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## G = D30.44D4order 480 = 25·3·5

### 17th non-split extension by D30 of D4 acting via D4/C22=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C60 — D30.44D4
 Chief series C1 — C5 — C15 — C30 — C60 — C3×Dic10 — D12⋊D5 — D30.44D4
 Lower central C15 — C30 — C60 — D30.44D4
 Upper central C1 — C2 — C4 — Q8

Generators and relations for D30.44D4
G = < a,b,c,d | a30=b2=1, c4=d2=a15, bab=a-1, cac-1=dad-1=a19, cbc-1=dbd-1=a3b, dcd-1=a15c3 >

Subgroups: 684 in 120 conjugacy classes, 38 normal (all characteristic)
C1, C2, C2 [×2], C3, C4, C4 [×4], C22 [×2], C5, S3 [×2], C6, C8 [×2], C2×C4 [×3], D4 [×2], Q8, Q8 [×3], D5, C10, C10, Dic3 [×2], C12, C12 [×2], D6 [×2], C15, M4(2), SD16 [×2], Q16 [×2], C2×Q8, C4○D4, Dic5 [×3], C20, C20, D10, C2×C10, C3⋊C8, C24, Dic6 [×2], C4×S3 [×3], D12, D12, C3×Q8, C3×Q8, C5×S3, D15, C30, C8.C22, C52C8, C40, Dic10, Dic10 [×2], C4×D5 [×2], C2×Dic5, C5⋊D4, C5×D4, C5×Q8, C8⋊S3, C24⋊C2, Q82S3, C3⋊Q16, C3×Q16, S3×Q8, Q83S3, C3×Dic5, Dic15, Dic15, C60, C60, S3×C10, D30, C8⋊D5, Dic20, D4.D5, C5⋊Q16, C5×SD16, D42D5, Q8×D5, Q16⋊S3, C5×C3⋊C8, C3×C52C8, S3×Dic5, C5⋊D12, C3×Dic10, C5×D12, Dic30, Dic30, C4×D15, C4×D15, Q8×C15, SD16⋊D5, D30.5C4, D12.D5, C3⋊Dic20, C3×C5⋊Q16, C5×Q82S3, D12⋊D5, Q8×D15, D30.44D4
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], C22×S3, C8.C22, C22×D5, S3×D4, S3×D5, D4×D5, Q16⋊S3, C2×S3×D5, SD16⋊D5, D10⋊D6, D30.44D4

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

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

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

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

42 conjugacy classes

 class 1 2A 2B 2C 3 4A 4B 4C 4D 4E 5A 5B 6 8A 8B 10A 10B 10C 10D 12A 12B 12C 15A 15B 20A 20B 20C 20D 24A 24B 30A 30B 40A 40B 40C 40D 60A ··· 60F order 1 2 2 2 3 4 4 4 4 4 5 5 6 8 8 10 10 10 10 12 12 12 15 15 20 20 20 20 24 24 30 30 40 40 40 40 60 ··· 60 size 1 1 12 30 2 2 4 20 30 60 2 2 2 12 20 2 2 24 24 4 8 40 4 4 4 4 8 8 20 20 4 4 12 12 12 12 8 ··· 8

42 irreducible representations

 dim 1 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 8 type + + + + + + + + + + + + + + + + + + - + + + + - + - image C1 C2 C2 C2 C2 C2 C2 C2 S3 D4 D4 D5 D6 D6 D6 D10 D10 D10 C8.C22 S3×D4 S3×D5 D4×D5 Q16⋊S3 C2×S3×D5 SD16⋊D5 D10⋊D6 D30.44D4 kernel D30.44D4 D30.5C4 D12.D5 C3⋊Dic20 C3×C5⋊Q16 C5×Q8⋊2S3 D12⋊D5 Q8×D15 C5⋊Q16 Dic15 D30 Q8⋊2S3 C5⋊2C8 Dic10 C5×Q8 C3⋊C8 D12 C3×Q8 C15 C10 Q8 C6 C5 C4 C3 C2 C1 # reps 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 2 2 1 1 2 2 2 2 4 4 2

Matrix representation of D30.44D4 in GL6(𝔽241)

 189 240 0 0 0 0 1 0 0 0 0 0 0 0 0 240 0 0 0 0 1 1 0 0 0 0 0 0 0 240 0 0 0 0 1 1
,
 189 240 0 0 0 0 52 52 0 0 0 0 0 0 0 240 0 0 0 0 240 0 0 0 0 0 0 0 0 240 0 0 0 0 240 0
,
 240 0 0 0 0 0 52 1 0 0 0 0 0 0 47 94 47 94 0 0 147 194 147 194 0 0 194 147 47 94 0 0 94 47 147 194
,
 1 0 0 0 0 0 189 240 0 0 0 0 0 0 64 128 198 155 0 0 113 177 86 43 0 0 198 155 177 113 0 0 86 43 128 64

G:=sub<GL(6,GF(241))| [189,1,0,0,0,0,240,0,0,0,0,0,0,0,0,1,0,0,0,0,240,1,0,0,0,0,0,0,0,1,0,0,0,0,240,1],[189,52,0,0,0,0,240,52,0,0,0,0,0,0,0,240,0,0,0,0,240,0,0,0,0,0,0,0,0,240,0,0,0,0,240,0],[240,52,0,0,0,0,0,1,0,0,0,0,0,0,47,147,194,94,0,0,94,194,147,47,0,0,47,147,47,147,0,0,94,194,94,194],[1,189,0,0,0,0,0,240,0,0,0,0,0,0,64,113,198,86,0,0,128,177,155,43,0,0,198,86,177,128,0,0,155,43,113,64] >;

D30.44D4 in GAP, Magma, Sage, TeX

D_{30}._{44}D_4
% in TeX

G:=Group("D30.44D4");
// GroupNames label

G:=SmallGroup(480,600);
// by ID

G=gap.SmallGroup(480,600);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,254,303,100,675,346,185,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^30=b^2=1,c^4=d^2=a^15,b*a*b=a^-1,c*a*c^-1=d*a*d^-1=a^19,c*b*c^-1=d*b*d^-1=a^3*b,d*c*d^-1=a^15*c^3>;
// generators/relations

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