metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D12.29D10, C60.58C23, C30.34C24, C15⋊72- 1+4, Dic10.31D6, D30.40C23, Dic30.21C22, Dic15.20C23, (Q8×D5)⋊8S3, (Q8×D15)⋊5C2, Q8⋊3S3⋊4D5, (C4×D5).18D6, Q8.28(S3×D5), (C5×Q8).43D6, D12⋊5D5⋊6C2, D12⋊D5⋊6C2, C15⋊Q8.7C22, (S3×Dic10)⋊6C2, (C4×S3).18D10, (C3×Q8).26D10, C6.34(C23×D5), D6.D10⋊7C2, C20.58(C22×S3), C10.34(S3×C23), C5⋊3(Q8.15D6), D6.15(C22×D5), (C6×D5).48C23, C12.58(C22×D5), C15⋊D4.4C22, C5⋊D12.4C22, C3⋊D20.5C22, C3⋊4(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×Q8⋊3S3)⋊4C2, SmallGroup(480,1106)
Series: Derived ►Chief ►Lower central ►Upper central
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, C3, C4, C4, C22, C5, S3, C6, C6, C2×C4, D4, Q8, Q8, D5, C10, C10, Dic3, Dic3, C12, C12, D6, D6, C2×C6, C15, C2×Q8, C4○D4, Dic5, Dic5, C20, C20, D10, D10, C2×C10, Dic6, C4×S3, C4×S3, D12, D12, C3⋊D4, C2×C12, C3×Q8, C3×Q8, C5×S3, C3×D5, D15, C30, 2- 1+4, Dic10, Dic10, C4×D5, C4×D5, D20, C2×Dic5, C5⋊D4, C2×C20, C5×D4, C5×Q8, C4○D12, S3×Q8, Q8⋊3S3, Q8⋊3S3, C6×Q8, C5×Dic3, C3×Dic5, Dic15, C60, C6×D5, S3×C10, D30, C2×Dic10, C4○D20, D4⋊2D5, Q8×D5, Q8×D5, C5×C4○D4, Q8.15D6, S3×Dic5, C15⋊D4, C3⋊D20, C5⋊D12, C15⋊Q8, C3×Dic10, D5×C12, S3×C20, C5×D12, Dic30, C4×D15, Q8×C15, D4.10D10, S3×Dic10, D12⋊D5, D6.D10, D12⋊5D5, C3×Q8×D5, C5×Q8⋊3S3, Q8×D15, D12.29D10
Quotients: C1, C2, C22, S3, C23, D5, D6, C24, D10, C22×S3, 2- 1+4, C22×D5, S3×C23, S3×D5, C23×D5, Q8.15D6, C2×S3×D5, D4.10D10, C22×S3×D5, 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 36)(2 35)(3 34)(4 33)(5 32)(6 31)(7 30)(8 29)(9 28)(10 27)(11 26)(12 25)(13 177)(14 176)(15 175)(16 174)(17 173)(18 172)(19 171)(20 170)(21 169)(22 180)(23 179)(24 178)(37 186)(38 185)(39 184)(40 183)(41 182)(42 181)(43 192)(44 191)(45 190)(46 189)(47 188)(48 187)(49 212)(50 211)(51 210)(52 209)(53 208)(54 207)(55 206)(56 205)(57 216)(58 215)(59 214)(60 213)(61 121)(62 132)(63 131)(64 130)(65 129)(66 128)(67 127)(68 126)(69 125)(70 124)(71 123)(72 122)(73 105)(74 104)(75 103)(76 102)(77 101)(78 100)(79 99)(80 98)(81 97)(82 108)(83 107)(84 106)(85 161)(86 160)(87 159)(88 158)(89 157)(90 168)(91 167)(92 166)(93 165)(94 164)(95 163)(96 162)(109 223)(110 222)(111 221)(112 220)(113 219)(114 218)(115 217)(116 228)(117 227)(118 226)(119 225)(120 224)(133 194)(134 193)(135 204)(136 203)(137 202)(138 201)(139 200)(140 199)(141 198)(142 197)(143 196)(144 195)(145 232)(146 231)(147 230)(148 229)(149 240)(150 239)(151 238)(152 237)(153 236)(154 235)(155 234)(156 233)
(1 68 189 105 149 56 174 92 110 144)(2 61 190 98 150 49 175 85 111 137)(3 66 191 103 151 54 176 90 112 142)(4 71 192 108 152 59 177 95 113 135)(5 64 181 101 153 52 178 88 114 140)(6 69 182 106 154 57 179 93 115 133)(7 62 183 99 155 50 180 86 116 138)(8 67 184 104 156 55 169 91 117 143)(9 72 185 97 145 60 170 96 118 136)(10 65 186 102 146 53 171 89 119 141)(11 70 187 107 147 58 172 94 120 134)(12 63 188 100 148 51 173 87 109 139)(13 165 219 194 33 125 43 84 237 216)(14 158 220 199 34 130 44 77 238 209)(15 163 221 204 35 123 45 82 239 214)(16 168 222 197 36 128 46 75 240 207)(17 161 223 202 25 121 47 80 229 212)(18 166 224 195 26 126 48 73 230 205)(19 159 225 200 27 131 37 78 231 210)(20 164 226 193 28 124 38 83 232 215)(21 157 227 198 29 129 39 76 233 208)(22 162 228 203 30 122 40 81 234 213)(23 167 217 196 31 127 41 74 235 206)(24 160 218 201 32 132 42 79 236 211)
(1 152 7 146)(2 145 8 151)(3 150 9 156)(4 155 10 149)(5 148 11 154)(6 153 12 147)(13 224 19 218)(14 217 20 223)(15 222 21 228)(16 227 22 221)(17 220 23 226)(18 225 24 219)(25 238 31 232)(26 231 32 237)(27 236 33 230)(28 229 34 235)(29 234 35 240)(30 239 36 233)(37 42 43 48)(38 47 44 41)(39 40 45 46)(49 142 55 136)(50 135 56 141)(51 140 57 134)(52 133 58 139)(53 138 59 144)(54 143 60 137)(61 103 67 97)(62 108 68 102)(63 101 69 107)(64 106 70 100)(65 99 71 105)(66 104 72 98)(73 125 79 131)(74 130 80 124)(75 123 81 129)(76 128 82 122)(77 121 83 127)(78 126 84 132)(85 90 91 96)(86 95 92 89)(87 88 93 94)(109 172 115 178)(110 177 116 171)(111 170 117 176)(112 175 118 169)(113 180 119 174)(114 173 120 179)(157 168 163 162)(158 161 164 167)(159 166 165 160)(181 188 187 182)(183 186 189 192)(184 191 190 185)(193 206 199 212)(194 211 200 205)(195 216 201 210)(196 209 202 215)(197 214 203 208)(198 207 204 213)
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), (1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,177)(14,176)(15,175)(16,174)(17,173)(18,172)(19,171)(20,170)(21,169)(22,180)(23,179)(24,178)(37,186)(38,185)(39,184)(40,183)(41,182)(42,181)(43,192)(44,191)(45,190)(46,189)(47,188)(48,187)(49,212)(50,211)(51,210)(52,209)(53,208)(54,207)(55,206)(56,205)(57,216)(58,215)(59,214)(60,213)(61,121)(62,132)(63,131)(64,130)(65,129)(66,128)(67,127)(68,126)(69,125)(70,124)(71,123)(72,122)(73,105)(74,104)(75,103)(76,102)(77,101)(78,100)(79,99)(80,98)(81,97)(82,108)(83,107)(84,106)(85,161)(86,160)(87,159)(88,158)(89,157)(90,168)(91,167)(92,166)(93,165)(94,164)(95,163)(96,162)(109,223)(110,222)(111,221)(112,220)(113,219)(114,218)(115,217)(116,228)(117,227)(118,226)(119,225)(120,224)(133,194)(134,193)(135,204)(136,203)(137,202)(138,201)(139,200)(140,199)(141,198)(142,197)(143,196)(144,195)(145,232)(146,231)(147,230)(148,229)(149,240)(150,239)(151,238)(152,237)(153,236)(154,235)(155,234)(156,233), (1,68,189,105,149,56,174,92,110,144)(2,61,190,98,150,49,175,85,111,137)(3,66,191,103,151,54,176,90,112,142)(4,71,192,108,152,59,177,95,113,135)(5,64,181,101,153,52,178,88,114,140)(6,69,182,106,154,57,179,93,115,133)(7,62,183,99,155,50,180,86,116,138)(8,67,184,104,156,55,169,91,117,143)(9,72,185,97,145,60,170,96,118,136)(10,65,186,102,146,53,171,89,119,141)(11,70,187,107,147,58,172,94,120,134)(12,63,188,100,148,51,173,87,109,139)(13,165,219,194,33,125,43,84,237,216)(14,158,220,199,34,130,44,77,238,209)(15,163,221,204,35,123,45,82,239,214)(16,168,222,197,36,128,46,75,240,207)(17,161,223,202,25,121,47,80,229,212)(18,166,224,195,26,126,48,73,230,205)(19,159,225,200,27,131,37,78,231,210)(20,164,226,193,28,124,38,83,232,215)(21,157,227,198,29,129,39,76,233,208)(22,162,228,203,30,122,40,81,234,213)(23,167,217,196,31,127,41,74,235,206)(24,160,218,201,32,132,42,79,236,211), (1,152,7,146)(2,145,8,151)(3,150,9,156)(4,155,10,149)(5,148,11,154)(6,153,12,147)(13,224,19,218)(14,217,20,223)(15,222,21,228)(16,227,22,221)(17,220,23,226)(18,225,24,219)(25,238,31,232)(26,231,32,237)(27,236,33,230)(28,229,34,235)(29,234,35,240)(30,239,36,233)(37,42,43,48)(38,47,44,41)(39,40,45,46)(49,142,55,136)(50,135,56,141)(51,140,57,134)(52,133,58,139)(53,138,59,144)(54,143,60,137)(61,103,67,97)(62,108,68,102)(63,101,69,107)(64,106,70,100)(65,99,71,105)(66,104,72,98)(73,125,79,131)(74,130,80,124)(75,123,81,129)(76,128,82,122)(77,121,83,127)(78,126,84,132)(85,90,91,96)(86,95,92,89)(87,88,93,94)(109,172,115,178)(110,177,116,171)(111,170,117,176)(112,175,118,169)(113,180,119,174)(114,173,120,179)(157,168,163,162)(158,161,164,167)(159,166,165,160)(181,188,187,182)(183,186,189,192)(184,191,190,185)(193,206,199,212)(194,211,200,205)(195,216,201,210)(196,209,202,215)(197,214,203,208)(198,207,204,213)>;
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), (1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,177)(14,176)(15,175)(16,174)(17,173)(18,172)(19,171)(20,170)(21,169)(22,180)(23,179)(24,178)(37,186)(38,185)(39,184)(40,183)(41,182)(42,181)(43,192)(44,191)(45,190)(46,189)(47,188)(48,187)(49,212)(50,211)(51,210)(52,209)(53,208)(54,207)(55,206)(56,205)(57,216)(58,215)(59,214)(60,213)(61,121)(62,132)(63,131)(64,130)(65,129)(66,128)(67,127)(68,126)(69,125)(70,124)(71,123)(72,122)(73,105)(74,104)(75,103)(76,102)(77,101)(78,100)(79,99)(80,98)(81,97)(82,108)(83,107)(84,106)(85,161)(86,160)(87,159)(88,158)(89,157)(90,168)(91,167)(92,166)(93,165)(94,164)(95,163)(96,162)(109,223)(110,222)(111,221)(112,220)(113,219)(114,218)(115,217)(116,228)(117,227)(118,226)(119,225)(120,224)(133,194)(134,193)(135,204)(136,203)(137,202)(138,201)(139,200)(140,199)(141,198)(142,197)(143,196)(144,195)(145,232)(146,231)(147,230)(148,229)(149,240)(150,239)(151,238)(152,237)(153,236)(154,235)(155,234)(156,233), (1,68,189,105,149,56,174,92,110,144)(2,61,190,98,150,49,175,85,111,137)(3,66,191,103,151,54,176,90,112,142)(4,71,192,108,152,59,177,95,113,135)(5,64,181,101,153,52,178,88,114,140)(6,69,182,106,154,57,179,93,115,133)(7,62,183,99,155,50,180,86,116,138)(8,67,184,104,156,55,169,91,117,143)(9,72,185,97,145,60,170,96,118,136)(10,65,186,102,146,53,171,89,119,141)(11,70,187,107,147,58,172,94,120,134)(12,63,188,100,148,51,173,87,109,139)(13,165,219,194,33,125,43,84,237,216)(14,158,220,199,34,130,44,77,238,209)(15,163,221,204,35,123,45,82,239,214)(16,168,222,197,36,128,46,75,240,207)(17,161,223,202,25,121,47,80,229,212)(18,166,224,195,26,126,48,73,230,205)(19,159,225,200,27,131,37,78,231,210)(20,164,226,193,28,124,38,83,232,215)(21,157,227,198,29,129,39,76,233,208)(22,162,228,203,30,122,40,81,234,213)(23,167,217,196,31,127,41,74,235,206)(24,160,218,201,32,132,42,79,236,211), (1,152,7,146)(2,145,8,151)(3,150,9,156)(4,155,10,149)(5,148,11,154)(6,153,12,147)(13,224,19,218)(14,217,20,223)(15,222,21,228)(16,227,22,221)(17,220,23,226)(18,225,24,219)(25,238,31,232)(26,231,32,237)(27,236,33,230)(28,229,34,235)(29,234,35,240)(30,239,36,233)(37,42,43,48)(38,47,44,41)(39,40,45,46)(49,142,55,136)(50,135,56,141)(51,140,57,134)(52,133,58,139)(53,138,59,144)(54,143,60,137)(61,103,67,97)(62,108,68,102)(63,101,69,107)(64,106,70,100)(65,99,71,105)(66,104,72,98)(73,125,79,131)(74,130,80,124)(75,123,81,129)(76,128,82,122)(77,121,83,127)(78,126,84,132)(85,90,91,96)(86,95,92,89)(87,88,93,94)(109,172,115,178)(110,177,116,171)(111,170,117,176)(112,175,118,169)(113,180,119,174)(114,173,120,179)(157,168,163,162)(158,161,164,167)(159,166,165,160)(181,188,187,182)(183,186,189,192)(184,191,190,185)(193,206,199,212)(194,211,200,205)(195,216,201,210)(196,209,202,215)(197,214,203,208)(198,207,204,213) );
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)], [(1,36),(2,35),(3,34),(4,33),(5,32),(6,31),(7,30),(8,29),(9,28),(10,27),(11,26),(12,25),(13,177),(14,176),(15,175),(16,174),(17,173),(18,172),(19,171),(20,170),(21,169),(22,180),(23,179),(24,178),(37,186),(38,185),(39,184),(40,183),(41,182),(42,181),(43,192),(44,191),(45,190),(46,189),(47,188),(48,187),(49,212),(50,211),(51,210),(52,209),(53,208),(54,207),(55,206),(56,205),(57,216),(58,215),(59,214),(60,213),(61,121),(62,132),(63,131),(64,130),(65,129),(66,128),(67,127),(68,126),(69,125),(70,124),(71,123),(72,122),(73,105),(74,104),(75,103),(76,102),(77,101),(78,100),(79,99),(80,98),(81,97),(82,108),(83,107),(84,106),(85,161),(86,160),(87,159),(88,158),(89,157),(90,168),(91,167),(92,166),(93,165),(94,164),(95,163),(96,162),(109,223),(110,222),(111,221),(112,220),(113,219),(114,218),(115,217),(116,228),(117,227),(118,226),(119,225),(120,224),(133,194),(134,193),(135,204),(136,203),(137,202),(138,201),(139,200),(140,199),(141,198),(142,197),(143,196),(144,195),(145,232),(146,231),(147,230),(148,229),(149,240),(150,239),(151,238),(152,237),(153,236),(154,235),(155,234),(156,233)], [(1,68,189,105,149,56,174,92,110,144),(2,61,190,98,150,49,175,85,111,137),(3,66,191,103,151,54,176,90,112,142),(4,71,192,108,152,59,177,95,113,135),(5,64,181,101,153,52,178,88,114,140),(6,69,182,106,154,57,179,93,115,133),(7,62,183,99,155,50,180,86,116,138),(8,67,184,104,156,55,169,91,117,143),(9,72,185,97,145,60,170,96,118,136),(10,65,186,102,146,53,171,89,119,141),(11,70,187,107,147,58,172,94,120,134),(12,63,188,100,148,51,173,87,109,139),(13,165,219,194,33,125,43,84,237,216),(14,158,220,199,34,130,44,77,238,209),(15,163,221,204,35,123,45,82,239,214),(16,168,222,197,36,128,46,75,240,207),(17,161,223,202,25,121,47,80,229,212),(18,166,224,195,26,126,48,73,230,205),(19,159,225,200,27,131,37,78,231,210),(20,164,226,193,28,124,38,83,232,215),(21,157,227,198,29,129,39,76,233,208),(22,162,228,203,30,122,40,81,234,213),(23,167,217,196,31,127,41,74,235,206),(24,160,218,201,32,132,42,79,236,211)], [(1,152,7,146),(2,145,8,151),(3,150,9,156),(4,155,10,149),(5,148,11,154),(6,153,12,147),(13,224,19,218),(14,217,20,223),(15,222,21,228),(16,227,22,221),(17,220,23,226),(18,225,24,219),(25,238,31,232),(26,231,32,237),(27,236,33,230),(28,229,34,235),(29,234,35,240),(30,239,36,233),(37,42,43,48),(38,47,44,41),(39,40,45,46),(49,142,55,136),(50,135,56,141),(51,140,57,134),(52,133,58,139),(53,138,59,144),(54,143,60,137),(61,103,67,97),(62,108,68,102),(63,101,69,107),(64,106,70,100),(65,99,71,105),(66,104,72,98),(73,125,79,131),(74,130,80,124),(75,123,81,129),(76,128,82,122),(77,121,83,127),(78,126,84,132),(85,90,91,96),(86,95,92,89),(87,88,93,94),(109,172,115,178),(110,177,116,171),(111,170,117,176),(112,175,118,169),(113,180,119,174),(114,173,120,179),(157,168,163,162),(158,161,164,167),(159,166,165,160),(181,188,187,182),(183,186,189,192),(184,191,190,185),(193,206,199,212),(194,211,200,205),(195,216,201,210),(196,209,202,215),(197,214,203,208),(198,207,204,213)]])
57 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 5A | 5B | 6A | 6B | 6C | 10A | 10B | 10C | ··· | 10H | 12A | 12B | 12C | 12D | 12E | 12F | 15A | 15B | 20A | ··· | 20F | 20G | 20H | 20I | 20J | 30A | 30B | 60A | ··· | 60F |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 10 | 10 | 10 | ··· | 10 | 12 | 12 | 12 | 12 | 12 | 12 | 15 | 15 | 20 | ··· | 20 | 20 | 20 | 20 | 20 | 30 | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 6 | 6 | 6 | 10 | 30 | 2 | 2 | 2 | 2 | 6 | 10 | 10 | 10 | 30 | 30 | 30 | 2 | 2 | 2 | 10 | 10 | 2 | 2 | 12 | ··· | 12 | 4 | 4 | 4 | 20 | 20 | 20 | 4 | 4 | 4 | ··· | 4 | 6 | 6 | 6 | 6 | 4 | 4 | 8 | ··· | 8 |
57 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 8 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | - | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | S3 | D5 | D6 | D6 | D6 | D10 | D10 | D10 | 2- 1+4 | S3×D5 | Q8.15D6 | C2×S3×D5 | D4.10D10 | D12.29D10 |
| kernel | D12.29D10 | S3×Dic10 | D12⋊D5 | D6.D10 | D12⋊5D5 | C3×Q8×D5 | C5×Q8⋊3S3 | Q8×D15 | Q8×D5 | Q8⋊3S3 | Dic10 | C4×D5 | C5×Q8 | C4×S3 | D12 | C3×Q8 | C15 | Q8 | C5 | C4 | C3 | C1 |
| # reps | 1 | 3 | 3 | 3 | 3 | 1 | 1 | 1 | 1 | 2 | 3 | 3 | 1 | 6 | 6 | 2 | 1 | 2 | 2 | 6 | 4 | 2 |
Matrix representation of D12.29D10 ►in GL8(𝔽61)
| 60 | 0 | 60 | 0 | 0 | 0 | 0 | 0 |
| 0 | 60 | 0 | 60 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 30 | 0 | 5 | 0 |
| 0 | 0 | 0 | 0 | 0 | 30 | 0 | 5 |
| 0 | 0 | 0 | 0 | 15 | 0 | 31 | 0 |
| 0 | 0 | 0 | 0 | 0 | 15 | 0 | 31 |
| 13 | 16 | 1 | 45 | 0 | 0 | 0 | 0 |
| 12 | 1 | 49 | 13 | 0 | 0 | 0 | 0 |
| 49 | 29 | 48 | 45 | 0 | 0 | 0 | 0 |
| 37 | 12 | 49 | 60 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 25 | 7 | 14 | 21 |
| 0 | 0 | 0 | 0 | 50 | 36 | 28 | 47 |
| 0 | 0 | 0 | 0 | 24 | 36 | 36 | 54 |
| 0 | 0 | 0 | 0 | 48 | 37 | 11 | 25 |
| 33 | 10 | 5 | 28 | 0 | 0 | 0 | 0 |
| 38 | 56 | 21 | 45 | 0 | 0 | 0 | 0 |
| 33 | 18 | 28 | 51 | 0 | 0 | 0 | 0 |
| 44 | 50 | 23 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 60 | 41 | 10 |
| 0 | 0 | 0 | 0 | 19 | 44 | 54 | 48 |
| 0 | 0 | 0 | 0 | 1 | 30 | 59 | 1 |
| 0 | 0 | 0 | 0 | 40 | 22 | 42 | 17 |
| 44 | 18 | 0 | 0 | 0 | 0 | 0 | 0 |
| 45 | 17 | 0 | 0 | 0 | 0 | 0 | 0 |
| 17 | 43 | 17 | 43 | 0 | 0 | 0 | 0 |
| 16 | 44 | 16 | 44 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 22 | 32 | 24 |
| 0 | 0 | 0 | 0 | 40 | 52 | 27 | 29 |
| 0 | 0 | 0 | 0 | 35 | 11 | 52 | 39 |
| 0 | 0 | 0 | 0 | 20 | 26 | 21 | 9 |
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