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G = D4.5D30order 480 = 25·3·5

5th non-split extension by D4 of D30 acting via D30/D15=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D4.5D30, C40.33D6, C8.11D30, Q8.7D30, SD163D15, D30.18D4, C24.33D10, C60.70C23, C120.28C22, Dic15.50D4, D60.22C22, Dic30.24C22, (C8×D15)⋊5C2, C24⋊D58C2, D4⋊D1512C2, C1531(C4○D8), (C5×SD16)⋊4S3, (C3×SD16)⋊4D5, (C5×D4).17D6, C2.21(D4×D15), C6.114(D4×D5), (C5×Q8).31D6, Q83D159C2, (C15×SD16)⋊4C2, (C3×D4).17D10, C157Q1610C2, C30.321(C2×D4), C10.116(S3×D4), C55(Q8.7D6), (C3×Q8).14D10, D42D1510C2, C4.7(C22×D15), C35(SD163D5), C20.108(C22×S3), C153C8.32C22, (C4×D15).45C22, (D4×C15).24C22, C12.108(C22×D5), (Q8×C15).23C22, SmallGroup(480,881)

Series: Derived Chief Lower central Upper central

C1C60 — D4.5D30
C1C5C15C30C60C4×D15D42D15 — D4.5D30
C15C30C60 — D4.5D30
C1C2C4SD16

Generators and relations for D4.5D30
 G = < a,b,c,d | a4=b2=d2=1, c30=a2, bab=cac-1=dad=a-1, cbc-1=a-1b, dbd=ab, dcd=a2c29 >

Subgroups: 804 in 124 conjugacy classes, 41 normal (all characteristic)
C1, C2, C2 [×3], C3, C4, C4 [×3], C22 [×3], C5, S3 [×2], C6, C6, C8, C8, C2×C4 [×3], D4, D4 [×3], Q8, Q8, D5 [×2], C10, C10, Dic3 [×2], C12, C12, D6 [×2], C2×C6, C15, C2×C8, D8, SD16, SD16, Q16, C4○D4 [×2], Dic5 [×2], C20, C20, D10 [×2], C2×C10, C3⋊C8, C24, Dic6, C4×S3 [×2], D12 [×2], C2×Dic3, C3⋊D4, C3×D4, C3×Q8, D15 [×2], C30, C30, C4○D8, C52C8, C40, Dic10, C4×D5 [×2], D20 [×2], C2×Dic5, C5⋊D4, C5×D4, C5×Q8, S3×C8, C24⋊C2, D4⋊S3, C3⋊Q16, C3×SD16, D42S3, Q83S3, Dic15, Dic15, C60, C60, D30, D30, C2×C30, C8×D5, C40⋊C2, D4⋊D5, C5⋊Q16, C5×SD16, D42D5, Q82D5, Q8.7D6, C153C8, C120, Dic30, C4×D15, C4×D15, D60, D60, C2×Dic15, C157D4, D4×C15, Q8×C15, SD163D5, C8×D15, C24⋊D5, D4⋊D15, C157Q16, C15×SD16, D42D15, Q83D15, D4.5D30
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], C22×S3, D15, C4○D8, C22×D5, S3×D4, D30 [×3], D4×D5, Q8.7D6, C22×D15, SD163D5, D4×D15, D4.5D30

Smallest permutation representation of D4.5D30
On 240 points
Generators in S240
(1 203 31 233)(2 234 32 204)(3 205 33 235)(4 236 34 206)(5 207 35 237)(6 238 36 208)(7 209 37 239)(8 240 38 210)(9 211 39 181)(10 182 40 212)(11 213 41 183)(12 184 42 214)(13 215 43 185)(14 186 44 216)(15 217 45 187)(16 188 46 218)(17 219 47 189)(18 190 48 220)(19 221 49 191)(20 192 50 222)(21 223 51 193)(22 194 52 224)(23 225 53 195)(24 196 54 226)(25 227 55 197)(26 198 56 228)(27 229 57 199)(28 200 58 230)(29 231 59 201)(30 202 60 232)(61 152 91 122)(62 123 92 153)(63 154 93 124)(64 125 94 155)(65 156 95 126)(66 127 96 157)(67 158 97 128)(68 129 98 159)(69 160 99 130)(70 131 100 161)(71 162 101 132)(72 133 102 163)(73 164 103 134)(74 135 104 165)(75 166 105 136)(76 137 106 167)(77 168 107 138)(78 139 108 169)(79 170 109 140)(80 141 110 171)(81 172 111 142)(82 143 112 173)(83 174 113 144)(84 145 114 175)(85 176 115 146)(86 147 116 177)(87 178 117 148)(88 149 118 179)(89 180 119 150)(90 151 120 121)
(1 79)(2 171)(3 81)(4 173)(5 83)(6 175)(7 85)(8 177)(9 87)(10 179)(11 89)(12 121)(13 91)(14 123)(15 93)(16 125)(17 95)(18 127)(19 97)(20 129)(21 99)(22 131)(23 101)(24 133)(25 103)(26 135)(27 105)(28 137)(29 107)(30 139)(31 109)(32 141)(33 111)(34 143)(35 113)(36 145)(37 115)(38 147)(39 117)(40 149)(41 119)(42 151)(43 61)(44 153)(45 63)(46 155)(47 65)(48 157)(49 67)(50 159)(51 69)(52 161)(53 71)(54 163)(55 73)(56 165)(57 75)(58 167)(59 77)(60 169)(62 186)(64 188)(66 190)(68 192)(70 194)(72 196)(74 198)(76 200)(78 202)(80 204)(82 206)(84 208)(86 210)(88 212)(90 214)(92 216)(94 218)(96 220)(98 222)(100 224)(102 226)(104 228)(106 230)(108 232)(110 234)(112 236)(114 238)(116 240)(118 182)(120 184)(122 185)(124 187)(126 189)(128 191)(130 193)(132 195)(134 197)(136 199)(138 201)(140 203)(142 205)(144 207)(146 209)(148 211)(150 213)(152 215)(154 217)(156 219)(158 221)(160 223)(162 225)(164 227)(166 229)(168 231)(170 233)(172 235)(174 237)(176 239)(178 181)(180 183)
(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 60)(32 59)(33 58)(34 57)(35 56)(36 55)(37 54)(38 53)(39 52)(40 51)(41 50)(42 49)(43 48)(44 47)(45 46)(61 96)(62 95)(63 94)(64 93)(65 92)(66 91)(67 90)(68 89)(69 88)(70 87)(71 86)(72 85)(73 84)(74 83)(75 82)(76 81)(77 80)(78 79)(97 120)(98 119)(99 118)(100 117)(101 116)(102 115)(103 114)(104 113)(105 112)(106 111)(107 110)(108 109)(121 158)(122 157)(123 156)(124 155)(125 154)(126 153)(127 152)(128 151)(129 150)(130 149)(131 148)(132 147)(133 146)(134 145)(135 144)(136 143)(137 142)(138 141)(139 140)(159 180)(160 179)(161 178)(162 177)(163 176)(164 175)(165 174)(166 173)(167 172)(168 171)(169 170)(181 194)(182 193)(183 192)(184 191)(185 190)(186 189)(187 188)(195 240)(196 239)(197 238)(198 237)(199 236)(200 235)(201 234)(202 233)(203 232)(204 231)(205 230)(206 229)(207 228)(208 227)(209 226)(210 225)(211 224)(212 223)(213 222)(214 221)(215 220)(216 219)(217 218)

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

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

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

63 conjugacy classes

class 1 2A2B2C2D 3 4A4B4C4D4E5A5B6A6B8A8B8C8D10A10B10C10D12A12B15A15B15C15D20A20B20C20D24A24B30A30B30C30D30E30F30G30H40A40B40C40D60A60B60C60D60E60F60G60H120A···120H
order1222234444455668888101010101212151515152020202024243030303030303030404040406060606060606060120···120
size114306022415156022282230302288482222448844222288884444444488884···4

63 irreducible representations

dim11111111222222222222222444444
type+++++++++++++++++++++++++
imageC1C2C2C2C2C2C2C2S3D4D4D5D6D6D6D10D10D10D15C4○D8D30D30D30S3×D4D4×D5Q8.7D6SD163D5D4×D15D4.5D30
kernelD4.5D30C8×D15C24⋊D5D4⋊D15C157Q16C15×SD16D42D15Q83D15C5×SD16Dic15D30C3×SD16C40C5×D4C5×Q8C24C3×D4C3×Q8SD16C15C8D4Q8C10C6C5C3C2C1
# reps11111111111211122244444122448

Matrix representation of D4.5D30 in GL4(𝔽241) generated by

1000
0100
00640
0058177
,
240000
024000
00233134
001568
,
1779300
1326800
0024077
00971
,
21113100
983000
001164
000240
G:=sub<GL(4,GF(241))| [1,0,0,0,0,1,0,0,0,0,64,58,0,0,0,177],[240,0,0,0,0,240,0,0,0,0,233,156,0,0,134,8],[177,132,0,0,93,68,0,0,0,0,240,97,0,0,77,1],[211,98,0,0,131,30,0,0,0,0,1,0,0,0,164,240] >;

D4.5D30 in GAP, Magma, Sage, TeX

D_4._5D_{30}
% in TeX

G:=Group("D4.5D30");
// GroupNames label

G:=SmallGroup(480,881);
// by ID

G=gap.SmallGroup(480,881);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,253,422,135,100,346,185,80,2693,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^4=b^2=d^2=1,c^30=a^2,b*a*b=c*a*c^-1=d*a*d=a^-1,c*b*c^-1=a^-1*b,d*b*d=a*b,d*c*d=a^2*c^29>;
// generators/relations

׿
×
𝔽