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G = Dic10.27D6order 480 = 25·3·5

10th non-split extension by Dic10 of D6 acting via D6/S3=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D12.15D10, C60.43C23, Dic10.27D6, D60.15C22, C5⋊D247C2, C5⋊Q167S3, C1522(C4○D8), Q83S33D5, C52C8.20D6, Q8.12(S3×D5), (C3×Q8).7D10, (C5×Q8).39D6, D60⋊C23C2, C55(D24⋊C2), Q82D157C2, (C4×S3).26D10, (S3×C10).15D4, C30.205(C2×D4), C10.153(S3×D4), C20.D68C2, D6.4(C5⋊D4), C35(D4.8D10), C20.43(C22×S3), (C5×Dic3).41D4, C12.43(C22×D5), (S3×C20).15C22, C153C8.17C22, (C5×D12).16C22, (Q8×C15).13C22, Dic3.23(C5⋊D4), (C3×Dic10).15C22, C4.43(C2×S3×D5), (S3×C52C8)⋊7C2, (C3×C5⋊Q16)⋊5C2, C2.34(S3×C5⋊D4), C6.56(C2×C5⋊D4), (C5×Q83S3)⋊3C2, (C3×C52C8).13C22, SmallGroup(480,595)

Series: Derived Chief Lower central Upper central

C1C60 — Dic10.27D6
C1C5C15C30C60C3×Dic10D60⋊C2 — Dic10.27D6
C15C30C60 — Dic10.27D6
C1C2C4Q8

Generators and relations for Dic10.27D6
 G = < a,b,c,d | a20=d2=1, b2=c6=a10, bab-1=a-1, cac-1=dad=a11, cbc-1=dbd=a5b, dcd=c5 >

Subgroups: 652 in 124 conjugacy classes, 40 normal (all characteristic)
C1, C2, C2 [×3], C3, C4, C4 [×3], C22 [×3], C5, S3 [×3], C6, C8 [×2], C2×C4 [×3], D4 [×4], Q8, Q8, D5, C10, C10 [×2], Dic3, C12, C12 [×2], D6, D6 [×2], C15, C2×C8, D8, SD16 [×2], Q16, C4○D4 [×2], Dic5, C20, C20 [×2], D10, C2×C10 [×2], C3⋊C8, C24, C4×S3, C4×S3 [×2], D12, D12 [×3], C3×Q8, C3×Q8, C5×S3 [×2], D15, C30, C4○D8, C52C8, C52C8, Dic10, C4×D5, D20, C5⋊D4, C2×C20 [×2], C5×D4 [×2], C5×Q8, S3×C8, D24, Q82S3 [×2], C3×Q16, Q83S3, Q83S3, C5×Dic3, C3×Dic5, C60, C60, S3×C10, S3×C10, D30, C2×C52C8, D4⋊D5, D4.D5, Q8⋊D5, C5⋊Q16, C4○D20, C5×C4○D4, D24⋊C2, C3×C52C8, C153C8, D30.C2, C5⋊D12, C3×Dic10, S3×C20, S3×C20, C5×D12, C5×D12, D60, Q8×C15, D4.8D10, S3×C52C8, C5⋊D24, C20.D6, C3×C5⋊Q16, Q82D15, D60⋊C2, C5×Q83S3, Dic10.27D6
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], C22×S3, C4○D8, C5⋊D4 [×2], C22×D5, S3×D4, S3×D5, C2×C5⋊D4, D24⋊C2, C2×S3×D5, D4.8D10, S3×C5⋊D4, Dic10.27D6

Smallest permutation representation of Dic10.27D6
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)
(1 201 11 211)(2 220 12 210)(3 219 13 209)(4 218 14 208)(5 217 15 207)(6 216 16 206)(7 215 17 205)(8 214 18 204)(9 213 19 203)(10 212 20 202)(21 46 31 56)(22 45 32 55)(23 44 33 54)(24 43 34 53)(25 42 35 52)(26 41 36 51)(27 60 37 50)(28 59 38 49)(29 58 39 48)(30 57 40 47)(61 111 71 101)(62 110 72 120)(63 109 73 119)(64 108 74 118)(65 107 75 117)(66 106 76 116)(67 105 77 115)(68 104 78 114)(69 103 79 113)(70 102 80 112)(81 155 91 145)(82 154 92 144)(83 153 93 143)(84 152 94 142)(85 151 95 141)(86 150 96 160)(87 149 97 159)(88 148 98 158)(89 147 99 157)(90 146 100 156)(121 221 131 231)(122 240 132 230)(123 239 133 229)(124 238 134 228)(125 237 135 227)(126 236 136 226)(127 235 137 225)(128 234 138 224)(129 233 139 223)(130 232 140 222)(161 181 171 191)(162 200 172 190)(163 199 173 189)(164 198 174 188)(165 197 175 187)(166 196 176 186)(167 195 177 185)(168 194 178 184)(169 193 179 183)(170 192 180 182)
(1 35 200 122 63 94 11 25 190 132 73 84)(2 26 181 133 64 85 12 36 191 123 74 95)(3 37 182 124 65 96 13 27 192 134 75 86)(4 28 183 135 66 87 14 38 193 125 76 97)(5 39 184 126 67 98 15 29 194 136 77 88)(6 30 185 137 68 89 16 40 195 127 78 99)(7 21 186 128 69 100 17 31 196 138 79 90)(8 32 187 139 70 91 18 22 197 129 80 81)(9 23 188 130 71 82 19 33 198 140 61 92)(10 34 189 121 72 93 20 24 199 131 62 83)(41 166 229 103 151 205 51 176 239 113 141 215)(42 177 230 114 152 216 52 167 240 104 142 206)(43 168 231 105 153 207 53 178 221 115 143 217)(44 179 232 116 154 218 54 169 222 106 144 208)(45 170 233 107 155 209 55 180 223 117 145 219)(46 161 234 118 156 220 56 171 224 108 146 210)(47 172 235 109 157 211 57 162 225 119 147 201)(48 163 236 120 158 202 58 173 226 110 148 212)(49 174 237 111 159 213 59 164 227 101 149 203)(50 165 238 102 160 204 60 175 228 112 150 214)
(1 99)(2 90)(3 81)(4 92)(5 83)(6 94)(7 85)(8 96)(9 87)(10 98)(11 89)(12 100)(13 91)(14 82)(15 93)(16 84)(17 95)(18 86)(19 97)(20 88)(21 74)(22 65)(23 76)(24 67)(25 78)(26 69)(27 80)(28 71)(29 62)(30 73)(31 64)(32 75)(33 66)(34 77)(35 68)(36 79)(37 70)(38 61)(39 72)(40 63)(41 118)(42 109)(43 120)(44 111)(45 102)(46 113)(47 104)(48 115)(49 106)(50 117)(51 108)(52 119)(53 110)(54 101)(55 112)(56 103)(57 114)(58 105)(59 116)(60 107)(121 194)(122 185)(123 196)(124 187)(125 198)(126 189)(127 200)(128 191)(129 182)(130 193)(131 184)(132 195)(133 186)(134 197)(135 188)(136 199)(137 190)(138 181)(139 192)(140 183)(141 220)(142 211)(143 202)(144 213)(145 204)(146 215)(147 206)(148 217)(149 208)(150 219)(151 210)(152 201)(153 212)(154 203)(155 214)(156 205)(157 216)(158 207)(159 218)(160 209)(161 229)(162 240)(163 231)(164 222)(165 233)(166 224)(167 235)(168 226)(169 237)(170 228)(171 239)(172 230)(173 221)(174 232)(175 223)(176 234)(177 225)(178 236)(179 227)(180 238)

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

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

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

51 conjugacy classes

class 1 2A2B2C2D 3 4A4B4C4D4E5A5B 6 8A8B8C8D10A10B10C···10H12A12B12C15A15B20A···20F20G20H20I20J24A24B30A30B60A···60F
order122223444445568888101010···10121212151520···20202020202424303060···60
size11612602233420222101030302212···124840444···466662020448···8

51 irreducible representations

dim1111111122222222222224444448
type+++++++++++++++++++++++
imageC1C2C2C2C2C2C2C2S3D4D4D5D6D6D6D10D10D10C4○D8C5⋊D4C5⋊D4S3×D4S3×D5D24⋊C2C2×S3×D5D4.8D10S3×C5⋊D4Dic10.27D6
kernelDic10.27D6S3×C52C8C5⋊D24C20.D6C3×C5⋊Q16Q82D15D60⋊C2C5×Q83S3C5⋊Q16C5×Dic3S3×C10Q83S3C52C8Dic10C5×Q8C4×S3D12C3×Q8C15Dic3D6C10Q8C5C4C3C2C1
# reps1111111111121112224441222442

Matrix representation of Dic10.27D6 in GL6(𝔽241)

12400000
531890000
001000
000100
0000640
0000123177
,
892250000
131520000
001000
000100
000023324
00001688
,
2141920000
187270000
001100
00240000
00002403
00001601
,
27490000
542140000
001100
00024000
00006449
0000123177

G:=sub<GL(6,GF(241))| [1,53,0,0,0,0,240,189,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,64,123,0,0,0,0,0,177],[89,13,0,0,0,0,225,152,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,233,168,0,0,0,0,24,8],[214,187,0,0,0,0,192,27,0,0,0,0,0,0,1,240,0,0,0,0,1,0,0,0,0,0,0,0,240,160,0,0,0,0,3,1],[27,54,0,0,0,0,49,214,0,0,0,0,0,0,1,0,0,0,0,0,1,240,0,0,0,0,0,0,64,123,0,0,0,0,49,177] >;

Dic10.27D6 in GAP, Magma, Sage, TeX

{\rm Dic}_{10}._{27}D_6
% in TeX

G:=Group("Dic10.27D6");
// GroupNames label

G:=SmallGroup(480,595);
// by ID

G=gap.SmallGroup(480,595);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,120,254,100,675,185,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^20=d^2=1,b^2=c^6=a^10,b*a*b^-1=a^-1,c*a*c^-1=d*a*d=a^11,c*b*c^-1=d*b*d=a^5*b,d*c*d=c^5>;
// generators/relations

׿
×
𝔽