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## G = D30.29D4order 480 = 25·3·5

### 2nd non-split extension by D30 of D4 acting via D4/C22=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C30 — D30.29D4
 Chief series C1 — C5 — C15 — C30 — C2×C30 — C22×D15 — C2×C4×D15 — D30.29D4
 Lower central C15 — C2×C30 — D30.29D4
 Upper central C1 — C22 — C4⋊C4

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 [×3], C2 [×3], C3, C4 [×5], C22, C22 [×7], C5, S3 [×3], C6 [×3], C2×C4 [×3], C2×C4 [×4], D4 [×2], C23 [×2], D5 [×3], C10 [×3], Dic3 [×2], C12 [×3], D6 [×7], C2×C6, C15, C22⋊C4 [×3], C4⋊C4, C4⋊C4, C22×C4, C2×D4, Dic5 [×2], C20 [×3], D10 [×7], C2×C10, C4×S3 [×2], D12 [×2], C2×Dic3 [×2], C2×C12 [×3], C22×S3 [×2], D15 [×3], C30 [×3], C22.D4, C4×D5 [×2], D20 [×2], C2×Dic5 [×2], C2×C20 [×3], C22×D5 [×2], Dic3⋊C4, D6⋊C4 [×3], C3×C4⋊C4, S3×C2×C4, C2×D12, Dic15 [×2], C60 [×3], D30 [×2], D30 [×5], C2×C30, C10.D4, D10⋊C4 [×3], C5×C4⋊C4, C2×C4×D5, C2×D20, D6.D4, C4×D15 [×2], D60 [×2], C2×Dic15 [×2], C2×C60 [×3], C22×D15 [×2], D10.13D4, C30.4Q8, D303C4 [×3], C15×C4⋊C4, C2×C4×D15, C2×D60, D30.29D4
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, C4○D4 [×2], D10 [×3], C22×S3, D15, C22.D4, C22×D5, C4○D12, S3×D4, Q83S3, D30 [×3], C4○D20, D4×D5, Q82D5, D6.D4, C22×D15, D10.13D4, D6011C2, D4×D15, Q83D15, D30.29D4

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

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

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

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

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`

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