metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic15⋊17D4, C15⋊30(C4×D4), C3⋊D4⋊Dic5, C3⋊3(D4×Dic5), C6.88(D4×D5), D6⋊4(C2×Dic5), C10.89(S3×D4), D6⋊Dic5⋊33C2, C30.240(C2×D4), C23.D5⋊10S3, C22⋊3(S3×Dic5), C23.52(S3×D5), Dic3⋊2(C2×Dic5), C5⋊8(Dic3⋊4D4), C6.Dic10⋊36C2, (C22×C6).39D10, (C22×C10).54D6, (Dic3×Dic5)⋊38C2, C30.154(C4○D4), C6.84(D4⋊2D5), C2.6(D10⋊D6), (C2×C30).202C23, C30.150(C22×C4), (C2×Dic5).132D6, (C22×S3).55D10, C10.84(D4⋊2S3), 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
Generators and relations for Dic15⋊17D4
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, C2, C3, C4, C22, C22, C22, C5, S3, C6, C6, C2×C4, D4, C23, C23, C10, C10, Dic3, Dic3, C12, D6, D6, C2×C6, C2×C6, C2×C6, C15, C42, C22⋊C4, C4⋊C4, C22×C4, C2×D4, Dic5, C20, C2×C10, C2×C10, C2×C10, C4×S3, C2×Dic3, C2×Dic3, C3⋊D4, C2×C12, C22×S3, C22×C6, C5×S3, C30, C30, C4×D4, C2×Dic5, C2×Dic5, C2×C20, C5×D4, C22×C10, C22×C10, C4×Dic3, Dic3⋊C4, D6⋊C4, C3×C22⋊C4, S3×C2×C4, C22×Dic3, C2×C3⋊D4, C5×Dic3, C3×Dic5, Dic15, Dic15, S3×C10, S3×C10, C2×C30, C2×C30, C2×C30, C4×Dic5, C4⋊Dic5, C23.D5, C23.D5, C22×Dic5, D4×C10, Dic3⋊4D4, S3×Dic5, C6×Dic5, C10×Dic3, C5×C3⋊D4, C2×Dic15, C2×Dic15, S3×C2×C10, C22×C30, D4×Dic5, Dic3×Dic5, D6⋊Dic5, C6.Dic10, C3×C23.D5, C2×S3×Dic5, C10×C3⋊D4, C22×Dic15, Dic15⋊17D4
Quotients: C1, C2, C4, C22, S3, C2×C4, D4, C23, D5, D6, C22×C4, C2×D4, C4○D4, Dic5, D10, C4×S3, C22×S3, C4×D4, C2×Dic5, C22×D5, S3×C2×C4, S3×D4, D4⋊2S3, S3×D5, D4×D5, D4⋊2D5, C22×Dic5, Dic3⋊4D4, S3×Dic5, C2×S3×D5, D4×Dic5, C30.C23, C2×S3×Dic5, D10⋊D6, Dic15⋊17D4
►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 91 16 106)(2 120 17 105)(3 119 18 104)(4 118 19 103)(5 117 20 102)(6 116 21 101)(7 115 22 100)(8 114 23 99)(9 113 24 98)(10 112 25 97)(11 111 26 96)(12 110 27 95)(13 109 28 94)(14 108 29 93)(15 107 30 92)(31 133 46 148)(32 132 47 147)(33 131 48 146)(34 130 49 145)(35 129 50 144)(36 128 51 143)(37 127 52 142)(38 126 53 141)(39 125 54 140)(40 124 55 139)(41 123 56 138)(42 122 57 137)(43 121 58 136)(44 150 59 135)(45 149 60 134)(61 220 76 235)(62 219 77 234)(63 218 78 233)(64 217 79 232)(65 216 80 231)(66 215 81 230)(67 214 82 229)(68 213 83 228)(69 212 84 227)(70 211 85 226)(71 240 86 225)(72 239 87 224)(73 238 88 223)(74 237 89 222)(75 236 90 221)(151 190 166 205)(152 189 167 204)(153 188 168 203)(154 187 169 202)(155 186 170 201)(156 185 171 200)(157 184 172 199)(158 183 173 198)(159 182 174 197)(160 181 175 196)(161 210 176 195)(162 209 177 194)(163 208 178 193)(164 207 179 192)(165 206 180 191)
(1 180 132 61)(2 161 133 72)(3 172 134 83)(4 153 135 64)(5 164 136 75)(6 175 137 86)(7 156 138 67)(8 167 139 78)(9 178 140 89)(10 159 141 70)(11 170 142 81)(12 151 143 62)(13 162 144 73)(14 173 145 84)(15 154 146 65)(16 165 147 76)(17 176 148 87)(18 157 149 68)(19 168 150 79)(20 179 121 90)(21 160 122 71)(22 171 123 82)(23 152 124 63)(24 163 125 74)(25 174 126 85)(26 155 127 66)(27 166 128 77)(28 177 129 88)(29 158 130 69)(30 169 131 80)(31 224 105 195)(32 235 106 206)(33 216 107 187)(34 227 108 198)(35 238 109 209)(36 219 110 190)(37 230 111 201)(38 211 112 182)(39 222 113 193)(40 233 114 204)(41 214 115 185)(42 225 116 196)(43 236 117 207)(44 217 118 188)(45 228 119 199)(46 239 120 210)(47 220 91 191)(48 231 92 202)(49 212 93 183)(50 223 94 194)(51 234 95 205)(52 215 96 186)(53 226 97 197)(54 237 98 208)(55 218 99 189)(56 229 100 200)(57 240 101 181)(58 221 102 192)(59 232 103 203)(60 213 104 184)
(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 36)(32 47)(33 58)(34 39)(35 50)(37 42)(38 53)(40 45)(41 56)(43 48)(44 59)(46 51)(49 54)(52 57)(55 60)(61 165)(62 176)(63 157)(64 168)(65 179)(66 160)(67 171)(68 152)(69 163)(70 174)(71 155)(72 166)(73 177)(74 158)(75 169)(76 180)(77 161)(78 172)(79 153)(80 164)(81 175)(82 156)(83 167)(84 178)(85 159)(86 170)(87 151)(88 162)(89 173)(90 154)(91 106)(92 117)(93 98)(94 109)(95 120)(96 101)(97 112)(99 104)(100 115)(102 107)(103 118)(105 110)(108 113)(111 116)(114 119)(121 146)(122 127)(123 138)(124 149)(125 130)(126 141)(128 133)(129 144)(131 136)(132 147)(134 139)(135 150)(137 142)(140 145)(143 148)(181 215)(182 226)(183 237)(184 218)(185 229)(186 240)(187 221)(188 232)(189 213)(190 224)(191 235)(192 216)(193 227)(194 238)(195 219)(196 230)(197 211)(198 222)(199 233)(200 214)(201 225)(202 236)(203 217)(204 228)(205 239)(206 220)(207 231)(208 212)(209 223)(210 234)
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), (1,91,16,106)(2,120,17,105)(3,119,18,104)(4,118,19,103)(5,117,20,102)(6,116,21,101)(7,115,22,100)(8,114,23,99)(9,113,24,98)(10,112,25,97)(11,111,26,96)(12,110,27,95)(13,109,28,94)(14,108,29,93)(15,107,30,92)(31,133,46,148)(32,132,47,147)(33,131,48,146)(34,130,49,145)(35,129,50,144)(36,128,51,143)(37,127,52,142)(38,126,53,141)(39,125,54,140)(40,124,55,139)(41,123,56,138)(42,122,57,137)(43,121,58,136)(44,150,59,135)(45,149,60,134)(61,220,76,235)(62,219,77,234)(63,218,78,233)(64,217,79,232)(65,216,80,231)(66,215,81,230)(67,214,82,229)(68,213,83,228)(69,212,84,227)(70,211,85,226)(71,240,86,225)(72,239,87,224)(73,238,88,223)(74,237,89,222)(75,236,90,221)(151,190,166,205)(152,189,167,204)(153,188,168,203)(154,187,169,202)(155,186,170,201)(156,185,171,200)(157,184,172,199)(158,183,173,198)(159,182,174,197)(160,181,175,196)(161,210,176,195)(162,209,177,194)(163,208,178,193)(164,207,179,192)(165,206,180,191), (1,180,132,61)(2,161,133,72)(3,172,134,83)(4,153,135,64)(5,164,136,75)(6,175,137,86)(7,156,138,67)(8,167,139,78)(9,178,140,89)(10,159,141,70)(11,170,142,81)(12,151,143,62)(13,162,144,73)(14,173,145,84)(15,154,146,65)(16,165,147,76)(17,176,148,87)(18,157,149,68)(19,168,150,79)(20,179,121,90)(21,160,122,71)(22,171,123,82)(23,152,124,63)(24,163,125,74)(25,174,126,85)(26,155,127,66)(27,166,128,77)(28,177,129,88)(29,158,130,69)(30,169,131,80)(31,224,105,195)(32,235,106,206)(33,216,107,187)(34,227,108,198)(35,238,109,209)(36,219,110,190)(37,230,111,201)(38,211,112,182)(39,222,113,193)(40,233,114,204)(41,214,115,185)(42,225,116,196)(43,236,117,207)(44,217,118,188)(45,228,119,199)(46,239,120,210)(47,220,91,191)(48,231,92,202)(49,212,93,183)(50,223,94,194)(51,234,95,205)(52,215,96,186)(53,226,97,197)(54,237,98,208)(55,218,99,189)(56,229,100,200)(57,240,101,181)(58,221,102,192)(59,232,103,203)(60,213,104,184), (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)(31,36)(32,47)(33,58)(34,39)(35,50)(37,42)(38,53)(40,45)(41,56)(43,48)(44,59)(46,51)(49,54)(52,57)(55,60)(61,165)(62,176)(63,157)(64,168)(65,179)(66,160)(67,171)(68,152)(69,163)(70,174)(71,155)(72,166)(73,177)(74,158)(75,169)(76,180)(77,161)(78,172)(79,153)(80,164)(81,175)(82,156)(83,167)(84,178)(85,159)(86,170)(87,151)(88,162)(89,173)(90,154)(91,106)(92,117)(93,98)(94,109)(95,120)(96,101)(97,112)(99,104)(100,115)(102,107)(103,118)(105,110)(108,113)(111,116)(114,119)(121,146)(122,127)(123,138)(124,149)(125,130)(126,141)(128,133)(129,144)(131,136)(132,147)(134,139)(135,150)(137,142)(140,145)(143,148)(181,215)(182,226)(183,237)(184,218)(185,229)(186,240)(187,221)(188,232)(189,213)(190,224)(191,235)(192,216)(193,227)(194,238)(195,219)(196,230)(197,211)(198,222)(199,233)(200,214)(201,225)(202,236)(203,217)(204,228)(205,239)(206,220)(207,231)(208,212)(209,223)(210,234)>;
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), (1,91,16,106)(2,120,17,105)(3,119,18,104)(4,118,19,103)(5,117,20,102)(6,116,21,101)(7,115,22,100)(8,114,23,99)(9,113,24,98)(10,112,25,97)(11,111,26,96)(12,110,27,95)(13,109,28,94)(14,108,29,93)(15,107,30,92)(31,133,46,148)(32,132,47,147)(33,131,48,146)(34,130,49,145)(35,129,50,144)(36,128,51,143)(37,127,52,142)(38,126,53,141)(39,125,54,140)(40,124,55,139)(41,123,56,138)(42,122,57,137)(43,121,58,136)(44,150,59,135)(45,149,60,134)(61,220,76,235)(62,219,77,234)(63,218,78,233)(64,217,79,232)(65,216,80,231)(66,215,81,230)(67,214,82,229)(68,213,83,228)(69,212,84,227)(70,211,85,226)(71,240,86,225)(72,239,87,224)(73,238,88,223)(74,237,89,222)(75,236,90,221)(151,190,166,205)(152,189,167,204)(153,188,168,203)(154,187,169,202)(155,186,170,201)(156,185,171,200)(157,184,172,199)(158,183,173,198)(159,182,174,197)(160,181,175,196)(161,210,176,195)(162,209,177,194)(163,208,178,193)(164,207,179,192)(165,206,180,191), (1,180,132,61)(2,161,133,72)(3,172,134,83)(4,153,135,64)(5,164,136,75)(6,175,137,86)(7,156,138,67)(8,167,139,78)(9,178,140,89)(10,159,141,70)(11,170,142,81)(12,151,143,62)(13,162,144,73)(14,173,145,84)(15,154,146,65)(16,165,147,76)(17,176,148,87)(18,157,149,68)(19,168,150,79)(20,179,121,90)(21,160,122,71)(22,171,123,82)(23,152,124,63)(24,163,125,74)(25,174,126,85)(26,155,127,66)(27,166,128,77)(28,177,129,88)(29,158,130,69)(30,169,131,80)(31,224,105,195)(32,235,106,206)(33,216,107,187)(34,227,108,198)(35,238,109,209)(36,219,110,190)(37,230,111,201)(38,211,112,182)(39,222,113,193)(40,233,114,204)(41,214,115,185)(42,225,116,196)(43,236,117,207)(44,217,118,188)(45,228,119,199)(46,239,120,210)(47,220,91,191)(48,231,92,202)(49,212,93,183)(50,223,94,194)(51,234,95,205)(52,215,96,186)(53,226,97,197)(54,237,98,208)(55,218,99,189)(56,229,100,200)(57,240,101,181)(58,221,102,192)(59,232,103,203)(60,213,104,184), (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)(31,36)(32,47)(33,58)(34,39)(35,50)(37,42)(38,53)(40,45)(41,56)(43,48)(44,59)(46,51)(49,54)(52,57)(55,60)(61,165)(62,176)(63,157)(64,168)(65,179)(66,160)(67,171)(68,152)(69,163)(70,174)(71,155)(72,166)(73,177)(74,158)(75,169)(76,180)(77,161)(78,172)(79,153)(80,164)(81,175)(82,156)(83,167)(84,178)(85,159)(86,170)(87,151)(88,162)(89,173)(90,154)(91,106)(92,117)(93,98)(94,109)(95,120)(96,101)(97,112)(99,104)(100,115)(102,107)(103,118)(105,110)(108,113)(111,116)(114,119)(121,146)(122,127)(123,138)(124,149)(125,130)(126,141)(128,133)(129,144)(131,136)(132,147)(134,139)(135,150)(137,142)(140,145)(143,148)(181,215)(182,226)(183,237)(184,218)(185,229)(186,240)(187,221)(188,232)(189,213)(190,224)(191,235)(192,216)(193,227)(194,238)(195,219)(196,230)(197,211)(198,222)(199,233)(200,214)(201,225)(202,236)(203,217)(204,228)(205,239)(206,220)(207,231)(208,212)(209,223)(210,234) );
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)], [(1,91,16,106),(2,120,17,105),(3,119,18,104),(4,118,19,103),(5,117,20,102),(6,116,21,101),(7,115,22,100),(8,114,23,99),(9,113,24,98),(10,112,25,97),(11,111,26,96),(12,110,27,95),(13,109,28,94),(14,108,29,93),(15,107,30,92),(31,133,46,148),(32,132,47,147),(33,131,48,146),(34,130,49,145),(35,129,50,144),(36,128,51,143),(37,127,52,142),(38,126,53,141),(39,125,54,140),(40,124,55,139),(41,123,56,138),(42,122,57,137),(43,121,58,136),(44,150,59,135),(45,149,60,134),(61,220,76,235),(62,219,77,234),(63,218,78,233),(64,217,79,232),(65,216,80,231),(66,215,81,230),(67,214,82,229),(68,213,83,228),(69,212,84,227),(70,211,85,226),(71,240,86,225),(72,239,87,224),(73,238,88,223),(74,237,89,222),(75,236,90,221),(151,190,166,205),(152,189,167,204),(153,188,168,203),(154,187,169,202),(155,186,170,201),(156,185,171,200),(157,184,172,199),(158,183,173,198),(159,182,174,197),(160,181,175,196),(161,210,176,195),(162,209,177,194),(163,208,178,193),(164,207,179,192),(165,206,180,191)], [(1,180,132,61),(2,161,133,72),(3,172,134,83),(4,153,135,64),(5,164,136,75),(6,175,137,86),(7,156,138,67),(8,167,139,78),(9,178,140,89),(10,159,141,70),(11,170,142,81),(12,151,143,62),(13,162,144,73),(14,173,145,84),(15,154,146,65),(16,165,147,76),(17,176,148,87),(18,157,149,68),(19,168,150,79),(20,179,121,90),(21,160,122,71),(22,171,123,82),(23,152,124,63),(24,163,125,74),(25,174,126,85),(26,155,127,66),(27,166,128,77),(28,177,129,88),(29,158,130,69),(30,169,131,80),(31,224,105,195),(32,235,106,206),(33,216,107,187),(34,227,108,198),(35,238,109,209),(36,219,110,190),(37,230,111,201),(38,211,112,182),(39,222,113,193),(40,233,114,204),(41,214,115,185),(42,225,116,196),(43,236,117,207),(44,217,118,188),(45,228,119,199),(46,239,120,210),(47,220,91,191),(48,231,92,202),(49,212,93,183),(50,223,94,194),(51,234,95,205),(52,215,96,186),(53,226,97,197),(54,237,98,208),(55,218,99,189),(56,229,100,200),(57,240,101,181),(58,221,102,192),(59,232,103,203),(60,213,104,184)], [(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),(31,36),(32,47),(33,58),(34,39),(35,50),(37,42),(38,53),(40,45),(41,56),(43,48),(44,59),(46,51),(49,54),(52,57),(55,60),(61,165),(62,176),(63,157),(64,168),(65,179),(66,160),(67,171),(68,152),(69,163),(70,174),(71,155),(72,166),(73,177),(74,158),(75,169),(76,180),(77,161),(78,172),(79,153),(80,164),(81,175),(82,156),(83,167),(84,178),(85,159),(86,170),(87,151),(88,162),(89,173),(90,154),(91,106),(92,117),(93,98),(94,109),(95,120),(96,101),(97,112),(99,104),(100,115),(102,107),(103,118),(105,110),(108,113),(111,116),(114,119),(121,146),(122,127),(123,138),(124,149),(125,130),(126,141),(128,133),(129,144),(131,136),(132,147),(134,139),(135,150),(137,142),(140,145),(143,148),(181,215),(182,226),(183,237),(184,218),(185,229),(186,240),(187,221),(188,232),(189,213),(190,224),(191,235),(192,216),(193,227),(194,238),(195,219),(196,230),(197,211),(198,222),(199,233),(200,214),(201,225),(202,236),(203,217),(204,228),(205,239),(206,220),(207,231),(208,212),(209,223),(210,234)]])
66 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 5A | 5B | 6A | 6B | 6C | 6D | 6E | 10A | ··· | 10F | 10G | 10H | 10I | 10J | 10K | 10L | 10M | 10N | 12A | 12B | 12C | 12D | 15A | 15B | 20A | 20B | 20C | 20D | 30A | ··· | 30N |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 6 | 6 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 12 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 20 | 30 | ··· | 30 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 6 | 6 | 2 | 6 | 6 | 10 | 10 | 10 | 10 | 15 | 15 | 15 | 15 | 30 | 30 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 12 | 12 | 12 | 12 | 20 | 20 | 20 | 20 | 4 | 4 | 12 | 12 | 12 | 12 | 4 | ··· | 4 |
66 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | + | - | + | + | - | - | + | - | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | S3 | D4 | D5 | D6 | D6 | C4○D4 | D10 | Dic5 | D10 | D10 | C4×S3 | S3×D4 | D4⋊2S3 | S3×D5 | D4×D5 | D4⋊2D5 | S3×Dic5 | C2×S3×D5 | C30.C23 | D10⋊D6 |
| kernel | Dic15⋊17D4 | Dic3×Dic5 | D6⋊Dic5 | C6.Dic10 | C3×C23.D5 | C2×S3×Dic5 | C10×C3⋊D4 | C22×Dic15 | C5×C3⋊D4 | C23.D5 | Dic15 | C2×C3⋊D4 | C2×Dic5 | C22×C10 | C30 | C2×Dic3 | C3⋊D4 | C22×S3 | C22×C6 | C2×C10 | C10 | C10 | C23 | C6 | C6 | C22 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8 | 1 | 2 | 2 | 2 | 1 | 2 | 2 | 8 | 2 | 2 | 4 | 1 | 1 | 2 | 2 | 2 | 4 | 2 | 4 | 4 |
Matrix representation of Dic15⋊17D4 ►in GL6(𝔽61)
| 0 | 60 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 20 | 0 | 0 | 0 |
| 0 | 0 | 15 | 58 | 0 | 0 |
| 0 | 0 | 0 | 0 | 60 | 0 |
| 0 | 0 | 0 | 0 | 0 | 60 |
| 11 | 0 | 0 | 0 | 0 | 0 |
| 50 | 50 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 5 | 0 | 0 |
| 0 | 0 | 29 | 51 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 0 |
| 0 | 0 | 0 | 0 | 0 | 11 |
| 60 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 60 | 0 | 0 | 0 |
| 0 | 0 | 0 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 6 | 46 |
| 0 | 0 | 0 | 0 | 35 | 55 |
| 60 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 60 | 0 |
| 0 | 0 | 0 | 0 | 48 | 1 |
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] >;
Dic15⋊17D4 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