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G = Dic15.48D4order 480 = 25·3·5

16th non-split extension by Dic15 of D4 acting via D4/C22=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: Dic15.48D4, (C2×C30)⋊4Q8, C6.94(D4×D5), (C2×C6)⋊2Dic10, (C2×C10)⋊5Dic6, C10.96(S3×D4), C224(C15⋊Q8), C30.64(C2×Q8), C30.256(C2×D4), C1524(C22⋊Q8), C23.57(S3×D5), C23.D5.5S3, C6.Dic1041C2, C30.Q841C2, Dic155C441C2, (C2×Dic5).68D6, C6.31(C2×Dic10), C10.31(C2×Dic6), C6.D4.5D5, (C22×C6).51D10, (C22×C10).66D6, C30.162(C4○D4), C6.87(D42D5), (C2×C30).218C23, (C2×Dic3).67D10, C54(Dic3.D4), C10.87(D42S3), C2.46(D10⋊D6), C34(Dic5.14D4), (C22×C30).80C22, C2.31(C30.C23), (C22×Dic15).13C2, (C6×Dic5).125C22, (C2×Dic15).230C22, (C10×Dic3).125C22, (C2×C15⋊Q8)⋊18C2, C2.13(C2×C15⋊Q8), C22.247(C2×S3×D5), (C3×C23.D5).6C2, (C5×C6.D4).6C2, (C2×C6).230(C22×D5), (C2×C10).230(C22×S3), SmallGroup(480,652)

Series: Derived Chief Lower central Upper central

C1C2×C30 — Dic15.48D4
C1C5C15C30C2×C30C6×Dic5C2×C15⋊Q8 — Dic15.48D4
C15C2×C30 — Dic15.48D4
C1C22C23

Generators and relations for Dic15.48D4
 G = < a,b,c,d | a30=c4=1, b2=d2=a15, bab-1=a-1, cac-1=dad-1=a19, cbc-1=dbd-1=a15b, dcd-1=a15c-1 >

Subgroups: 684 in 148 conjugacy classes, 54 normal (44 characteristic)
C1, C2 [×3], C2 [×2], C3, C4 [×7], C22, C22 [×2], C22 [×2], C5, C6 [×3], C6 [×2], C2×C4 [×8], Q8 [×2], C23, C10 [×3], C10 [×2], Dic3 [×5], C12 [×2], C2×C6, C2×C6 [×2], C2×C6 [×2], C15, C22⋊C4 [×2], C4⋊C4 [×3], C22×C4, C2×Q8, Dic5 [×5], C20 [×2], C2×C10, C2×C10 [×2], C2×C10 [×2], Dic6 [×2], C2×Dic3 [×2], C2×Dic3 [×4], C2×C12 [×2], C22×C6, C30 [×3], C30 [×2], C22⋊Q8, Dic10 [×2], C2×Dic5 [×2], C2×Dic5 [×4], C2×C20 [×2], C22×C10, Dic3⋊C4 [×2], C4⋊Dic3, C6.D4, C3×C22⋊C4, C2×Dic6, C22×Dic3, C5×Dic3 [×2], C3×Dic5 [×2], Dic15 [×2], Dic15, C2×C30, C2×C30 [×2], C2×C30 [×2], C10.D4 [×2], C4⋊Dic5, C23.D5, C5×C22⋊C4, C2×Dic10, C22×Dic5, Dic3.D4, C15⋊Q8 [×2], C6×Dic5 [×2], C10×Dic3 [×2], C2×Dic15 [×2], C2×Dic15 [×2], C22×C30, Dic5.14D4, C30.Q8, Dic155C4, C6.Dic10, C3×C23.D5, C5×C6.D4, C2×C15⋊Q8, C22×Dic15, Dic15.48D4
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], Q8 [×2], C23, D5, D6 [×3], C2×D4, C2×Q8, C4○D4, D10 [×3], Dic6 [×2], C22×S3, C22⋊Q8, Dic10 [×2], C22×D5, C2×Dic6, S3×D4, D42S3, S3×D5, C2×Dic10, D4×D5, D42D5, Dic3.D4, C15⋊Q8 [×2], C2×S3×D5, Dic5.14D4, C30.C23, C2×C15⋊Q8, D10⋊D6, Dic15.48D4

Smallest permutation representation of Dic15.48D4
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 39 16 54)(2 38 17 53)(3 37 18 52)(4 36 19 51)(5 35 20 50)(6 34 21 49)(7 33 22 48)(8 32 23 47)(9 31 24 46)(10 60 25 45)(11 59 26 44)(12 58 27 43)(13 57 28 42)(14 56 29 41)(15 55 30 40)(61 144 76 129)(62 143 77 128)(63 142 78 127)(64 141 79 126)(65 140 80 125)(66 139 81 124)(67 138 82 123)(68 137 83 122)(69 136 84 121)(70 135 85 150)(71 134 86 149)(72 133 87 148)(73 132 88 147)(74 131 89 146)(75 130 90 145)(91 213 106 228)(92 212 107 227)(93 211 108 226)(94 240 109 225)(95 239 110 224)(96 238 111 223)(97 237 112 222)(98 236 113 221)(99 235 114 220)(100 234 115 219)(101 233 116 218)(102 232 117 217)(103 231 118 216)(104 230 119 215)(105 229 120 214)(151 187 166 202)(152 186 167 201)(153 185 168 200)(154 184 169 199)(155 183 170 198)(156 182 171 197)(157 181 172 196)(158 210 173 195)(159 209 174 194)(160 208 175 193)(161 207 176 192)(162 206 177 191)(163 205 178 190)(164 204 179 189)(165 203 180 188)
(1 148 239 161)(2 137 240 180)(3 126 211 169)(4 145 212 158)(5 134 213 177)(6 123 214 166)(7 142 215 155)(8 131 216 174)(9 150 217 163)(10 139 218 152)(11 128 219 171)(12 147 220 160)(13 136 221 179)(14 125 222 168)(15 144 223 157)(16 133 224 176)(17 122 225 165)(18 141 226 154)(19 130 227 173)(20 149 228 162)(21 138 229 151)(22 127 230 170)(23 146 231 159)(24 135 232 178)(25 124 233 167)(26 143 234 156)(27 132 235 175)(28 121 236 164)(29 140 237 153)(30 129 238 172)(31 85 102 190)(32 74 103 209)(33 63 104 198)(34 82 105 187)(35 71 106 206)(36 90 107 195)(37 79 108 184)(38 68 109 203)(39 87 110 192)(40 76 111 181)(41 65 112 200)(42 84 113 189)(43 73 114 208)(44 62 115 197)(45 81 116 186)(46 70 117 205)(47 89 118 194)(48 78 119 183)(49 67 120 202)(50 86 91 191)(51 75 92 210)(52 64 93 199)(53 83 94 188)(54 72 95 207)(55 61 96 196)(56 80 97 185)(57 69 98 204)(58 88 99 193)(59 77 100 182)(60 66 101 201)
(1 176 16 161)(2 165 17 180)(3 154 18 169)(4 173 19 158)(5 162 20 177)(6 151 21 166)(7 170 22 155)(8 159 23 174)(9 178 24 163)(10 167 25 152)(11 156 26 171)(12 175 27 160)(13 164 28 179)(14 153 29 168)(15 172 30 157)(31 205 46 190)(32 194 47 209)(33 183 48 198)(34 202 49 187)(35 191 50 206)(36 210 51 195)(37 199 52 184)(38 188 53 203)(39 207 54 192)(40 196 55 181)(41 185 56 200)(42 204 57 189)(43 193 58 208)(44 182 59 197)(45 201 60 186)(61 96 76 111)(62 115 77 100)(63 104 78 119)(64 93 79 108)(65 112 80 97)(66 101 81 116)(67 120 82 105)(68 109 83 94)(69 98 84 113)(70 117 85 102)(71 106 86 91)(72 95 87 110)(73 114 88 99)(74 103 89 118)(75 92 90 107)(121 236 136 221)(122 225 137 240)(123 214 138 229)(124 233 139 218)(125 222 140 237)(126 211 141 226)(127 230 142 215)(128 219 143 234)(129 238 144 223)(130 227 145 212)(131 216 146 231)(132 235 147 220)(133 224 148 239)(134 213 149 228)(135 232 150 217)

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

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

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

60 conjugacy classes

class 1 2A2B2C2D2E 3 4A4B4C4D4E4F4G4H5A5B6A6B6C6D6E10A···10F10G10H10I10J12A12B12C12D15A15B20A···20H30A···30N
order122222344444444556666610···101010101012121212151520···2030···30
size1111222121220203030303022222442···24444202020204412···124···4

60 irreducible representations

dim1111111122222222222444444444
type++++++++++-+++++--+-++--+-+
imageC1C2C2C2C2C2C2C2S3D4Q8D5D6D6C4○D4D10D10Dic6Dic10S3×D4D42S3S3×D5D4×D5D42D5C15⋊Q8C2×S3×D5C30.C23D10⋊D6
kernelDic15.48D4C30.Q8Dic155C4C6.Dic10C3×C23.D5C5×C6.D4C2×C15⋊Q8C22×Dic15C23.D5Dic15C2×C30C6.D4C2×Dic5C22×C10C30C2×Dic3C22×C6C2×C10C2×C6C10C10C23C6C6C22C22C2C2
# reps1111111112222124248112224244

Matrix representation of Dic15.48D4 in GL6(𝔽61)

0600000
1440000
0072000
00495300
000010
000001
,
1080000
56510000
00203800
00204100
0000600
0000060
,
20580000
32410000
0060000
0006000
0000560
00002656
,
20580000
32410000
0060000
0006000
0000560
00002456

G:=sub<GL(6,GF(61))| [0,1,0,0,0,0,60,44,0,0,0,0,0,0,7,49,0,0,0,0,20,53,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[10,56,0,0,0,0,8,51,0,0,0,0,0,0,20,20,0,0,0,0,38,41,0,0,0,0,0,0,60,0,0,0,0,0,0,60],[20,32,0,0,0,0,58,41,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,5,26,0,0,0,0,60,56],[20,32,0,0,0,0,58,41,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,5,24,0,0,0,0,60,56] >;

Dic15.48D4 in GAP, Magma, Sage, TeX

{\rm Dic}_{15}._{48}D_4
% in TeX

G:=Group("Dic15.48D4");
// GroupNames label

G:=SmallGroup(480,652);
// by ID

G=gap.SmallGroup(480,652);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,141,64,422,219,1356,18822]);
// Polycyclic

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

׿
×
𝔽