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G = D30.4D4order 480 = 25·3·5

4th non-split extension by D30 of D4 acting via D4/C2=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D30.4D4, C40.26D6, Dic206S3, D12.5D10, C24.29D10, Dic6.5D10, Dic15.4D4, Dic10.5D6, C120.39C22, C60.148C23, C8.6(S3×D5), C24⋊C24D5, C6.37(D4×D5), C40⋊S36C2, D15⋊Q810C2, C10.37(S3×D4), C30.30(C2×D4), C52(Q16⋊S3), (C3×Dic20)⋊9C2, C15⋊Q1612C2, C32(SD16⋊D5), C156(C8.C22), D12⋊D5.2C2, C20.D612C2, C20.83(C22×S3), C12.83(C22×D5), C2.15(C20⋊D6), C153C8.24C22, (C4×D15).33C22, (C5×D12).29C22, (C5×Dic6).31C22, (C3×Dic10).31C22, C4.121(C2×S3×D5), (C5×C24⋊C2)⋊6C2, SmallGroup(480,356)

Series: Derived Chief Lower central Upper central

C1C60 — D30.4D4
C1C5C15C30C60C3×Dic10D12⋊D5 — D30.4D4
C15C30C60 — D30.4D4
C1C2C4C8

Generators and relations for D30.4D4
 G = < a,b,c,d | a30=b2=1, c4=d2=a15, bab=a-1, ac=ca, dad-1=a11, cbc-1=a15b, dbd-1=a10b, 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 [×2], C6, C8, C8, C2×C4 [×3], D4 [×2], Q8 [×4], 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, Dic6, C4×S3 [×3], D12, D12, C3×Q8 [×2], C5×S3, D15, C30, C8.C22, C52C8, C40, Dic10 [×2], Dic10, C4×D5 [×2], C2×Dic5, C5⋊D4, C5×D4, C5×Q8, C8⋊S3, C24⋊C2, Q82S3, C3⋊Q16, C3×Q16, S3×Q8, Q83S3, C5×Dic3, C3×Dic5 [×2], Dic15, C60, S3×C10, D30, C8⋊D5, Dic20, D4.D5, C5⋊Q16, C5×SD16, D42D5, Q8×D5, Q16⋊S3, C153C8, C120, S3×Dic5, D30.C2, C5⋊D12, C15⋊Q8, C3×Dic10 [×2], C5×Dic6, C5×D12, C4×D15, SD16⋊D5, C20.D6, C15⋊Q16, C3×Dic20, C5×C24⋊C2, C40⋊S3, D12⋊D5, D15⋊Q8, D30.4D4
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, C20⋊D6, D30.4D4

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

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

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

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

48 conjugacy classes

class 1 2A2B2C 3 4A4B4C4D4E5A5B 6 8A8B10A10B10C10D12A12B12C15A15B20A20B20C20D24A24B30A30B40A40B40C40D60A60B60C60D120A···120H
order12223444445568810101010121212151520202020242430304040404060606060120···120
size111230221220203022246022242444040444424244444444444444···4

48 irreducible representations

dim11111111222222222444444444
type+++++++++++++++++-++++-
imageC1C2C2C2C2C2C2C2S3D4D4D5D6D6D10D10D10C8.C22S3×D4S3×D5D4×D5Q16⋊S3C2×S3×D5SD16⋊D5C20⋊D6D30.4D4
kernelD30.4D4C20.D6C15⋊Q16C3×Dic20C5×C24⋊C2C40⋊S3D12⋊D5D15⋊Q8Dic20Dic15D30C24⋊C2C40Dic10C24Dic6D12C15C10C8C6C5C4C3C2C1
# reps11111111111212222112222448

Matrix representation of D30.4D4 in GL4(𝔽241) generated by

512401901
102400
5124000
1000
,
190100
515100
190151240
5151190190
,
49331470
208450147
94019633
094208192
,
2317625203
165103815
153810165
2032576231
G:=sub<GL(4,GF(241))| [51,1,51,1,240,0,240,0,190,240,0,0,1,0,0,0],[190,51,190,51,1,51,1,51,0,0,51,190,0,0,240,190],[49,208,94,0,33,45,0,94,147,0,196,208,0,147,33,192],[231,165,15,203,76,10,38,25,25,38,10,76,203,15,165,231] >;

D30.4D4 in GAP, Magma, Sage, TeX

D_{30}._4D_4
% in TeX

G:=Group("D30.4D4");
// GroupNames label

G:=SmallGroup(480,356);
// by ID

G=gap.SmallGroup(480,356);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,254,303,142,675,346,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^30=b^2=1,c^4=d^2=a^15,b*a*b=a^-1,a*c=c*a,d*a*d^-1=a^11,c*b*c^-1=a^15*b,d*b*d^-1=a^10*b,d*c*d^-1=c^3>;
// generators/relations

׿
×
𝔽