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G = Dic158D4order 480 = 25·3·5

3rd semidirect product of Dic15 and D4 acting via D4/C4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: Dic158D4, D125Dic5, C207(C4×S3), C1514(C4×D4), C32(D4×Dic5), C6021(C2×C4), C42(S3×Dic5), C6.41(D4×D5), (C5×D12)⋊12C4, C4⋊Dic513S3, D62(C2×Dic5), (C2×D12).9D5, C122(C2×Dic5), C10.42(S3×D4), C30.53(C2×D4), C56(Dic35D4), D6⋊Dic511C2, (C10×D12).9C2, (C2×C20).127D6, (C4×Dic15)⋊26C2, C30.74(C4○D4), (C2×C12).128D10, C2.2(C20⋊D6), C6.14(D42D5), C2.5(D12⋊D5), (C2×C60).201C22, (C2×C30).125C23, C30.131(C22×C4), (C2×Dic5).113D6, (C22×S3).43D10, C6.13(C22×Dic5), C10.36(Q83S3), (C6×Dic5).77C22, (C2×Dic15).207C22, (C2×S3×Dic5)⋊7C2, C10.120(S3×C2×C4), (S3×C10)⋊11(C2×C4), C2.14(C2×S3×Dic5), C22.59(C2×S3×D5), (C3×C4⋊Dic5)⋊10C2, (C2×C4).211(S3×D5), (S3×C2×C10).24C22, (C2×C6).137(C22×D5), (C2×C10).137(C22×S3), SmallGroup(480,511)

Series: Derived Chief Lower central Upper central

C1C30 — Dic158D4
C1C5C15C30C2×C30C6×Dic5C2×S3×Dic5 — Dic158D4
C15C30 — Dic158D4
C1C22C2×C4

Generators and relations for Dic158D4
 G = < a,b,c,d | a12=b2=c10=1, d2=c5, bab=a-1, ac=ca, dad-1=a7, bc=cb, dbd-1=a6b, dcd-1=c-1 >

Subgroups: 812 in 188 conjugacy classes, 70 normal (32 characteristic)
C1, C2 [×3], C2 [×4], C3, C4 [×2], C4 [×5], C22, C22 [×8], C5, S3 [×4], C6 [×3], C2×C4, C2×C4 [×8], D4 [×4], C23 [×2], C10 [×3], C10 [×4], Dic3 [×3], C12 [×2], C12 [×2], D6 [×4], D6 [×4], C2×C6, C15, C42, C22⋊C4 [×2], C4⋊C4, C22×C4 [×2], C2×D4, Dic5 [×5], C20 [×2], C2×C10, C2×C10 [×8], C4×S3 [×4], D12 [×4], C2×Dic3 [×2], C2×C12, C2×C12 [×2], C22×S3 [×2], C5×S3 [×4], C30 [×3], C4×D4, C2×Dic5 [×2], C2×Dic5 [×6], C2×C20, C5×D4 [×4], C22×C10 [×2], C4×Dic3, D6⋊C4 [×2], C3×C4⋊C4, S3×C2×C4 [×2], C2×D12, C3×Dic5 [×2], Dic15 [×2], Dic15, C60 [×2], S3×C10 [×4], S3×C10 [×4], C2×C30, C4×Dic5, C4⋊Dic5, C23.D5 [×2], C22×Dic5 [×2], D4×C10, Dic35D4, S3×Dic5 [×4], C6×Dic5 [×2], C5×D12 [×4], C2×Dic15 [×2], C2×C60, S3×C2×C10 [×2], D4×Dic5, D6⋊Dic5 [×2], C3×C4⋊Dic5, C4×Dic15, C2×S3×Dic5 [×2], C10×D12, Dic158D4
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], S3, C2×C4 [×6], D4 [×2], C23, D5, D6 [×3], C22×C4, C2×D4, C4○D4, Dic5 [×4], D10 [×3], C4×S3 [×2], C22×S3, C4×D4, C2×Dic5 [×6], C22×D5, S3×C2×C4, S3×D4, Q83S3, S3×D5, D4×D5, D42D5, C22×Dic5, Dic35D4, S3×Dic5 [×2], C2×S3×D5, D4×Dic5, D12⋊D5, C20⋊D6, C2×S3×Dic5, Dic158D4

Smallest permutation representation of Dic158D4
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 3)(4 12)(5 11)(6 10)(7 9)(13 23)(14 22)(15 21)(16 20)(17 19)(25 27)(28 36)(29 35)(30 34)(31 33)(38 48)(39 47)(40 46)(41 45)(42 44)(50 60)(51 59)(52 58)(53 57)(54 56)(62 72)(63 71)(64 70)(65 69)(66 68)(74 84)(75 83)(76 82)(77 81)(78 80)(85 87)(88 96)(89 95)(90 94)(91 93)(97 103)(98 102)(99 101)(104 108)(105 107)(109 117)(110 116)(111 115)(112 114)(118 120)(122 132)(123 131)(124 130)(125 129)(126 128)(134 144)(135 143)(136 142)(137 141)(138 140)(145 147)(148 156)(149 155)(150 154)(151 153)(157 167)(158 166)(159 165)(160 164)(161 163)(170 180)(171 179)(172 178)(173 177)(174 176)(181 183)(184 192)(185 191)(186 190)(187 189)(193 199)(194 198)(195 197)(200 204)(201 203)(205 209)(206 208)(210 216)(211 215)(212 214)(217 225)(218 224)(219 223)(220 222)(226 228)(230 240)(231 239)(232 238)(233 237)(234 236)
(1 187 17 66 195 167 240 212 112 145)(2 188 18 67 196 168 229 213 113 146)(3 189 19 68 197 157 230 214 114 147)(4 190 20 69 198 158 231 215 115 148)(5 191 21 70 199 159 232 216 116 149)(6 192 22 71 200 160 233 205 117 150)(7 181 23 72 201 161 234 206 118 151)(8 182 24 61 202 162 235 207 119 152)(9 183 13 62 203 163 236 208 120 153)(10 184 14 63 204 164 237 209 109 154)(11 185 15 64 193 165 238 210 110 155)(12 186 16 65 194 166 239 211 111 156)(25 84 54 91 138 42 105 220 126 174)(26 73 55 92 139 43 106 221 127 175)(27 74 56 93 140 44 107 222 128 176)(28 75 57 94 141 45 108 223 129 177)(29 76 58 95 142 46 97 224 130 178)(30 77 59 96 143 47 98 225 131 179)(31 78 60 85 144 48 99 226 132 180)(32 79 49 86 133 37 100 227 121 169)(33 80 50 87 134 38 101 228 122 170)(34 81 51 88 135 39 102 217 123 171)(35 82 52 89 136 40 103 218 124 172)(36 83 53 90 137 41 104 219 125 173)
(1 135 167 171)(2 142 168 178)(3 137 157 173)(4 144 158 180)(5 139 159 175)(6 134 160 170)(7 141 161 177)(8 136 162 172)(9 143 163 179)(10 138 164 174)(11 133 165 169)(12 140 166 176)(13 59 208 225)(14 54 209 220)(15 49 210 227)(16 56 211 222)(17 51 212 217)(18 58 213 224)(19 53 214 219)(20 60 215 226)(21 55 216 221)(22 50 205 228)(23 57 206 223)(24 52 207 218)(25 154 42 204)(26 149 43 199)(27 156 44 194)(28 151 45 201)(29 146 46 196)(30 153 47 203)(31 148 48 198)(32 155 37 193)(33 150 38 200)(34 145 39 195)(35 152 40 202)(36 147 41 197)(61 82 119 103)(62 77 120 98)(63 84 109 105)(64 79 110 100)(65 74 111 107)(66 81 112 102)(67 76 113 97)(68 83 114 104)(69 78 115 99)(70 73 116 106)(71 80 117 101)(72 75 118 108)(85 231 132 190)(86 238 121 185)(87 233 122 192)(88 240 123 187)(89 235 124 182)(90 230 125 189)(91 237 126 184)(92 232 127 191)(93 239 128 186)(94 234 129 181)(95 229 130 188)(96 236 131 183)

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

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

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

66 conjugacy classes

class 1 2A2B2C2D2E2F2G 3 4A4B4C4D4E4F4G4H4I4J4K4L5A5B6A6B6C10A···10F10G···10N12A12B12C12D12E12F15A15B20A20B20C20D30A···30F60A···60H
order1222222234444444444445566610···1010···1012121212121215152020202030···3060···60
size1111666622210101010151515153030222222···212···1244202020204444444···44···4

66 irreducible representations

dim11111112222222222444444444
type+++++++++++-++++++--+
imageC1C2C2C2C2C2C4S3D4D5D6D6C4○D4Dic5D10D10C4×S3S3×D4Q83S3S3×D5D4×D5D42D5S3×Dic5C2×S3×D5D12⋊D5C20⋊D6
kernelDic158D4D6⋊Dic5C3×C4⋊Dic5C4×Dic15C2×S3×Dic5C10×D12C5×D12C4⋊Dic5Dic15C2×D12C2×Dic5C2×C20C30D12C2×C12C22×S3C20C10C10C2×C4C6C6C4C22C2C2
# reps12112181222128244112224244

Matrix representation of Dic158D4 in GL6(𝔽61)

100000
010000
001100
0060000
0000060
000010
,
100000
010000
00606000
000100
000010
0000060
,
18600000
100000
0060000
0006000
000010
000001
,
30530000
44310000
0050000
0005000
0000060
0000600

G:=sub<GL(6,GF(61))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,60,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,60,0],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,60,0,0,0,0,0,60,1,0,0,0,0,0,0,1,0,0,0,0,0,0,60],[18,1,0,0,0,0,60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[30,44,0,0,0,0,53,31,0,0,0,0,0,0,50,0,0,0,0,0,0,50,0,0,0,0,0,0,0,60,0,0,0,0,60,0] >;

Dic158D4 in GAP, Magma, Sage, TeX

{\rm Dic}_{15}\rtimes_8D_4
% in TeX

G:=Group("Dic15:8D4");
// GroupNames label

G:=SmallGroup(480,511);
// by ID

G=gap.SmallGroup(480,511);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,422,219,100,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^12=b^2=c^10=1,d^2=c^5,b*a*b=a^-1,a*c=c*a,d*a*d^-1=a^7,b*c=c*b,d*b*d^-1=a^6*b,d*c*d^-1=c^-1>;
// generators/relations

׿
×
𝔽