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G = D30.9D4order 480 = 25·3·5

9th non-split extension by D30 of D4 acting via D4/C2=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D30.9D4, C60.12C23, Dic6.7D10, Dic10.7D6, Dic15.41D4, Dic30.3C22, C3⋊C8.6D10, D15⋊Q82C2, D4.D53S3, D4.S33D5, (C5×D4).4D6, C6.70(D4×D5), C52C8.6D6, C3⋊Dic202C2, D4.14(S3×D5), (C3×D4).4D10, C5⋊Dic122C2, C10.71(S3×D4), C53(D4.D6), C30.174(C2×D4), C33(SD16⋊D5), D30.5C42C2, D42D15.1C2, C1515(C8.C22), C20.12(C22×S3), (C4×D15).4C22, (D4×C15).6C22, C12.12(C22×D5), C2.23(D10⋊D6), (C5×Dic6).3C22, (C3×Dic10).3C22, C4.12(C2×S3×D5), (C5×D4.S3)⋊4C2, (C3×D4.D5)⋊4C2, (C5×C3⋊C8).2C22, (C3×C52C8).2C22, SmallGroup(480,564)

Series: Derived Chief Lower central Upper central

C1C60 — D30.9D4
C1C5C15C30C60C3×Dic10D15⋊Q8 — D30.9D4
C15C30C60 — D30.9D4
C1C2C4D4

Generators and relations for D30.9D4
 G = < a,b,c,d | a30=b2=1, c4=d2=a15, bab=a-1, cac-1=dad-1=a19, cbc-1=a3b, dbd-1=a18b, dcd-1=c3 >

Subgroups: 668 in 120 conjugacy classes, 38 normal (all characteristic)
C1, C2, C2 [×2], C3, C4, C4 [×4], C22 [×2], C5, S3, C6, C6, C8 [×2], C2×C4 [×3], D4, D4, Q8 [×4], D5, C10, C10, Dic3 [×3], C12, C12, D6, C2×C6, C15, M4(2), SD16 [×2], Q16 [×2], C2×Q8, C4○D4, Dic5 [×3], C20, C20, D10, C2×C10, C3⋊C8, C24, Dic6, Dic6 [×2], C4×S3 [×2], C2×Dic3, C3⋊D4, C3×D4, C3×Q8, D15, C30, C30, C8.C22, C52C8, C40, Dic10, Dic10 [×2], C4×D5 [×2], C2×Dic5, C5⋊D4, C5×D4, C5×Q8, C8⋊S3, Dic12, D4.S3, C3⋊Q16, C3×SD16, D42S3, S3×Q8, C5×Dic3, C3×Dic5, Dic15, Dic15, C60, D30, C2×C30, C8⋊D5, Dic20, D4.D5, C5⋊Q16, C5×SD16, D42D5, Q8×D5, D4.D6, C5×C3⋊C8, C3×C52C8, D30.C2, C15⋊Q8, C3×Dic10, C5×Dic6, Dic30, C4×D15, C2×Dic15, C157D4, D4×C15, SD16⋊D5, D30.5C4, C3⋊Dic20, C5⋊Dic12, C3×D4.D5, C5×D4.S3, D15⋊Q8, D42D15, D30.9D4
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, D4.D6, C2×S3×D5, SD16⋊D5, D10⋊D6, D30.9D4

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

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

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

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

42 conjugacy classes

class 1 2A2B2C 3 4A4B4C4D4E5A5B6A6B8A8B10A10B10C10D12A12B15A15B20A20B20C20D24A24B30A30B30C30D30E30F40A40B40C40D60A60B
order12223444445566881010101012121515202020202424303030303030404040406060
size1143022122030602228122022884404444242420204488881212121288

42 irreducible representations

dim111111112222222222444444448
type++++++++++++++++++-+++-+-+-
imageC1C2C2C2C2C2C2C2S3D4D4D5D6D6D6D10D10D10C8.C22S3×D4S3×D5D4×D5D4.D6C2×S3×D5SD16⋊D5D10⋊D6D30.9D4
kernelD30.9D4D30.5C4C3⋊Dic20C5⋊Dic12C3×D4.D5C5×D4.S3D15⋊Q8D42D15D4.D5Dic15D30D4.S3C52C8Dic10C5×D4C3⋊C8Dic6C3×D4C15C10D4C6C5C4C3C2C1
# reps111111111112111222112222442

Matrix representation of D30.9D4 in GL8(𝔽241)

5211892400000
2400100000
521000000
2400000000
000052100
0000240000
000000521
0000002400
,
521000000
189189000000
5211892400000
18918952520000
000052100
000018918900
000000521
000000189189
,
12279230830000
1119173110000
111581111620000
682301741300000
000031293129
0000104210104210
00002102123129
000013731104210
,
12279230830000
1119173110000
111581111620000
682301741300000
00009601720
00006914521469
000017201450
00002146917296

G:=sub<GL(8,GF(241))| [52,240,52,240,0,0,0,0,1,0,1,0,0,0,0,0,189,1,0,0,0,0,0,0,240,0,0,0,0,0,0,0,0,0,0,0,52,240,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,52,240,0,0,0,0,0,0,1,0],[52,189,52,189,0,0,0,0,1,189,1,189,0,0,0,0,0,0,189,52,0,0,0,0,0,0,240,52,0,0,0,0,0,0,0,0,52,189,0,0,0,0,0,0,1,189,0,0,0,0,0,0,0,0,52,189,0,0,0,0,0,0,1,189],[122,1,11,68,0,0,0,0,79,119,158,230,0,0,0,0,230,173,111,174,0,0,0,0,83,11,162,130,0,0,0,0,0,0,0,0,31,104,210,137,0,0,0,0,29,210,212,31,0,0,0,0,31,104,31,104,0,0,0,0,29,210,29,210],[122,1,11,68,0,0,0,0,79,119,158,230,0,0,0,0,230,173,111,174,0,0,0,0,83,11,162,130,0,0,0,0,0,0,0,0,96,69,172,214,0,0,0,0,0,145,0,69,0,0,0,0,172,214,145,172,0,0,0,0,0,69,0,96] >;

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

D_{30}._9D_4
% in TeX

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

G:=SmallGroup(480,564);
// by ID

G=gap.SmallGroup(480,564);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,120,254,303,675,346,185,80,1356,18822]);
// 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=a^3*b,d*b*d^-1=a^18*b,d*c*d^-1=c^3>;
// generators/relations

׿
×
𝔽