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G = D12.29D10order 480 = 25·3·5

12nd non-split extension by D12 of D10 acting via D10/D5=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D12.29D10, C60.58C23, C30.34C24, C1572- 1+4, Dic10.31D6, D30.40C23, Dic30.21C22, Dic15.20C23, (Q8×D5)⋊8S3, (Q8×D15)⋊5C2, Q83S34D5, (C4×D5).18D6, Q8.28(S3×D5), (C5×Q8).43D6, D125D56C2, D12⋊D56C2, C15⋊Q8.7C22, (S3×Dic10)⋊6C2, (C4×S3).18D10, (C3×Q8).26D10, C6.34(C23×D5), D6.D107C2, C20.58(C22×S3), C10.34(S3×C23), C53(Q8.15D6), D6.15(C22×D5), (C6×D5).48C23, C12.58(C22×D5), C15⋊D4.4C22, C5⋊D12.4C22, C3⋊D20.5C22, C34(D4.10D10), (S3×C10).17C23, (S3×C20).21C22, D10.44(C22×S3), (C5×D12).19C22, (D5×C12).21C22, (C4×D15).21C22, (Q8×C15).21C22, (S3×Dic5).4C22, (C5×Dic3).31C23, Dic3.28(C22×D5), Dic5.19(C22×S3), (C3×Dic5).17C23, (C3×Dic10).21C22, (C3×Q8×D5)⋊5C2, C4.58(C2×S3×D5), C2.37(C22×S3×D5), (C5×Q83S3)⋊4C2, SmallGroup(480,1106)

Series: Derived Chief Lower central Upper central

C1C30 — D12.29D10
C1C5C15C30C6×D5C15⋊D4D6.D10 — D12.29D10
C15C30 — D12.29D10
C1C2Q8

Generators and relations for D12.29D10
 G = < a,b,c,d | a12=b2=c10=1, d2=a6, bab=a-1, cac-1=dad-1=a5, cbc-1=a10b, dbd-1=a4b, dcd-1=a6c-1 >

Subgroups: 1324 in 292 conjugacy classes, 108 normal (24 characteristic)
C1, C2, C2 [×5], C3, C4 [×3], C4 [×7], C22 [×5], C5, S3 [×4], C6, C6, C2×C4 [×15], D4 [×10], Q8, Q8 [×9], D5 [×2], C10, C10 [×3], Dic3, Dic3 [×3], C12 [×3], C12 [×3], D6 [×3], D6, C2×C6, C15, C2×Q8 [×5], C4○D4 [×10], Dic5 [×3], Dic5 [×3], C20 [×3], C20, D10, D10, C2×C10 [×3], Dic6 [×6], C4×S3 [×3], C4×S3 [×9], D12 [×3], D12 [×3], C3⋊D4 [×4], C2×C12 [×3], C3×Q8, C3×Q8 [×3], C5×S3 [×3], C3×D5, D15, C30, 2- 1+4, Dic10 [×3], Dic10 [×6], C4×D5 [×3], C4×D5 [×3], D20, C2×Dic5 [×6], C5⋊D4 [×6], C2×C20 [×3], C5×D4 [×3], C5×Q8, C4○D12 [×6], S3×Q8 [×4], Q83S3, Q83S3 [×3], C6×Q8, C5×Dic3, C3×Dic5 [×3], Dic15 [×3], C60 [×3], C6×D5, S3×C10 [×3], D30, C2×Dic10 [×3], C4○D20 [×3], D42D5 [×6], Q8×D5, Q8×D5, C5×C4○D4, Q8.15D6, S3×Dic5 [×6], C15⋊D4 [×3], C3⋊D20, C5⋊D12 [×3], C15⋊Q8 [×3], C3×Dic10 [×3], D5×C12 [×3], S3×C20 [×3], C5×D12 [×3], Dic30 [×3], C4×D15 [×3], Q8×C15, D4.10D10, S3×Dic10 [×3], D12⋊D5 [×3], D6.D10 [×3], D125D5 [×3], C3×Q8×D5, C5×Q83S3, Q8×D15, D12.29D10
Quotients: C1, C2 [×15], C22 [×35], S3, C23 [×15], D5, D6 [×7], C24, D10 [×7], C22×S3 [×7], 2- 1+4, C22×D5 [×7], S3×C23, S3×D5, C23×D5, Q8.15D6, C2×S3×D5 [×3], D4.10D10, C22×S3×D5, D12.29D10

Smallest permutation representation of D12.29D10
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)
(1 125)(2 124)(3 123)(4 122)(5 121)(6 132)(7 131)(8 130)(9 129)(10 128)(11 127)(12 126)(13 62)(14 61)(15 72)(16 71)(17 70)(18 69)(19 68)(20 67)(21 66)(22 65)(23 64)(24 63)(25 174)(26 173)(27 172)(28 171)(29 170)(30 169)(31 180)(32 179)(33 178)(34 177)(35 176)(36 175)(37 223)(38 222)(39 221)(40 220)(41 219)(42 218)(43 217)(44 228)(45 227)(46 226)(47 225)(48 224)(49 101)(50 100)(51 99)(52 98)(53 97)(54 108)(55 107)(56 106)(57 105)(58 104)(59 103)(60 102)(73 158)(74 157)(75 168)(76 167)(77 166)(78 165)(79 164)(80 163)(81 162)(82 161)(83 160)(84 159)(85 111)(86 110)(87 109)(88 120)(89 119)(90 118)(91 117)(92 116)(93 115)(94 114)(95 113)(96 112)(133 202)(134 201)(135 200)(136 199)(137 198)(138 197)(139 196)(140 195)(141 194)(142 193)(143 204)(144 203)(145 206)(146 205)(147 216)(148 215)(149 214)(150 213)(151 212)(152 211)(153 210)(154 209)(155 208)(156 207)(181 230)(182 229)(183 240)(184 239)(185 238)(186 237)(187 236)(188 235)(189 234)(190 233)(191 232)(192 231)
(1 92 151 31 194 107 69 190 159 37)(2 85 152 36 195 100 70 183 160 42)(3 90 153 29 196 105 71 188 161 47)(4 95 154 34 197 98 72 181 162 40)(5 88 155 27 198 103 61 186 163 45)(6 93 156 32 199 108 62 191 164 38)(7 86 145 25 200 101 63 184 165 43)(8 91 146 30 201 106 64 189 166 48)(9 96 147 35 202 99 65 182 167 41)(10 89 148 28 203 104 66 187 168 46)(11 94 149 33 204 97 67 192 157 39)(12 87 150 26 193 102 68 185 158 44)(13 234 79 224 132 117 207 169 136 56)(14 239 80 217 121 110 208 174 137 49)(15 232 81 222 122 115 209 179 138 54)(16 237 82 227 123 120 210 172 139 59)(17 230 83 220 124 113 211 177 140 52)(18 235 84 225 125 118 212 170 141 57)(19 240 73 218 126 111 213 175 142 50)(20 233 74 223 127 116 214 180 143 55)(21 238 75 228 128 109 215 173 144 60)(22 231 76 221 129 114 216 178 133 53)(23 236 77 226 130 119 205 171 134 58)(24 229 78 219 131 112 206 176 135 51)
(1 197 7 203)(2 202 8 196)(3 195 9 201)(4 200 10 194)(5 193 11 199)(6 198 12 204)(13 76 19 82)(14 81 20 75)(15 74 21 80)(16 79 22 73)(17 84 23 78)(18 77 24 83)(25 95 31 89)(26 88 32 94)(27 93 33 87)(28 86 34 92)(29 91 35 85)(30 96 36 90)(37 104 43 98)(38 97 44 103)(39 102 45 108)(40 107 46 101)(41 100 47 106)(42 105 48 99)(49 228 55 222)(50 221 56 227)(51 226 57 220)(52 219 58 225)(53 224 59 218)(54 217 60 223)(61 158 67 164)(62 163 68 157)(63 168 69 162)(64 161 70 167)(65 166 71 160)(66 159 72 165)(109 180 115 174)(110 173 116 179)(111 178 117 172)(112 171 118 177)(113 176 119 170)(114 169 120 175)(121 138 127 144)(122 143 128 137)(123 136 129 142)(124 141 130 135)(125 134 131 140)(126 139 132 133)(145 148 151 154)(146 153 152 147)(149 156 155 150)(181 190 187 184)(182 183 188 189)(185 186 191 192)(205 206 211 212)(207 216 213 210)(208 209 214 215)(229 236 235 230)(231 234 237 240)(232 239 238 233)

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

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

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

57 conjugacy classes

class 1 2A2B2C2D2E2F 3 4A4B4C4D4E4F4G4H4I4J5A5B6A6B6C10A10B10C···10H12A12B12C12D12E12F15A15B20A···20F20G20H20I20J30A30B60A···60F
order12222223444444444455666101010···10121212121212151520···2020202020303060···60
size1166610302222610101030303022210102212···12444202020444···46666448···8

57 irreducible representations

dim1111111122222222444448
type++++++++++++++++-++--
imageC1C2C2C2C2C2C2C2S3D5D6D6D6D10D10D102- 1+4S3×D5Q8.15D6C2×S3×D5D4.10D10D12.29D10
kernelD12.29D10S3×Dic10D12⋊D5D6.D10D125D5C3×Q8×D5C5×Q83S3Q8×D15Q8×D5Q83S3Dic10C4×D5C5×Q8C4×S3D12C3×Q8C15Q8C5C4C3C1
# reps1333311112331662122642

Matrix representation of D12.29D10 in GL8(𝔽61)

6006000000
0600600000
10000000
01000000
000030050
000003005
0000150310
0000015031
,
13161450000
12149130000
492948450000
371249600000
00002571421
000050362847
000024363654
000048371125
,
33105280000
385621450000
331828510000
44502350000
00002604110
000019445448
0000130591
000040224217
,
4418000000
4517000000
174317430000
164416440000
00009223224
000040522729
000035115239
00002026219

G:=sub<GL(8,GF(61))| [60,0,1,0,0,0,0,0,0,60,0,1,0,0,0,0,60,0,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,0,0,0,30,0,15,0,0,0,0,0,0,30,0,15,0,0,0,0,5,0,31,0,0,0,0,0,0,5,0,31],[13,12,49,37,0,0,0,0,16,1,29,12,0,0,0,0,1,49,48,49,0,0,0,0,45,13,45,60,0,0,0,0,0,0,0,0,25,50,24,48,0,0,0,0,7,36,36,37,0,0,0,0,14,28,36,11,0,0,0,0,21,47,54,25],[33,38,33,44,0,0,0,0,10,56,18,50,0,0,0,0,5,21,28,23,0,0,0,0,28,45,51,5,0,0,0,0,0,0,0,0,2,19,1,40,0,0,0,0,60,44,30,22,0,0,0,0,41,54,59,42,0,0,0,0,10,48,1,17],[44,45,17,16,0,0,0,0,18,17,43,44,0,0,0,0,0,0,17,16,0,0,0,0,0,0,43,44,0,0,0,0,0,0,0,0,9,40,35,20,0,0,0,0,22,52,11,26,0,0,0,0,32,27,52,21,0,0,0,0,24,29,39,9] >;

D12.29D10 in GAP, Magma, Sage, TeX

D_{12}._{29}D_{10}
% in TeX

G:=Group("D12.29D10");
// GroupNames label

G:=SmallGroup(480,1106);
// by ID

G=gap.SmallGroup(480,1106);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,253,100,346,185,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^12=b^2=c^10=1,d^2=a^6,b*a*b=a^-1,c*a*c^-1=d*a*d^-1=a^5,c*b*c^-1=a^10*b,d*b*d^-1=a^4*b,d*c*d^-1=a^6*c^-1>;
// generators/relations

׿
×
𝔽