Copied to
clipboard

G = D4.9D30order 480 = 25·3·5

4th non-split extension by D4 of D30 acting via D30/C30=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D4.9D30, C60.207D4, Q8.14D30, C60.82C23, Dic30.43C22, C4○D4.4D15, (C5×D4).33D6, (C2×C4).22D30, (C2×C30).10D4, (C5×Q8).52D6, D4.D1514C2, C157Q1614C2, (C3×D4).33D10, C30.393(C2×D4), (C2×C20).160D6, C55(Q8.14D6), (C3×Q8).35D10, C60.7C422C2, (C2×Dic30)⋊14C2, (C2×C12).158D10, C35(D4.9D10), C4.25(C157D4), C1537(C8.C22), (C2×C60).85C22, C4.19(C22×D15), C12.104(C5⋊D4), C20.104(C3⋊D4), C20.120(C22×S3), C153C8.22C22, (D4×C15).38C22, C12.120(C22×D5), C22.6(C157D4), (Q8×C15).40C22, (C3×C4○D4).3D5, (C5×C4○D4).7S3, (C15×C4○D4).3C2, C6.120(C2×C5⋊D4), C2.25(C2×C157D4), C10.120(C2×C3⋊D4), (C2×C6).22(C5⋊D4), (C2×C10).21(C3⋊D4), SmallGroup(480,916)

Series: Derived Chief Lower central Upper central

C1C60 — D4.9D30
C1C5C15C30C60Dic30C2×Dic30 — D4.9D30
C15C30C60 — D4.9D30
C1C2C2×C4C4○D4

Generators and relations for D4.9D30
 G = < a,b,c,d | a4=b2=c30=1, d2=a2, bab=dad-1=a-1, ac=ca, cbc-1=a2b, dbd-1=a-1b, dcd-1=c-1 >

Subgroups: 548 in 120 conjugacy classes, 47 normal (39 characteristic)
C1, C2, C2 [×2], C3, C4 [×2], C4 [×3], C22, C22, C5, C6, C6 [×2], C8 [×2], C2×C4, C2×C4 [×2], D4, D4, Q8, Q8 [×3], C10, C10 [×2], Dic3 [×2], C12 [×2], C12, C2×C6, C2×C6, C15, M4(2), SD16 [×2], Q16 [×2], C2×Q8, C4○D4, Dic5 [×2], C20 [×2], C20, C2×C10, C2×C10, C3⋊C8 [×2], Dic6 [×3], C2×Dic3, C2×C12, C2×C12, C3×D4, C3×D4, C3×Q8, C30, C30 [×2], C8.C22, C52C8 [×2], Dic10 [×3], C2×Dic5, C2×C20, C2×C20, C5×D4, C5×D4, C5×Q8, C4.Dic3, D4.S3 [×2], C3⋊Q16 [×2], C2×Dic6, C3×C4○D4, Dic15 [×2], C60 [×2], C60, C2×C30, C2×C30, C4.Dic5, D4.D5 [×2], C5⋊Q16 [×2], C2×Dic10, C5×C4○D4, Q8.14D6, C153C8 [×2], Dic30 [×2], Dic30, C2×Dic15, C2×C60, C2×C60, D4×C15, D4×C15, Q8×C15, D4.9D10, C60.7C4, D4.D15 [×2], C157Q16 [×2], C2×Dic30, C15×C4○D4, D4.9D30
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], C3⋊D4 [×2], C22×S3, D15, C8.C22, C5⋊D4 [×2], C22×D5, C2×C3⋊D4, D30 [×3], C2×C5⋊D4, Q8.14D6, C157D4 [×2], C22×D15, D4.9D10, C2×C157D4, D4.9D30

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

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

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

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

81 conjugacy classes

class 1 2A2B2C 3 4A4B4C4D4E5A5B6A6B6C6D8A8B10A10B10C···10H12A12B12C12D12E15A15B15C15D20A20B20C20D20E···20J30A30B30C30D30E···30P60A···60H60I···60T
order122234444455666688101010···101212121212151515152020202020···203030303030···3060···6060···60
size1124222460602224446060224···422444222222224···422224···42···24···4

81 irreducible representations

dim111111222222222222222222224444
type++++++++++++++++++++----
imageC1C2C2C2C2C2S3D4D4D5D6D6D6D10D10D10C3⋊D4C3⋊D4D15C5⋊D4C5⋊D4D30D30D30C157D4C157D4C8.C22Q8.14D6D4.9D10D4.9D30
kernelD4.9D30C60.7C4D4.D15C157Q16C2×Dic30C15×C4○D4C5×C4○D4C60C2×C30C3×C4○D4C2×C20C5×D4C5×Q8C2×C12C3×D4C3×Q8C20C2×C10C4○D4C12C2×C6C2×C4D4Q8C4C22C15C5C3C1
# reps112211111211122222444444881248

Matrix representation of D4.9D30 in GL4(𝔽241) generated by

4415600
8819700
11421920085
1359215641
,
23011912846
5639174174
149125792
11917743206
,
1616400
679400
16797211177
236956416
,
947500
22614700
194108169166
106613772
G:=sub<GL(4,GF(241))| [44,88,114,135,156,197,219,92,0,0,200,156,0,0,85,41],[230,56,149,119,119,39,125,177,128,174,7,43,46,174,92,206],[161,67,167,236,64,94,97,95,0,0,211,64,0,0,177,16],[94,226,194,106,75,147,108,61,0,0,169,37,0,0,166,72] >;

D4.9D30 in GAP, Magma, Sage, TeX

D_4._9D_{30}
% in TeX

G:=Group("D4.9D30");
// GroupNames label

G:=SmallGroup(480,916);
// by ID

G=gap.SmallGroup(480,916);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,254,219,675,185,80,2693,18822]);
// Polycyclic

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

׿
×
𝔽