 | 0 | 0 |
| 52 | 53 | 0 | 0 | 0 | 0 |
| 0 | 0 | 50 | 34 | 0 | 0 |
| 0 | 0 | 18 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 48 |
| 0 | 0 | 0 | 0 | 51 | 33 |
| 43 | 1 | 0 | 0 | 0 | 0 |
| 43 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 8 | 0 | 0 |
| 0 | 0 | 0 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 30 |
| 0 | 0 | 0 | 0 | 0 | 60 |
G:=sub<GL(6,GF(61))| [11,0,0,0,0,0,0,11,0,0,0,0,0,0,1,15,0,0,0,0,8,60,0,0,0,0,0,0,11,0,0,0,0,0,0,11],[43,42,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,14,0,0,0,0,0,39,48],[8,52,0,0,0,0,14,53,0,0,0,0,0,0,50,18,0,0,0,0,34,11,0,0,0,0,0,0,28,51,0,0,0,0,48,33],[43,43,0,0,0,0,1,18,0,0,0,0,0,0,1,0,0,0,0,0,8,60,0,0,0,0,0,0,1,0,0,0,0,0,30,60] >;
(C4×Dic15)⋊C2 in GAP, Magma, Sage, TeX
(C_4\times {\rm Dic}_{15})\rtimes C_2 % in TeX
G:=Group("(C4xDic15):C2"); // GroupNames label
G:=SmallGroup(480,442);
// by ID
G=gap.SmallGroup(480,442);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,141,120,422,219,58,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^30=d^2=1,c^2=b^15,a*b=b*a,a*c=c*a,d*a*d=a^-1*b^15,c*b*c^-1=b^-1,d*b*d=b^19,d*c*d=a^2*c>;
// generators/relations