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G = Dic5×D12order 480 = 25·3·5

Direct product of Dic5 and D12

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: Dic5×D12, C159(C4×D4), C56(C4×D12), C205(C4×S3), C31(D4×Dic5), C6018(C2×C4), (C5×D12)⋊9C4, C41(S3×Dic5), C2.3(D5×D12), C6.16(D4×D5), D6⋊Dic58C2, (C3×Dic5)⋊7D4, D61(C2×Dic5), (C4×Dic5)⋊5S3, C605C432C2, C124(C2×Dic5), C30.40(C2×D4), (C12×Dic5)⋊5C2, (C10×D12).5C2, (C2×D12).10D5, C10.16(C2×D12), (C2×C20).124D6, C30.60(C4○D4), (C2×C12).303D10, C10.56(C4○D12), C2.4(D125D5), C6.24(D42D5), (C2×C30).105C23, (C2×C60).147C22, C30.125(C22×C4), (C2×Dic5).176D6, (C22×S3).37D10, C6.11(C22×Dic5), (C6×Dic5).201C22, (C2×Dic15).85C22, (C2×S3×Dic5)⋊3C2, C10.118(S3×C2×C4), (S3×C10)⋊10(C2×C4), C2.12(C2×S3×Dic5), C22.53(C2×S3×D5), (C2×C4).160(S3×D5), (S3×C2×C10).17C22, (C2×C6).117(C22×D5), (C2×C10).117(C22×S3), SmallGroup(480,491)

Series: Derived Chief Lower central Upper central

C1C30 — Dic5×D12
C1C5C15C30C2×C30C6×Dic5C2×S3×Dic5 — Dic5×D12
C15C30 — Dic5×D12
C1C22C2×C4

Generators and relations for Dic5×D12
 G = < a,b,c,d | a10=c12=d2=1, b2=a5, bab-1=a-1, ac=ca, ad=da, bc=cb, bd=db, dcd=c-1 >

Subgroups: 812 in 188 conjugacy classes, 72 normal (34 characteristic)
C1, C2 [×3], C2 [×4], C3, C4 [×2], C4 [×5], C22, C22 [×8], C5, S3 [×4], C6 [×3], C2×C4, C2×C4 [×8], D4 [×4], C23 [×2], C10 [×3], C10 [×4], Dic3 [×2], C12 [×2], C12 [×3], D6 [×4], D6 [×4], C2×C6, C15, C42, C22⋊C4 [×2], C4⋊C4, C22×C4 [×2], C2×D4, Dic5 [×2], Dic5 [×3], C20 [×2], C2×C10, C2×C10 [×8], C4×S3 [×4], D12 [×4], C2×Dic3 [×2], C2×C12, C2×C12 [×2], C22×S3 [×2], C5×S3 [×4], C30 [×3], C4×D4, C2×Dic5 [×2], C2×Dic5 [×6], C2×C20, C5×D4 [×4], C22×C10 [×2], C4⋊Dic3, D6⋊C4 [×2], C4×C12, S3×C2×C4 [×2], C2×D12, C3×Dic5 [×2], C3×Dic5, Dic15 [×2], C60 [×2], S3×C10 [×4], S3×C10 [×4], C2×C30, C4×Dic5, C4⋊Dic5, C23.D5 [×2], C22×Dic5 [×2], D4×C10, C4×D12, S3×Dic5 [×4], C6×Dic5 [×2], C5×D12 [×4], C2×Dic15 [×2], C2×C60, S3×C2×C10 [×2], D4×Dic5, D6⋊Dic5 [×2], C12×Dic5, C605C4, C2×S3×Dic5 [×2], C10×D12, Dic5×D12
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], D12 [×2], C22×S3, C4×D4, C2×Dic5 [×6], C22×D5, S3×C2×C4, C2×D12, C4○D12, S3×D5, D4×D5, D42D5, C22×Dic5, C4×D12, S3×Dic5 [×2], C2×S3×D5, D4×Dic5, D125D5, D5×D12, C2×S3×Dic5, Dic5×D12

Smallest permutation representation of Dic5×D12
On 240 points
Generators in S240
(1 164 56 73 106 110 215 23 144 179)(2 165 57 74 107 111 216 24 133 180)(3 166 58 75 108 112 205 13 134 169)(4 167 59 76 97 113 206 14 135 170)(5 168 60 77 98 114 207 15 136 171)(6 157 49 78 99 115 208 16 137 172)(7 158 50 79 100 116 209 17 138 173)(8 159 51 80 101 117 210 18 139 174)(9 160 52 81 102 118 211 19 140 175)(10 161 53 82 103 119 212 20 141 176)(11 162 54 83 104 120 213 21 142 177)(12 163 55 84 105 109 214 22 143 178)(25 228 130 189 41 93 197 70 148 233)(26 217 131 190 42 94 198 71 149 234)(27 218 132 191 43 95 199 72 150 235)(28 219 121 192 44 96 200 61 151 236)(29 220 122 181 45 85 201 62 152 237)(30 221 123 182 46 86 202 63 153 238)(31 222 124 183 47 87 203 64 154 239)(32 223 125 184 48 88 204 65 155 240)(33 224 126 185 37 89 193 66 156 229)(34 225 127 186 38 90 194 67 145 230)(35 226 128 187 39 91 195 68 146 231)(36 227 129 188 40 92 196 69 147 232)
(1 218 110 199)(2 219 111 200)(3 220 112 201)(4 221 113 202)(5 222 114 203)(6 223 115 204)(7 224 116 193)(8 225 117 194)(9 226 118 195)(10 227 119 196)(11 228 120 197)(12 217 109 198)(13 45 58 237)(14 46 59 238)(15 47 60 239)(16 48 49 240)(17 37 50 229)(18 38 51 230)(19 39 52 231)(20 40 53 232)(21 41 54 233)(22 42 55 234)(23 43 56 235)(24 44 57 236)(25 213 93 162)(26 214 94 163)(27 215 95 164)(28 216 96 165)(29 205 85 166)(30 206 86 167)(31 207 87 168)(32 208 88 157)(33 209 89 158)(34 210 90 159)(35 211 91 160)(36 212 92 161)(61 180 121 107)(62 169 122 108)(63 170 123 97)(64 171 124 98)(65 172 125 99)(66 173 126 100)(67 174 127 101)(68 175 128 102)(69 176 129 103)(70 177 130 104)(71 178 131 105)(72 179 132 106)(73 150 144 191)(74 151 133 192)(75 152 134 181)(76 153 135 182)(77 154 136 183)(78 155 137 184)(79 156 138 185)(80 145 139 186)(81 146 140 187)(82 147 141 188)(83 148 142 189)(84 149 143 190)
(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 3)(4 12)(5 11)(6 10)(7 9)(13 23)(14 22)(15 21)(16 20)(17 19)(25 31)(26 30)(27 29)(32 36)(33 35)(37 39)(40 48)(41 47)(42 46)(43 45)(49 53)(50 52)(54 60)(55 59)(56 58)(62 72)(63 71)(64 70)(65 69)(66 68)(73 75)(76 84)(77 83)(78 82)(79 81)(85 95)(86 94)(87 93)(88 92)(89 91)(97 105)(98 104)(99 103)(100 102)(106 108)(109 113)(110 112)(114 120)(115 119)(116 118)(122 132)(123 131)(124 130)(125 129)(126 128)(134 144)(135 143)(136 142)(137 141)(138 140)(146 156)(147 155)(148 154)(149 153)(150 152)(157 161)(158 160)(162 168)(163 167)(164 166)(169 179)(170 178)(171 177)(172 176)(173 175)(181 191)(182 190)(183 189)(184 188)(185 187)(193 195)(196 204)(197 203)(198 202)(199 201)(205 215)(206 214)(207 213)(208 212)(209 211)(217 221)(218 220)(222 228)(223 227)(224 226)(229 231)(232 240)(233 239)(234 238)(235 237)

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

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

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

72 conjugacy classes

class 1 2A2B2C2D2E2F2G 3 4A4B4C4D4E4F4G4H4I4J4K4L5A5B6A6B6C10A···10F10G···10N12A12B12C12D12E···12L15A15B20A20B20C20D30A···30F60A···60H
order1222222234444444444445566610···1010···101212121212···1215152020202030···3060···60
size111166662225555101030303030222222···212···12222210···104444444···44···4

72 irreducible representations

dim11111112222222222224444444
type+++++++++++-+++++--+-+
imageC1C2C2C2C2C2C4S3D4D5D6D6C4○D4Dic5D10D10D12C4×S3C4○D12S3×D5D4×D5D42D5S3×Dic5C2×S3×D5D125D5D5×D12
kernelDic5×D12D6⋊Dic5C12×Dic5C605C4C2×S3×Dic5C10×D12C5×D12C4×Dic5C3×Dic5C2×D12C2×Dic5C2×C20C30D12C2×C12C22×S3Dic5C20C10C2×C4C6C6C4C22C2C2
# reps12112181222128244442224244

Matrix representation of Dic5×D12 in GL5(𝔽61)

600000
01000
00100
000431
000600
,
500000
060000
006000
000476
0005914
,
10000
0382300
0381500
000600
000060
,
600000
01100
006000
00010
00001

G:=sub<GL(5,GF(61))| [60,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,43,60,0,0,0,1,0],[50,0,0,0,0,0,60,0,0,0,0,0,60,0,0,0,0,0,47,59,0,0,0,6,14],[1,0,0,0,0,0,38,38,0,0,0,23,15,0,0,0,0,0,60,0,0,0,0,0,60],[60,0,0,0,0,0,1,0,0,0,0,1,60,0,0,0,0,0,1,0,0,0,0,0,1] >;

Dic5×D12 in GAP, Magma, Sage, TeX

{\rm Dic}_5\times D_{12}
% in TeX

G:=Group("Dic5xD12");
// GroupNames label

G:=SmallGroup(480,491);
// by ID

G=gap.SmallGroup(480,491);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,219,100,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^10=c^12=d^2=1,b^2=a^5,b*a*b^-1=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d=c^-1>;
// generators/relations

׿
×
𝔽