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G = Dic1517D4order 480 = 25·3·5

7th semidirect product of Dic15 and D4 acting via D4/C22=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: Dic1517D4, C1530(C4×D4), C3⋊D4⋊Dic5, C33(D4×Dic5), C6.88(D4×D5), D64(C2×Dic5), C10.89(S3×D4), D6⋊Dic533C2, C30.240(C2×D4), C23.D510S3, C223(S3×Dic5), C23.52(S3×D5), Dic32(C2×Dic5), C58(Dic34D4), C6.Dic1036C2, (C22×C6).39D10, (C22×C10).54D6, (Dic3×Dic5)⋊38C2, C30.154(C4○D4), C6.84(D42D5), C2.6(D10⋊D6), (C2×C30).202C23, C30.150(C22×C4), (C2×Dic5).132D6, (C22×S3).55D10, C10.84(D42S3), C6.20(C22×Dic5), (C2×Dic3).125D10, C2.7(C30.C23), (C22×Dic15)⋊15C2, (C22×C30).64C22, (C6×Dic5).118C22, (C2×Dic15).228C22, (C10×Dic3).118C22, (C5×C3⋊D4)⋊4C4, (C2×C10)⋊12(C4×S3), (C2×C30)⋊21(C2×C4), C10.127(S3×C2×C4), (C2×S3×Dic5)⋊17C2, (C2×C6)⋊2(C2×Dic5), (C2×C3⋊D4).6D5, (S3×C10)⋊17(C2×C4), C2.20(C2×S3×Dic5), C22.90(C2×S3×D5), (C10×C3⋊D4).7C2, (C5×Dic3)⋊12(C2×C4), (S3×C2×C10).52C22, (C3×C23.D5)⋊12C2, (C2×C6).214(C22×D5), (C2×C10).214(C22×S3), SmallGroup(480,636)

Series: Derived Chief Lower central Upper central

C1C30 — Dic1517D4
C1C5C15C30C2×C30C6×Dic5C2×S3×Dic5 — Dic1517D4
C15C30 — Dic1517D4
C1C22C23

Generators and relations for Dic1517D4
 G = < a,b,c,d | a30=c4=d2=1, b2=a15, bab-1=a-1, cac-1=dad=a11, bc=cb, bd=db, dcd=c-1 >

Subgroups: 780 in 188 conjugacy classes, 70 normal (44 characteristic)
C1, C2 [×3], C2 [×4], C3, C4 [×7], C22, C22 [×2], C22 [×6], C5, S3 [×2], C6 [×3], C6 [×2], C2×C4 [×9], D4 [×4], C23, C23, C10 [×3], C10 [×4], Dic3 [×2], Dic3 [×3], C12 [×2], D6 [×2], D6 [×2], C2×C6, C2×C6 [×2], C2×C6 [×2], C15, C42, C22⋊C4 [×2], C4⋊C4, C22×C4 [×2], C2×D4, Dic5 [×5], C20 [×2], C2×C10, C2×C10 [×2], C2×C10 [×6], C4×S3 [×2], C2×Dic3, C2×Dic3 [×4], C3⋊D4 [×4], C2×C12 [×2], C22×S3, C22×C6, C5×S3 [×2], C30 [×3], C30 [×2], C4×D4, C2×Dic5 [×2], C2×Dic5 [×6], C2×C20, C5×D4 [×4], C22×C10, C22×C10, C4×Dic3, Dic3⋊C4, D6⋊C4, C3×C22⋊C4, S3×C2×C4, C22×Dic3, C2×C3⋊D4, C5×Dic3 [×2], C3×Dic5 [×2], Dic15 [×2], Dic15, S3×C10 [×2], S3×C10 [×2], C2×C30, C2×C30 [×2], C2×C30 [×2], C4×Dic5, C4⋊Dic5, C23.D5, C23.D5, C22×Dic5 [×2], D4×C10, Dic34D4, S3×Dic5 [×2], C6×Dic5 [×2], C10×Dic3, C5×C3⋊D4 [×4], C2×Dic15 [×2], C2×Dic15 [×2], S3×C2×C10, C22×C30, D4×Dic5, Dic3×Dic5, D6⋊Dic5, C6.Dic10, C3×C23.D5, C2×S3×Dic5, C10×C3⋊D4, C22×Dic15, Dic1517D4
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], S3, C2×C4 [×6], D4 [×2], C23, D5, D6 [×3], C22×C4, C2×D4, C4○D4, Dic5 [×4], D10 [×3], C4×S3 [×2], C22×S3, C4×D4, C2×Dic5 [×6], C22×D5, S3×C2×C4, S3×D4, D42S3, S3×D5, D4×D5, D42D5, C22×Dic5, Dic34D4, S3×Dic5 [×2], C2×S3×D5, D4×Dic5, C30.C23, C2×S3×Dic5, D10⋊D6, Dic1517D4

Smallest permutation representation of Dic1517D4
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)
(1 205 16 190)(2 204 17 189)(3 203 18 188)(4 202 19 187)(5 201 20 186)(6 200 21 185)(7 199 22 184)(8 198 23 183)(9 197 24 182)(10 196 25 181)(11 195 26 210)(12 194 27 209)(13 193 28 208)(14 192 29 207)(15 191 30 206)(31 170 46 155)(32 169 47 154)(33 168 48 153)(34 167 49 152)(35 166 50 151)(36 165 51 180)(37 164 52 179)(38 163 53 178)(39 162 54 177)(40 161 55 176)(41 160 56 175)(42 159 57 174)(43 158 58 173)(44 157 59 172)(45 156 60 171)(61 105 76 120)(62 104 77 119)(63 103 78 118)(64 102 79 117)(65 101 80 116)(66 100 81 115)(67 99 82 114)(68 98 83 113)(69 97 84 112)(70 96 85 111)(71 95 86 110)(72 94 87 109)(73 93 88 108)(74 92 89 107)(75 91 90 106)(121 237 136 222)(122 236 137 221)(123 235 138 220)(124 234 139 219)(125 233 140 218)(126 232 141 217)(127 231 142 216)(128 230 143 215)(129 229 144 214)(130 228 145 213)(131 227 146 212)(132 226 147 211)(133 225 148 240)(134 224 149 239)(135 223 150 238)
(1 41 80 134)(2 52 81 145)(3 33 82 126)(4 44 83 137)(5 55 84 148)(6 36 85 129)(7 47 86 140)(8 58 87 121)(9 39 88 132)(10 50 89 143)(11 31 90 124)(12 42 61 135)(13 53 62 146)(14 34 63 127)(15 45 64 138)(16 56 65 149)(17 37 66 130)(18 48 67 141)(19 59 68 122)(20 40 69 133)(21 51 70 144)(22 32 71 125)(23 43 72 136)(24 54 73 147)(25 35 74 128)(26 46 75 139)(27 57 76 150)(28 38 77 131)(29 49 78 142)(30 60 79 123)(91 219 210 155)(92 230 181 166)(93 211 182 177)(94 222 183 158)(95 233 184 169)(96 214 185 180)(97 225 186 161)(98 236 187 172)(99 217 188 153)(100 228 189 164)(101 239 190 175)(102 220 191 156)(103 231 192 167)(104 212 193 178)(105 223 194 159)(106 234 195 170)(107 215 196 151)(108 226 197 162)(109 237 198 173)(110 218 199 154)(111 229 200 165)(112 240 201 176)(113 221 202 157)(114 232 203 168)(115 213 204 179)(116 224 205 160)(117 235 206 171)(118 216 207 152)(119 227 208 163)(120 238 209 174)
(1 16)(2 27)(3 8)(4 19)(5 30)(6 11)(7 22)(9 14)(10 25)(12 17)(13 28)(15 20)(18 23)(21 26)(24 29)(31 129)(32 140)(33 121)(34 132)(35 143)(36 124)(37 135)(38 146)(39 127)(40 138)(41 149)(42 130)(43 141)(44 122)(45 133)(46 144)(47 125)(48 136)(49 147)(50 128)(51 139)(52 150)(53 131)(54 142)(55 123)(56 134)(57 145)(58 126)(59 137)(60 148)(61 66)(62 77)(63 88)(64 69)(65 80)(67 72)(68 83)(70 75)(71 86)(73 78)(74 89)(76 81)(79 84)(82 87)(85 90)(91 96)(92 107)(93 118)(94 99)(95 110)(97 102)(98 113)(100 105)(101 116)(103 108)(104 119)(106 111)(109 114)(112 117)(115 120)(151 230)(152 211)(153 222)(154 233)(155 214)(156 225)(157 236)(158 217)(159 228)(160 239)(161 220)(162 231)(163 212)(164 223)(165 234)(166 215)(167 226)(168 237)(169 218)(170 229)(171 240)(172 221)(173 232)(174 213)(175 224)(176 235)(177 216)(178 227)(179 238)(180 219)(181 196)(182 207)(183 188)(184 199)(185 210)(186 191)(187 202)(189 194)(190 205)(192 197)(193 208)(195 200)(198 203)(201 206)(204 209)

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

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

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

66 conjugacy classes

class 1 2A2B2C2D2E2F2G 3 4A4B4C4D4E4F4G4H4I4J4K4L5A5B6A6B6C6D6E10A···10F10G10H10I10J10K10L10M10N12A12B12C12D15A15B20A20B20C20D30A···30N
order122222223444444444444556666610···1010101010101010101212121215152020202030···30
size111122662661010101015151515303022222442···24444121212122020202044121212124···4

66 irreducible representations

dim11111111122222222222444444444
type++++++++++++++-+++-++--+-+
imageC1C2C2C2C2C2C2C2C4S3D4D5D6D6C4○D4D10Dic5D10D10C4×S3S3×D4D42S3S3×D5D4×D5D42D5S3×Dic5C2×S3×D5C30.C23D10⋊D6
kernelDic1517D4Dic3×Dic5D6⋊Dic5C6.Dic10C3×C23.D5C2×S3×Dic5C10×C3⋊D4C22×Dic15C5×C3⋊D4C23.D5Dic15C2×C3⋊D4C2×Dic5C22×C10C30C2×Dic3C3⋊D4C22×S3C22×C6C2×C10C10C10C23C6C6C22C22C2C2
# reps11111111812221228224112224244

Matrix representation of Dic1517D4 in GL6(𝔽61)

0600000
110000
0020000
00155800
0000600
0000060
,
1100000
50500000
0010500
00295100
0000110
0000011
,
6000000
110000
0060000
0006000
0000646
00003555
,
6000000
110000
001000
000100
0000600
0000481

G:=sub<GL(6,GF(61))| [0,1,0,0,0,0,60,1,0,0,0,0,0,0,20,15,0,0,0,0,0,58,0,0,0,0,0,0,60,0,0,0,0,0,0,60],[11,50,0,0,0,0,0,50,0,0,0,0,0,0,10,29,0,0,0,0,5,51,0,0,0,0,0,0,11,0,0,0,0,0,0,11],[60,1,0,0,0,0,0,1,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,6,35,0,0,0,0,46,55],[60,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,60,48,0,0,0,0,0,1] >;

Dic1517D4 in GAP, Magma, Sage, TeX

{\rm Dic}_{15}\rtimes_{17}D_4
% in TeX

G:=Group("Dic15:17D4");
// GroupNames label

G:=SmallGroup(480,636);
// by ID

G=gap.SmallGroup(480,636);
# by ID

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

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

׿
×
𝔽