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G = D30.11D4order 480 = 25·3·5

11st non-split extension by D30 of D4 acting via D4/C2=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D30.11D4, D12.10D10, C60.23C23, Dic15.43D4, Dic10.10D6, Dic30.7C22, D4⋊S35D5, D4.D55S3, C3⋊C8.16D10, C6.73(D4×D5), C1518(C4○D8), C33(D83D5), (C5×D4).11D6, C3⋊Dic204C2, D4.17(S3×D5), C10.74(S3×D4), C52C8.16D6, D42D153C2, D12⋊D51C2, D152C84C2, (C3×D4).11D10, D12.D54C2, C30.185(C2×D4), C53(Q8.7D6), C20.23(C22×S3), (C4×D15).7C22, (C5×D12).7C22, C12.23(C22×D5), (D4×C15).17C22, C2.26(D10⋊D6), (C3×Dic10).7C22, C4.23(C2×S3×D5), (C5×D4⋊S3)⋊7C2, (C3×D4.D5)⋊7C2, (C5×C3⋊C8).6C22, (C3×C52C8).6C22, SmallGroup(480,575)

Series: Derived Chief Lower central Upper central

C1C60 — D30.11D4
C1C5C15C30C60C3×Dic10D12⋊D5 — D30.11D4
C15C30C60 — D30.11D4
C1C2C4D4

Generators and relations for D30.11D4
 G = < a,b,c,d | a30=b2=1, c4=d2=a15, bab=a-1, cac-1=dad-1=a19, cbc-1=a18b, dbd-1=a3b, dcd-1=c3 >

Subgroups: 700 in 124 conjugacy classes, 38 normal (all characteristic)
C1, C2, C2 [×3], C3, C4, C4 [×3], C22 [×3], C5, S3 [×2], C6, C6, C8 [×2], C2×C4 [×3], D4, D4 [×3], Q8 [×2], D5, C10, C10 [×2], Dic3 [×2], C12, C12, D6 [×2], C2×C6, C15, C2×C8, D8, SD16 [×2], Q16, C4○D4 [×2], Dic5 [×3], C20, D10, C2×C10 [×2], C3⋊C8, C24, Dic6, C4×S3 [×2], D12, D12, C2×Dic3, C3⋊D4, C3×D4, C3×Q8, C5×S3, D15, C30, C30, C4○D8, C52C8, C40, Dic10, Dic10, C4×D5, C2×Dic5 [×2], C5⋊D4 [×2], C5×D4, C5×D4, S3×C8, C24⋊C2, D4⋊S3, C3⋊Q16, C3×SD16, D42S3, Q83S3, C3×Dic5, Dic15, Dic15, C60, S3×C10, D30, C2×C30, C8×D5, Dic20, D4.D5, D4.D5, C5×D8, D42D5 [×2], Q8.7D6, C5×C3⋊C8, C3×C52C8, S3×Dic5, C5⋊D12, C3×Dic10, C5×D12, Dic30, C4×D15, C2×Dic15, C157D4, D4×C15, D83D5, D152C8, D12.D5, C3⋊Dic20, C3×D4.D5, C5×D4⋊S3, D12⋊D5, D42D15, D30.11D4
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], C22×S3, C4○D8, C22×D5, S3×D4, S3×D5, D4×D5, Q8.7D6, C2×S3×D5, D83D5, D10⋊D6, D30.11D4

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

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

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

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

45 conjugacy classes

class 1 2A2B2C2D 3 4A4B4C4D4E5A5B6A6B8A8B8C8D10A10B10C10D10E10F12A12B15A15B20A20B24A24B30A30B30C30D30E30F40A40B40C40D60A60B
order12222344444556688881010101010101212151520202424303030303030404040406060
size11412302215152060222866101022882424440444420204488881212121288

45 irreducible representations

dim111111112222222222244444448
type++++++++++++++++++++++-+-
imageC1C2C2C2C2C2C2C2S3D4D4D5D6D6D6D10D10D10C4○D8S3×D4S3×D5D4×D5Q8.7D6C2×S3×D5D83D5D10⋊D6D30.11D4
kernelD30.11D4D152C8D12.D5C3⋊Dic20C3×D4.D5C5×D4⋊S3D12⋊D5D42D15D4.D5Dic15D30D4⋊S3C52C8Dic10C5×D4C3⋊C8D12C3×D4C15C10D4C6C5C4C3C2C1
# reps111111111112111222412222442

Matrix representation of D30.11D4 in GL6(𝔽241)

24000000
02400000
00240100
00240000
0000190240
0000191240
,
24000000
16010000
00240000
00240100
00000189
00001900
,
23300000
1682110000
001000
000100
0000511
000051190
,
211900000
73300000
001000
000100
0000511
000051190

G:=sub<GL(6,GF(241))| [240,0,0,0,0,0,0,240,0,0,0,0,0,0,240,240,0,0,0,0,1,0,0,0,0,0,0,0,190,191,0,0,0,0,240,240],[240,160,0,0,0,0,0,1,0,0,0,0,0,0,240,240,0,0,0,0,0,1,0,0,0,0,0,0,0,190,0,0,0,0,189,0],[233,168,0,0,0,0,0,211,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,51,51,0,0,0,0,1,190],[211,73,0,0,0,0,90,30,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,51,51,0,0,0,0,1,190] >;

D30.11D4 in GAP, Magma, Sage, TeX

D_{30}._{11}D_4
% in TeX

G:=Group("D30.11D4");
// GroupNames label

G:=SmallGroup(480,575);
// by ID

G=gap.SmallGroup(480,575);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,254,135,675,346,185,80,1356,18822]);
// 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^18*b,d*b*d^-1=a^3*b,d*c*d^-1=c^3>;
// generators/relations

׿
×
𝔽