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G = D62Dic10order 480 = 25·3·5

2nd semidirect product of D6 and Dic10 acting via Dic10/Dic5=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D62Dic10, Dic5.18D12, D6⋊C4.3D5, (S3×C10)⋊2Q8, C605C45C2, C6.18(D4×D5), C52(C4.D12), C2.20(D5×D12), (C2×C20).18D6, C30.42(C2×D4), C10.33(S3×Q8), C30.40(C2×Q8), (C2×C12).15D10, C10.D45S3, C10.18(C2×D12), (C2×C60).7C22, C1512(C22⋊Q8), (C3×Dic5).9D4, D6⋊Dic5.12C2, C30.Q821C2, C6.15(C2×Dic10), C2.16(S3×Dic10), C30.118(C4○D4), C6.71(D42D5), (C2×C30).107C23, (C2×Dic3).33D10, (C2×Dic5).108D6, (C22×S3).39D10, C10.70(D42S3), C31(Dic5.14D4), (C6×Dic5).62C22, C2.16(C30.C23), (C10×Dic3).65C22, (C2×Dic15).87C22, (C2×C15⋊Q8)⋊6C2, (C5×D6⋊C4).3C2, (C2×C4).44(S3×D5), (C2×S3×Dic5).5C2, C22.174(C2×S3×D5), (C3×C10.D4)⋊5C2, (S3×C2×C10).19C22, (C2×C6).119(C22×D5), (C2×C10).119(C22×S3), SmallGroup(480,493)

Series: Derived Chief Lower central Upper central

C1C2×C30 — D62Dic10
C1C5C15C30C2×C30C6×Dic5C2×S3×Dic5 — D62Dic10
C15C2×C30 — D62Dic10
C1C22C2×C4

Generators and relations for D62Dic10
 G = < a,b,c,d | a6=b2=c20=1, d2=c10, bab=cac-1=a-1, ad=da, cbc-1=ab, bd=db, dcd-1=c-1 >

Subgroups: 716 in 148 conjugacy classes, 52 normal (44 characteristic)
C1, C2 [×3], C2 [×2], C3, C4 [×7], C22, C22 [×4], C5, S3 [×2], C6 [×3], C2×C4, C2×C4 [×7], Q8 [×2], C23, C10 [×3], C10 [×2], Dic3 [×3], C12 [×4], D6 [×2], D6 [×2], C2×C6, C15, C22⋊C4 [×2], C4⋊C4 [×3], C22×C4, C2×Q8, Dic5 [×2], Dic5 [×3], C20 [×2], C2×C10, C2×C10 [×4], Dic6 [×2], C4×S3 [×2], C2×Dic3, C2×Dic3 [×2], C2×C12, C2×C12 [×2], C22×S3, C5×S3 [×2], C30 [×3], C22⋊Q8, Dic10 [×2], C2×Dic5 [×2], C2×Dic5 [×4], C2×C20, C2×C20, C22×C10, C4⋊Dic3 [×2], D6⋊C4, D6⋊C4, C3×C4⋊C4, C2×Dic6, S3×C2×C4, C5×Dic3, C3×Dic5 [×2], C3×Dic5, Dic15 [×2], C60, S3×C10 [×2], S3×C10 [×2], C2×C30, C10.D4, C10.D4, C4⋊Dic5, C23.D5, C5×C22⋊C4, C2×Dic10, C22×Dic5, C4.D12, S3×Dic5 [×2], C15⋊Q8 [×2], C6×Dic5 [×2], C10×Dic3, C2×Dic15 [×2], C2×C60, S3×C2×C10, Dic5.14D4, D6⋊Dic5, C30.Q8, C3×C10.D4, C5×D6⋊C4, C605C4, C2×S3×Dic5, C2×C15⋊Q8, D62Dic10
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], Q8 [×2], C23, D5, D6 [×3], C2×D4, C2×Q8, C4○D4, D10 [×3], D12 [×2], C22×S3, C22⋊Q8, Dic10 [×2], C22×D5, C2×D12, D42S3, S3×Q8, S3×D5, C2×Dic10, D4×D5, D42D5, C4.D12, C2×S3×D5, Dic5.14D4, S3×Dic10, D5×D12, C30.C23, D62Dic10

Smallest permutation representation of D62Dic10
On 240 points
Generators in S240
(1 212 140 154 52 23)(2 24 53 155 121 213)(3 214 122 156 54 25)(4 26 55 157 123 215)(5 216 124 158 56 27)(6 28 57 159 125 217)(7 218 126 160 58 29)(8 30 59 141 127 219)(9 220 128 142 60 31)(10 32 41 143 129 201)(11 202 130 144 42 33)(12 34 43 145 131 203)(13 204 132 146 44 35)(14 36 45 147 133 205)(15 206 134 148 46 37)(16 38 47 149 135 207)(17 208 136 150 48 39)(18 40 49 151 137 209)(19 210 138 152 50 21)(20 22 51 153 139 211)(61 195 90 120 179 223)(62 224 180 101 91 196)(63 197 92 102 161 225)(64 226 162 103 93 198)(65 199 94 104 163 227)(66 228 164 105 95 200)(67 181 96 106 165 229)(68 230 166 107 97 182)(69 183 98 108 167 231)(70 232 168 109 99 184)(71 185 100 110 169 233)(72 234 170 111 81 186)(73 187 82 112 171 235)(74 236 172 113 83 188)(75 189 84 114 173 237)(76 238 174 115 85 190)(77 191 86 116 175 239)(78 240 176 117 87 192)(79 193 88 118 177 221)(80 222 178 119 89 194)
(1 23)(2 53)(3 25)(4 55)(5 27)(6 57)(7 29)(8 59)(9 31)(10 41)(11 33)(12 43)(13 35)(14 45)(15 37)(16 47)(17 39)(18 49)(19 21)(20 51)(42 202)(44 204)(46 206)(48 208)(50 210)(52 212)(54 214)(56 216)(58 218)(60 220)(62 224)(64 226)(66 228)(68 230)(70 232)(72 234)(74 236)(76 238)(78 240)(80 222)(81 111)(82 171)(83 113)(84 173)(85 115)(86 175)(87 117)(88 177)(89 119)(90 179)(91 101)(92 161)(93 103)(94 163)(95 105)(96 165)(97 107)(98 167)(99 109)(100 169)(122 156)(124 158)(126 160)(128 142)(130 144)(132 146)(134 148)(136 150)(138 152)(140 154)(141 219)(143 201)(145 203)(147 205)(149 207)(151 209)(153 211)(155 213)(157 215)(159 217)(162 198)(164 200)(166 182)(168 184)(170 186)(172 188)(174 190)(176 192)(178 194)(180 196)(181 229)(183 231)(185 233)(187 235)(189 237)(191 239)(193 221)(195 223)(197 225)(199 227)
(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 83 11 93)(2 82 12 92)(3 81 13 91)(4 100 14 90)(5 99 15 89)(6 98 16 88)(7 97 17 87)(8 96 18 86)(9 95 19 85)(10 94 20 84)(21 115 31 105)(22 114 32 104)(23 113 33 103)(24 112 34 102)(25 111 35 101)(26 110 36 120)(27 109 37 119)(28 108 38 118)(29 107 39 117)(30 106 40 116)(41 163 51 173)(42 162 52 172)(43 161 53 171)(44 180 54 170)(45 179 55 169)(46 178 56 168)(47 177 57 167)(48 176 58 166)(49 175 59 165)(50 174 60 164)(61 123 71 133)(62 122 72 132)(63 121 73 131)(64 140 74 130)(65 139 75 129)(66 138 76 128)(67 137 77 127)(68 136 78 126)(69 135 79 125)(70 134 80 124)(141 229 151 239)(142 228 152 238)(143 227 153 237)(144 226 154 236)(145 225 155 235)(146 224 156 234)(147 223 157 233)(148 222 158 232)(149 221 159 231)(150 240 160 230)(181 209 191 219)(182 208 192 218)(183 207 193 217)(184 206 194 216)(185 205 195 215)(186 204 196 214)(187 203 197 213)(188 202 198 212)(189 201 199 211)(190 220 200 210)

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

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

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

60 conjugacy classes

class 1 2A2B2C2D2E 3 4A4B4C4D4E4F4G4H5A5B6A6B6C10A···10F10G10H10I10J12A12B12C12D12E12F15A15B20A20B20C20D20E20F20G20H30A···30F60A···60H
order1222223444444445566610···10101010101212121212121515202020202020202030···3060···60
size1111662410101220303060222222···2121212124420202020444444121212124···44···4

60 irreducible representations

dim11111111222222222222444444444
type++++++++++-+++++++---++-+-+-
imageC1C2C2C2C2C2C2C2S3D4Q8D5D6D6C4○D4D10D10D10D12Dic10D42S3S3×Q8S3×D5D4×D5D42D5C2×S3×D5S3×Dic10D5×D12C30.C23
kernelD62Dic10D6⋊Dic5C30.Q8C3×C10.D4C5×D6⋊C4C605C4C2×S3×Dic5C2×C15⋊Q8C10.D4C3×Dic5S3×C10D6⋊C4C2×Dic5C2×C20C30C2×Dic3C2×C12C22×S3Dic5D6C10C10C2×C4C6C6C22C2C2C2
# reps11111111122221222248112222444

Matrix representation of D62Dic10 in GL6(𝔽61)

100000
010000
0060000
0006000
0000060
0000160
,
100000
010000
0060000
0057100
0000160
0000060
,
4360000
25270000
00404100
00162100
0000060
0000600
,
0110000
1100000
0050000
00171100
0000600
0000060

G:=sub<GL(6,GF(61))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,0,1,0,0,0,0,60,60],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,60,57,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,60,60],[4,25,0,0,0,0,36,27,0,0,0,0,0,0,40,16,0,0,0,0,41,21,0,0,0,0,0,0,0,60,0,0,0,0,60,0],[0,11,0,0,0,0,11,0,0,0,0,0,0,0,50,17,0,0,0,0,0,11,0,0,0,0,0,0,60,0,0,0,0,0,0,60] >;

D62Dic10 in GAP, Magma, Sage, TeX

D_6\rtimes_2{\rm Dic}_{10}
% in TeX

G:=Group("D6:2Dic10");
// GroupNames label

G:=SmallGroup(480,493);
// by ID

G=gap.SmallGroup(480,493);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,254,219,142,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^6=b^2=c^20=1,d^2=c^10,b*a*b=c*a*c^-1=a^-1,a*d=d*a,c*b*c^-1=a*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations

׿
×
𝔽