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G = D12.33D10order 480 = 25·3·5

4th non-split extension by D12 of D10 acting via D10/C10=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C60 — D12.33D10
 Chief series C1 — C5 — C15 — C30 — C60 — C3×C5⋊2C8 — C5⋊Dic12 — D12.33D10
 Lower central C15 — C30 — C60 — D12.33D10
 Upper central C1 — C2 — C2×C4

Generators and relations for D12.33D10
G = < a,b,c,d | a12=b2=1, c10=d2=a6, bab=cac-1=dad-1=a-1, cbc-1=a10b, dbd-1=ab, dcd-1=a9c9 >

Subgroups: 572 in 120 conjugacy classes, 44 normal (34 characteristic)
C1, C2, C2 [×2], C3, C4 [×2], C4 [×3], C22, C22, C5, S3, C6, C6, C8 [×2], C2×C4, C2×C4 [×2], D4 [×2], Q8 [×4], C10, C10 [×2], Dic3 [×3], C12 [×2], D6, C2×C6, C15, M4(2), SD16 [×2], Q16 [×2], C2×Q8, C4○D4, Dic5 [×2], C20 [×2], C20, C2×C10, C2×C10, C24 [×2], Dic6, Dic6 [×3], C4×S3, D12, C2×Dic3, C3⋊D4, C2×C12, C5×S3, C30, C30, C8.C22, C52C8 [×2], Dic10 [×3], C2×Dic5, C2×C20, C2×C20, C5×D4 [×2], C5×Q8, C24⋊C2 [×2], Dic12 [×2], C3×M4(2), C2×Dic6, C4○D12, C5×Dic3, Dic15 [×2], C60 [×2], S3×C10, C2×C30, C4.Dic5, D4.D5 [×2], C5⋊Q16 [×2], C2×Dic10, C5×C4○D4, C8.D6, C3×C52C8 [×2], C5×Dic6, S3×C20, C5×D12, C5×C3⋊D4, Dic30 [×2], Dic30, C2×Dic15, C2×C60, D4.9D10, D12.D5 [×2], C5⋊Dic12 [×2], C3×C4.Dic5, C5×C4○D12, C2×Dic30, D12.33D10
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], D12 [×2], C22×S3, C8.C22, C5⋊D4 [×2], C22×D5, C2×D12, S3×D5, C2×C5⋊D4, C8.D6, C5⋊D12 [×2], C2×S3×D5, D4.9D10, C2×C5⋊D12, D12.33D10

Smallest permutation representation of D12.33D10
On 240 points
Generators in S240
```(1 162 239 109 147 59 11 172 229 119 157 49)(2 50 158 120 230 173 12 60 148 110 240 163)(3 164 221 111 149 41 13 174 231 101 159 51)(4 52 160 102 232 175 14 42 150 112 222 165)(5 166 223 113 151 43 15 176 233 103 141 53)(6 54 142 104 234 177 16 44 152 114 224 167)(7 168 225 115 153 45 17 178 235 105 143 55)(8 56 144 106 236 179 18 46 154 116 226 169)(9 170 227 117 155 47 19 180 237 107 145 57)(10 58 146 108 238 161 20 48 156 118 228 171)(21 91 68 186 210 130 31 81 78 196 220 140)(22 121 201 197 79 82 32 131 211 187 69 92)(23 93 70 188 212 132 33 83 80 198 202 122)(24 123 203 199 61 84 34 133 213 189 71 94)(25 95 72 190 214 134 35 85 62 200 204 124)(26 125 205 181 63 86 36 135 215 191 73 96)(27 97 74 192 216 136 37 87 64 182 206 126)(28 127 207 183 65 88 38 137 217 193 75 98)(29 99 76 194 218 138 39 89 66 184 208 128)(30 129 209 185 67 90 40 139 219 195 77 100)
(1 152)(2 225)(3 154)(4 227)(5 156)(6 229)(7 158)(8 231)(9 160)(10 233)(11 142)(12 235)(13 144)(14 237)(15 146)(16 239)(17 148)(18 221)(19 150)(20 223)(21 205)(22 64)(23 207)(24 66)(25 209)(26 68)(27 211)(28 70)(29 213)(30 72)(31 215)(32 74)(33 217)(34 76)(35 219)(36 78)(37 201)(38 80)(39 203)(40 62)(41 106)(42 180)(43 108)(44 162)(45 110)(46 164)(47 112)(48 166)(49 114)(50 168)(51 116)(52 170)(53 118)(54 172)(55 120)(56 174)(57 102)(58 176)(59 104)(60 178)(61 218)(63 220)(65 202)(67 204)(69 206)(71 208)(73 210)(75 212)(77 214)(79 216)(81 135)(82 192)(83 137)(84 194)(85 139)(86 196)(87 121)(88 198)(89 123)(90 200)(91 125)(92 182)(93 127)(94 184)(95 129)(96 186)(97 131)(98 188)(99 133)(100 190)(101 169)(103 171)(105 173)(107 175)(109 177)(111 179)(113 161)(115 163)(117 165)(119 167)(122 183)(124 185)(126 187)(128 189)(130 191)(132 193)(134 195)(136 197)(138 199)(140 181)(141 228)(143 230)(145 232)(147 234)(149 236)(151 238)(153 240)(155 222)(157 224)(159 226)
(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 40 11 30)(2 194 12 184)(3 38 13 28)(4 192 14 182)(5 36 15 26)(6 190 16 200)(7 34 17 24)(8 188 18 198)(9 32 19 22)(10 186 20 196)(21 118 31 108)(23 116 33 106)(25 114 35 104)(27 112 37 102)(29 110 39 120)(41 127 51 137)(42 64 52 74)(43 125 53 135)(44 62 54 72)(45 123 55 133)(46 80 56 70)(47 121 57 131)(48 78 58 68)(49 139 59 129)(50 76 60 66)(61 235 71 225)(63 233 73 223)(65 231 75 221)(67 229 77 239)(69 227 79 237)(81 146 91 156)(82 180 92 170)(83 144 93 154)(84 178 94 168)(85 142 95 152)(86 176 96 166)(87 160 97 150)(88 174 98 164)(89 158 99 148)(90 172 100 162)(101 193 111 183)(103 191 113 181)(105 189 115 199)(107 187 117 197)(109 185 119 195)(122 226 132 236)(124 224 134 234)(126 222 136 232)(128 240 138 230)(130 238 140 228)(141 215 151 205)(143 213 153 203)(145 211 155 201)(147 209 157 219)(149 207 159 217)(161 220 171 210)(163 218 173 208)(165 216 175 206)(167 214 177 204)(169 212 179 202)```

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

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

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

57 conjugacy classes

 class 1 2A 2B 2C 3 4A 4B 4C 4D 4E 5A 5B 6A 6B 8A 8B 10A 10B 10C 10D 10E 10F 10G 10H 12A 12B 12C 15A 15B 20A 20B 20C 20D 20E 20F 20G 20H 20I 20J 24A 24B 24C 24D 30A ··· 30F 60A ··· 60H order 1 2 2 2 3 4 4 4 4 4 5 5 6 6 8 8 10 10 10 10 10 10 10 10 12 12 12 15 15 20 20 20 20 20 20 20 20 20 20 24 24 24 24 30 ··· 30 60 ··· 60 size 1 1 2 12 2 2 2 12 60 60 2 2 2 4 20 20 2 2 4 4 12 12 12 12 2 2 4 4 4 2 2 2 2 4 4 12 12 12 12 20 20 20 20 4 ··· 4 4 ··· 4

57 irreducible representations

 dim 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 type + + + + + + + + + + + + + + + + + - + - + + + - - image C1 C2 C2 C2 C2 C2 S3 D4 D4 D5 D6 D6 D10 D10 D10 D12 D12 C5⋊D4 C5⋊D4 C8.C22 S3×D5 C8.D6 C5⋊D12 C2×S3×D5 C5⋊D12 D4.9D10 D12.33D10 kernel D12.33D10 D12.D5 C5⋊Dic12 C3×C4.Dic5 C5×C4○D12 C2×Dic30 C4.Dic5 C60 C2×C30 C4○D12 C5⋊2C8 C2×C20 Dic6 D12 C2×C12 C20 C2×C10 C12 C2×C6 C15 C2×C4 C5 C4 C4 C22 C3 C1 # reps 1 2 2 1 1 1 1 1 1 2 2 1 2 2 2 2 2 4 4 1 2 2 2 2 2 4 8

Matrix representation of D12.33D10 in GL6(𝔽241)

 1 0 0 0 0 0 0 1 0 0 0 0 0 0 99 142 0 0 0 0 99 198 0 0 0 0 0 0 198 99 0 0 0 0 142 99
,
 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 240 0 0 0 0 1 1 0 0 1 1 0 0 0 0 240 0 0 0
,
 0 51 0 0 0 0 189 52 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 240 0 0 0 0 0 0 240 0 0
,
 35 54 0 0 0 0 138 206 0 0 0 0 0 0 211 8 0 0 0 0 38 30 0 0 0 0 0 0 216 225 0 0 0 0 9 25

`G:=sub<GL(6,GF(241))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,99,99,0,0,0,0,142,198,0,0,0,0,0,0,198,142,0,0,0,0,99,99],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,240,0,0,0,0,1,0,0,0,0,1,0,0,0,0,240,1,0,0],[0,189,0,0,0,0,51,52,0,0,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,1,0,0,0,0,0,0,1,0,0],[35,138,0,0,0,0,54,206,0,0,0,0,0,0,211,38,0,0,0,0,8,30,0,0,0,0,0,0,216,9,0,0,0,0,225,25] >;`

D12.33D10 in GAP, Magma, Sage, TeX

`D_{12}._{33}D_{10}`
`% in TeX`

`G:=Group("D12.33D10");`
`// GroupNames label`

`G:=SmallGroup(480,398);`
`// by ID`

`G=gap.SmallGroup(480,398);`
`# by ID`

`G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,141,120,422,100,346,80,1356,18822]);`
`// Polycyclic`

`G:=Group<a,b,c,d|a^12=b^2=1,c^10=d^2=a^6,b*a*b=c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=a^10*b,d*b*d^-1=a*b,d*c*d^-1=a^9*c^9>;`
`// generators/relations`

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