metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D30.29D4, C4⋊C4⋊2D15, (C2×D60).4C2, C6.105(D4×D5), (C2×C4).12D30, C2.12(D4×D15), (C2×C20).38D6, (C2×C12).38D10, C30.313(C2×D4), C10.107(S3×D4), C5⋊5(D6.D4), C30.4Q8⋊7C2, D30⋊3C4⋊35C2, C30.173(C4○D4), C6.100(C4○D20), C2.5(Q8⋊3D15), C3⋊5(D10.13D4), (C2×C30).291C23, (C2×C60).179C22, C6.41(Q8⋊2D5), C10.100(C4○D12), C10.41(Q8⋊3S3), C15⋊31(C22.D4), C2.14(D60⋊11C2), (C22×D15).7C22, C22.49(C22×D15), (C2×Dic15).164C22, (C5×C4⋊C4)⋊5S3, (C3×C4⋊C4)⋊5D5, (C15×C4⋊C4)⋊5C2, (C2×C4×D15)⋊19C2, (C2×C6).287(C22×D5), (C2×C10).286(C22×S3), SmallGroup(480,859)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D30.29D4
G = < a,b,c,d | a30=b2=c4=1, d2=a15, bab=a-1, ac=ca, ad=da, cbc-1=dbd-1=a15b, dcd-1=c-1 >
Subgroups: 1092 in 156 conjugacy classes, 49 normal (47 characteristic)
C1, C2, C2, C3, C4, C22, C22, C5, S3, C6, C2×C4, C2×C4, D4, C23, D5, C10, Dic3, C12, D6, C2×C6, C15, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, Dic5, C20, D10, C2×C10, C4×S3, D12, C2×Dic3, C2×C12, C22×S3, D15, C30, C22.D4, C4×D5, D20, C2×Dic5, C2×C20, C22×D5, Dic3⋊C4, D6⋊C4, C3×C4⋊C4, S3×C2×C4, C2×D12, Dic15, C60, D30, D30, C2×C30, C10.D4, D10⋊C4, C5×C4⋊C4, C2×C4×D5, C2×D20, D6.D4, C4×D15, D60, C2×Dic15, C2×C60, C22×D15, D10.13D4, C30.4Q8, D30⋊3C4, C15×C4⋊C4, C2×C4×D15, C2×D60, D30.29D4
Quotients: C1, C2, C22, S3, D4, C23, D5, D6, C2×D4, C4○D4, D10, C22×S3, D15, C22.D4, C22×D5, C4○D12, S3×D4, Q8⋊3S3, D30, C4○D20, D4×D5, Q8⋊2D5, D6.D4, C22×D15, D10.13D4, D60⋊11C2, D4×D15, Q8⋊3D15, D30.29D4
►On 240 points
Generators in S240
(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 30)(2 29)(3 28)(4 27)(5 26)(6 25)(7 24)(8 23)(9 22)(10 21)(11 20)(12 19)(13 18)(14 17)(15 16)(31 35)(32 34)(36 60)(37 59)(38 58)(39 57)(40 56)(41 55)(42 54)(43 53)(44 52)(45 51)(46 50)(47 49)(61 83)(62 82)(63 81)(64 80)(65 79)(66 78)(67 77)(68 76)(69 75)(70 74)(71 73)(84 90)(85 89)(86 88)(91 111)(92 110)(93 109)(94 108)(95 107)(96 106)(97 105)(98 104)(99 103)(100 102)(112 120)(113 119)(114 118)(115 117)(121 126)(122 125)(123 124)(127 150)(128 149)(129 148)(130 147)(131 146)(132 145)(133 144)(134 143)(135 142)(136 141)(137 140)(138 139)(151 161)(152 160)(153 159)(154 158)(155 157)(162 180)(163 179)(164 178)(165 177)(166 176)(167 175)(168 174)(169 173)(170 172)(181 196)(182 195)(183 194)(184 193)(185 192)(186 191)(187 190)(188 189)(197 210)(198 209)(199 208)(200 207)(201 206)(202 205)(203 204)(211 216)(212 215)(213 214)(217 240)(218 239)(219 238)(220 237)(221 236)(222 235)(223 234)(224 233)(225 232)(226 231)(227 230)(228 229)
(1 80 229 164)(2 81 230 165)(3 82 231 166)(4 83 232 167)(5 84 233 168)(6 85 234 169)(7 86 235 170)(8 87 236 171)(9 88 237 172)(10 89 238 173)(11 90 239 174)(12 61 240 175)(13 62 211 176)(14 63 212 177)(15 64 213 178)(16 65 214 179)(17 66 215 180)(18 67 216 151)(19 68 217 152)(20 69 218 153)(21 70 219 154)(22 71 220 155)(23 72 221 156)(24 73 222 157)(25 74 223 158)(26 75 224 159)(27 76 225 160)(28 77 226 161)(29 78 227 162)(30 79 228 163)(31 129 99 194)(32 130 100 195)(33 131 101 196)(34 132 102 197)(35 133 103 198)(36 134 104 199)(37 135 105 200)(38 136 106 201)(39 137 107 202)(40 138 108 203)(41 139 109 204)(42 140 110 205)(43 141 111 206)(44 142 112 207)(45 143 113 208)(46 144 114 209)(47 145 115 210)(48 146 116 181)(49 147 117 182)(50 148 118 183)(51 149 119 184)(52 150 120 185)(53 121 91 186)(54 122 92 187)(55 123 93 188)(56 124 94 189)(57 125 95 190)(58 126 96 191)(59 127 97 192)(60 128 98 193)
(1 56 16 41)(2 57 17 42)(3 58 18 43)(4 59 19 44)(5 60 20 45)(6 31 21 46)(7 32 22 47)(8 33 23 48)(9 34 24 49)(10 35 25 50)(11 36 26 51)(12 37 27 52)(13 38 28 53)(14 39 29 54)(15 40 30 55)(61 200 76 185)(62 201 77 186)(63 202 78 187)(64 203 79 188)(65 204 80 189)(66 205 81 190)(67 206 82 191)(68 207 83 192)(69 208 84 193)(70 209 85 194)(71 210 86 195)(72 181 87 196)(73 182 88 197)(74 183 89 198)(75 184 90 199)(91 211 106 226)(92 212 107 227)(93 213 108 228)(94 214 109 229)(95 215 110 230)(96 216 111 231)(97 217 112 232)(98 218 113 233)(99 219 114 234)(100 220 115 235)(101 221 116 236)(102 222 117 237)(103 223 118 238)(104 224 119 239)(105 225 120 240)(121 176 136 161)(122 177 137 162)(123 178 138 163)(124 179 139 164)(125 180 140 165)(126 151 141 166)(127 152 142 167)(128 153 143 168)(129 154 144 169)(130 155 145 170)(131 156 146 171)(132 157 147 172)(133 158 148 173)(134 159 149 174)(135 160 150 175)
G:=sub<Sym(240)| (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), (1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(31,35)(32,34)(36,60)(37,59)(38,58)(39,57)(40,56)(41,55)(42,54)(43,53)(44,52)(45,51)(46,50)(47,49)(61,83)(62,82)(63,81)(64,80)(65,79)(66,78)(67,77)(68,76)(69,75)(70,74)(71,73)(84,90)(85,89)(86,88)(91,111)(92,110)(93,109)(94,108)(95,107)(96,106)(97,105)(98,104)(99,103)(100,102)(112,120)(113,119)(114,118)(115,117)(121,126)(122,125)(123,124)(127,150)(128,149)(129,148)(130,147)(131,146)(132,145)(133,144)(134,143)(135,142)(136,141)(137,140)(138,139)(151,161)(152,160)(153,159)(154,158)(155,157)(162,180)(163,179)(164,178)(165,177)(166,176)(167,175)(168,174)(169,173)(170,172)(181,196)(182,195)(183,194)(184,193)(185,192)(186,191)(187,190)(188,189)(197,210)(198,209)(199,208)(200,207)(201,206)(202,205)(203,204)(211,216)(212,215)(213,214)(217,240)(218,239)(219,238)(220,237)(221,236)(222,235)(223,234)(224,233)(225,232)(226,231)(227,230)(228,229), (1,80,229,164)(2,81,230,165)(3,82,231,166)(4,83,232,167)(5,84,233,168)(6,85,234,169)(7,86,235,170)(8,87,236,171)(9,88,237,172)(10,89,238,173)(11,90,239,174)(12,61,240,175)(13,62,211,176)(14,63,212,177)(15,64,213,178)(16,65,214,179)(17,66,215,180)(18,67,216,151)(19,68,217,152)(20,69,218,153)(21,70,219,154)(22,71,220,155)(23,72,221,156)(24,73,222,157)(25,74,223,158)(26,75,224,159)(27,76,225,160)(28,77,226,161)(29,78,227,162)(30,79,228,163)(31,129,99,194)(32,130,100,195)(33,131,101,196)(34,132,102,197)(35,133,103,198)(36,134,104,199)(37,135,105,200)(38,136,106,201)(39,137,107,202)(40,138,108,203)(41,139,109,204)(42,140,110,205)(43,141,111,206)(44,142,112,207)(45,143,113,208)(46,144,114,209)(47,145,115,210)(48,146,116,181)(49,147,117,182)(50,148,118,183)(51,149,119,184)(52,150,120,185)(53,121,91,186)(54,122,92,187)(55,123,93,188)(56,124,94,189)(57,125,95,190)(58,126,96,191)(59,127,97,192)(60,128,98,193), (1,56,16,41)(2,57,17,42)(3,58,18,43)(4,59,19,44)(5,60,20,45)(6,31,21,46)(7,32,22,47)(8,33,23,48)(9,34,24,49)(10,35,25,50)(11,36,26,51)(12,37,27,52)(13,38,28,53)(14,39,29,54)(15,40,30,55)(61,200,76,185)(62,201,77,186)(63,202,78,187)(64,203,79,188)(65,204,80,189)(66,205,81,190)(67,206,82,191)(68,207,83,192)(69,208,84,193)(70,209,85,194)(71,210,86,195)(72,181,87,196)(73,182,88,197)(74,183,89,198)(75,184,90,199)(91,211,106,226)(92,212,107,227)(93,213,108,228)(94,214,109,229)(95,215,110,230)(96,216,111,231)(97,217,112,232)(98,218,113,233)(99,219,114,234)(100,220,115,235)(101,221,116,236)(102,222,117,237)(103,223,118,238)(104,224,119,239)(105,225,120,240)(121,176,136,161)(122,177,137,162)(123,178,138,163)(124,179,139,164)(125,180,140,165)(126,151,141,166)(127,152,142,167)(128,153,143,168)(129,154,144,169)(130,155,145,170)(131,156,146,171)(132,157,147,172)(133,158,148,173)(134,159,149,174)(135,160,150,175)>;
G:=Group( (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), (1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(31,35)(32,34)(36,60)(37,59)(38,58)(39,57)(40,56)(41,55)(42,54)(43,53)(44,52)(45,51)(46,50)(47,49)(61,83)(62,82)(63,81)(64,80)(65,79)(66,78)(67,77)(68,76)(69,75)(70,74)(71,73)(84,90)(85,89)(86,88)(91,111)(92,110)(93,109)(94,108)(95,107)(96,106)(97,105)(98,104)(99,103)(100,102)(112,120)(113,119)(114,118)(115,117)(121,126)(122,125)(123,124)(127,150)(128,149)(129,148)(130,147)(131,146)(132,145)(133,144)(134,143)(135,142)(136,141)(137,140)(138,139)(151,161)(152,160)(153,159)(154,158)(155,157)(162,180)(163,179)(164,178)(165,177)(166,176)(167,175)(168,174)(169,173)(170,172)(181,196)(182,195)(183,194)(184,193)(185,192)(186,191)(187,190)(188,189)(197,210)(198,209)(199,208)(200,207)(201,206)(202,205)(203,204)(211,216)(212,215)(213,214)(217,240)(218,239)(219,238)(220,237)(221,236)(222,235)(223,234)(224,233)(225,232)(226,231)(227,230)(228,229), (1,80,229,164)(2,81,230,165)(3,82,231,166)(4,83,232,167)(5,84,233,168)(6,85,234,169)(7,86,235,170)(8,87,236,171)(9,88,237,172)(10,89,238,173)(11,90,239,174)(12,61,240,175)(13,62,211,176)(14,63,212,177)(15,64,213,178)(16,65,214,179)(17,66,215,180)(18,67,216,151)(19,68,217,152)(20,69,218,153)(21,70,219,154)(22,71,220,155)(23,72,221,156)(24,73,222,157)(25,74,223,158)(26,75,224,159)(27,76,225,160)(28,77,226,161)(29,78,227,162)(30,79,228,163)(31,129,99,194)(32,130,100,195)(33,131,101,196)(34,132,102,197)(35,133,103,198)(36,134,104,199)(37,135,105,200)(38,136,106,201)(39,137,107,202)(40,138,108,203)(41,139,109,204)(42,140,110,205)(43,141,111,206)(44,142,112,207)(45,143,113,208)(46,144,114,209)(47,145,115,210)(48,146,116,181)(49,147,117,182)(50,148,118,183)(51,149,119,184)(52,150,120,185)(53,121,91,186)(54,122,92,187)(55,123,93,188)(56,124,94,189)(57,125,95,190)(58,126,96,191)(59,127,97,192)(60,128,98,193), (1,56,16,41)(2,57,17,42)(3,58,18,43)(4,59,19,44)(5,60,20,45)(6,31,21,46)(7,32,22,47)(8,33,23,48)(9,34,24,49)(10,35,25,50)(11,36,26,51)(12,37,27,52)(13,38,28,53)(14,39,29,54)(15,40,30,55)(61,200,76,185)(62,201,77,186)(63,202,78,187)(64,203,79,188)(65,204,80,189)(66,205,81,190)(67,206,82,191)(68,207,83,192)(69,208,84,193)(70,209,85,194)(71,210,86,195)(72,181,87,196)(73,182,88,197)(74,183,89,198)(75,184,90,199)(91,211,106,226)(92,212,107,227)(93,213,108,228)(94,214,109,229)(95,215,110,230)(96,216,111,231)(97,217,112,232)(98,218,113,233)(99,219,114,234)(100,220,115,235)(101,221,116,236)(102,222,117,237)(103,223,118,238)(104,224,119,239)(105,225,120,240)(121,176,136,161)(122,177,137,162)(123,178,138,163)(124,179,139,164)(125,180,140,165)(126,151,141,166)(127,152,142,167)(128,153,143,168)(129,154,144,169)(130,155,145,170)(131,156,146,171)(132,157,147,172)(133,158,148,173)(134,159,149,174)(135,160,150,175) );
G=PermutationGroup([[(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)], [(1,30),(2,29),(3,28),(4,27),(5,26),(6,25),(7,24),(8,23),(9,22),(10,21),(11,20),(12,19),(13,18),(14,17),(15,16),(31,35),(32,34),(36,60),(37,59),(38,58),(39,57),(40,56),(41,55),(42,54),(43,53),(44,52),(45,51),(46,50),(47,49),(61,83),(62,82),(63,81),(64,80),(65,79),(66,78),(67,77),(68,76),(69,75),(70,74),(71,73),(84,90),(85,89),(86,88),(91,111),(92,110),(93,109),(94,108),(95,107),(96,106),(97,105),(98,104),(99,103),(100,102),(112,120),(113,119),(114,118),(115,117),(121,126),(122,125),(123,124),(127,150),(128,149),(129,148),(130,147),(131,146),(132,145),(133,144),(134,143),(135,142),(136,141),(137,140),(138,139),(151,161),(152,160),(153,159),(154,158),(155,157),(162,180),(163,179),(164,178),(165,177),(166,176),(167,175),(168,174),(169,173),(170,172),(181,196),(182,195),(183,194),(184,193),(185,192),(186,191),(187,190),(188,189),(197,210),(198,209),(199,208),(200,207),(201,206),(202,205),(203,204),(211,216),(212,215),(213,214),(217,240),(218,239),(219,238),(220,237),(221,236),(222,235),(223,234),(224,233),(225,232),(226,231),(227,230),(228,229)], [(1,80,229,164),(2,81,230,165),(3,82,231,166),(4,83,232,167),(5,84,233,168),(6,85,234,169),(7,86,235,170),(8,87,236,171),(9,88,237,172),(10,89,238,173),(11,90,239,174),(12,61,240,175),(13,62,211,176),(14,63,212,177),(15,64,213,178),(16,65,214,179),(17,66,215,180),(18,67,216,151),(19,68,217,152),(20,69,218,153),(21,70,219,154),(22,71,220,155),(23,72,221,156),(24,73,222,157),(25,74,223,158),(26,75,224,159),(27,76,225,160),(28,77,226,161),(29,78,227,162),(30,79,228,163),(31,129,99,194),(32,130,100,195),(33,131,101,196),(34,132,102,197),(35,133,103,198),(36,134,104,199),(37,135,105,200),(38,136,106,201),(39,137,107,202),(40,138,108,203),(41,139,109,204),(42,140,110,205),(43,141,111,206),(44,142,112,207),(45,143,113,208),(46,144,114,209),(47,145,115,210),(48,146,116,181),(49,147,117,182),(50,148,118,183),(51,149,119,184),(52,150,120,185),(53,121,91,186),(54,122,92,187),(55,123,93,188),(56,124,94,189),(57,125,95,190),(58,126,96,191),(59,127,97,192),(60,128,98,193)], [(1,56,16,41),(2,57,17,42),(3,58,18,43),(4,59,19,44),(5,60,20,45),(6,31,21,46),(7,32,22,47),(8,33,23,48),(9,34,24,49),(10,35,25,50),(11,36,26,51),(12,37,27,52),(13,38,28,53),(14,39,29,54),(15,40,30,55),(61,200,76,185),(62,201,77,186),(63,202,78,187),(64,203,79,188),(65,204,80,189),(66,205,81,190),(67,206,82,191),(68,207,83,192),(69,208,84,193),(70,209,85,194),(71,210,86,195),(72,181,87,196),(73,182,88,197),(74,183,89,198),(75,184,90,199),(91,211,106,226),(92,212,107,227),(93,213,108,228),(94,214,109,229),(95,215,110,230),(96,216,111,231),(97,217,112,232),(98,218,113,233),(99,219,114,234),(100,220,115,235),(101,221,116,236),(102,222,117,237),(103,223,118,238),(104,224,119,239),(105,225,120,240),(121,176,136,161),(122,177,137,162),(123,178,138,163),(124,179,139,164),(125,180,140,165),(126,151,141,166),(127,152,142,167),(128,153,143,168),(129,154,144,169),(130,155,145,170),(131,156,146,171),(132,157,147,172),(133,158,148,173),(134,159,149,174),(135,160,150,175)]])
84 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 5A | 5B | 6A | 6B | 6C | 10A | ··· | 10F | 12A | ··· | 12F | 15A | 15B | 15C | 15D | 20A | ··· | 20L | 30A | ··· | 30L | 60A | ··· | 60X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 10 | ··· | 10 | 12 | ··· | 12 | 15 | 15 | 15 | 15 | 20 | ··· | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 30 | 30 | 60 | 2 | 2 | 2 | 4 | 4 | 30 | 30 | 60 | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
84 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | S3 | D4 | D5 | D6 | C4○D4 | D10 | D15 | C4○D12 | D30 | C4○D20 | D60⋊11C2 | S3×D4 | Q8⋊3S3 | D4×D5 | Q8⋊2D5 | D4×D15 | Q8⋊3D15 |
| kernel | D30.29D4 | C30.4Q8 | D30⋊3C4 | C15×C4⋊C4 | C2×C4×D15 | C2×D60 | C5×C4⋊C4 | D30 | C3×C4⋊C4 | C2×C20 | C30 | C2×C12 | C4⋊C4 | C10 | C2×C4 | C6 | C2 | C10 | C10 | C6 | C6 | C2 | C2 |
| # reps | 1 | 1 | 3 | 1 | 1 | 1 | 1 | 2 | 2 | 3 | 4 | 6 | 4 | 4 | 12 | 8 | 16 | 1 | 1 | 2 | 2 | 4 | 4 |
Matrix representation of D30.29D4 ►in GL4(𝔽61) generated by
| 14 | 52 | 0 | 0 |
| 39 | 36 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 18 | 0 | 0 |
| 17 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 14 | 17 | 0 | 0 |
| 28 | 47 | 0 | 0 |
| 0 | 0 | 60 | 53 |
| 0 | 0 | 46 | 1 |
| 32 | 4 | 0 | 0 |
| 3 | 29 | 0 | 0 |
| 0 | 0 | 53 | 46 |
| 0 | 0 | 53 | 8 |
G:=sub<GL(4,GF(61))| [14,39,0,0,52,36,0,0,0,0,1,0,0,0,0,1],[0,17,0,0,18,0,0,0,0,0,1,0,0,0,0,1],[14,28,0,0,17,47,0,0,0,0,60,46,0,0,53,1],[32,3,0,0,4,29,0,0,0,0,53,53,0,0,46,8] >;
D30.29D4 in GAP, Magma, Sage, TeX
D_{30}._{29}D_4 % in TeX
G:=Group("D30.29D4"); // GroupNames label
G:=SmallGroup(480,859);
// by ID
G=gap.SmallGroup(480,859);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,64,254,219,100,2693,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^30=b^2=c^4=1,d^2=a^15,b*a*b=a^-1,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d^-1=a^15*b,d*c*d^-1=c^-1>;
// generators/relations