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G = Dic154D4order 480 = 25·3·5

4th semidirect product of Dic15 and D4 acting via D4/C2=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: Dic154D4, (S3×C10)⋊6D4, C6.86(D4×D5), D63(C5⋊D4), C57(Dic3⋊D4), C23.D59S3, C1520(C4⋊D4), C10.161(S3×D4), C30.238(C2×D4), D304C431C2, C23.22(S3×D5), C33(Dic5⋊D4), Dic155C437C2, (C2×Dic5).63D6, (C22×C6).37D10, (C22×C10).52D6, C10.85(C4○D12), C30.152(C4○D4), C6.58(D42D5), (C2×C30).200C23, (C2×Dic3).62D10, (C22×S3).54D10, C2.40(D10⋊D6), (C22×C30).62C22, C2.28(Dic3.D10), (C6×Dic5).116C22, (C22×D15).66C22, (C2×Dic15).139C22, (C10×Dic3).116C22, (C2×C3⋊D4)⋊3D5, (C10×C3⋊D4)⋊3C2, (C2×S3×Dic5)⋊16C2, C6.65(C2×C5⋊D4), C2.40(S3×C5⋊D4), (C2×C157D4)⋊15C2, (C2×C5⋊D12)⋊12C2, C22.232(C2×S3×D5), (S3×C2×C10).51C22, (C3×C23.D5)⋊11C2, (C2×C6).212(C22×D5), (C2×C10).212(C22×S3), SmallGroup(480,634)

Series: Derived Chief Lower central Upper central

C1C2×C30 — Dic154D4
C1C5C15C30C2×C30C6×Dic5C2×S3×Dic5 — Dic154D4
C15C2×C30 — Dic154D4
C1C22C23

Generators and relations for Dic154D4
 G = < a,b,c,d | a30=c4=d2=1, b2=a15, bab-1=a-1, cac-1=dad=a11, cbc-1=a15b, bd=db, dcd=c-1 >

Subgroups: 1068 in 188 conjugacy classes, 50 normal (44 characteristic)
C1, C2 [×3], C2 [×4], C3, C4 [×5], C22, C22 [×10], C5, S3 [×3], C6 [×3], C6, C2×C4 [×6], D4 [×6], C23, C23 [×2], D5, C10 [×3], C10 [×3], Dic3 [×3], C12 [×2], D6 [×2], D6 [×5], C2×C6, C2×C6 [×3], C15, C22⋊C4 [×2], C4⋊C4, C22×C4, C2×D4 [×3], Dic5 [×4], C20, D10 [×3], C2×C10, C2×C10 [×7], C4×S3 [×2], D12 [×2], C2×Dic3, C2×Dic3, C3⋊D4 [×4], C2×C12 [×2], C22×S3, C22×S3, C22×C6, C5×S3 [×2], D15, C30 [×3], C30, C4⋊D4, C2×Dic5 [×2], C2×Dic5 [×3], C5⋊D4 [×4], C2×C20, C5×D4 [×2], C22×D5, C22×C10, C22×C10, Dic3⋊C4, D6⋊C4, C3×C22⋊C4, S3×C2×C4, C2×D12, C2×C3⋊D4, C2×C3⋊D4, C5×Dic3, C3×Dic5 [×2], Dic15 [×2], S3×C10 [×2], S3×C10 [×2], D30 [×3], C2×C30, C2×C30 [×3], C10.D4, D10⋊C4, C23.D5, C22×Dic5, C2×C5⋊D4 [×2], D4×C10, Dic3⋊D4, S3×Dic5 [×2], C5⋊D12 [×2], C6×Dic5 [×2], C10×Dic3, C5×C3⋊D4 [×2], C2×Dic15, C157D4 [×2], S3×C2×C10, C22×D15, C22×C30, Dic5⋊D4, D304C4, Dic155C4, C3×C23.D5, C2×S3×Dic5, C2×C5⋊D12, C10×C3⋊D4, C2×C157D4, Dic154D4
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×4], C23, D5, D6 [×3], C2×D4 [×2], C4○D4, D10 [×3], C22×S3, C4⋊D4, C5⋊D4 [×2], C22×D5, C4○D12, S3×D4 [×2], S3×D5, D4×D5, D42D5, C2×C5⋊D4, Dic3⋊D4, C2×S3×D5, Dic5⋊D4, Dic3.D10, S3×C5⋊D4, D10⋊D6, Dic154D4

Smallest permutation representation of Dic154D4
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)
(1 203 16 188)(2 202 17 187)(3 201 18 186)(4 200 19 185)(5 199 20 184)(6 198 21 183)(7 197 22 182)(8 196 23 181)(9 195 24 210)(10 194 25 209)(11 193 26 208)(12 192 27 207)(13 191 28 206)(14 190 29 205)(15 189 30 204)(31 88 46 73)(32 87 47 72)(33 86 48 71)(34 85 49 70)(35 84 50 69)(36 83 51 68)(37 82 52 67)(38 81 53 66)(39 80 54 65)(40 79 55 64)(41 78 56 63)(42 77 57 62)(43 76 58 61)(44 75 59 90)(45 74 60 89)(91 227 106 212)(92 226 107 211)(93 225 108 240)(94 224 109 239)(95 223 110 238)(96 222 111 237)(97 221 112 236)(98 220 113 235)(99 219 114 234)(100 218 115 233)(101 217 116 232)(102 216 117 231)(103 215 118 230)(104 214 119 229)(105 213 120 228)(121 160 136 175)(122 159 137 174)(123 158 138 173)(124 157 139 172)(125 156 140 171)(126 155 141 170)(127 154 142 169)(128 153 143 168)(129 152 144 167)(130 151 145 166)(131 180 146 165)(132 179 147 164)(133 178 148 163)(134 177 149 162)(135 176 150 161)
(1 134 239 84)(2 145 240 65)(3 126 211 76)(4 137 212 87)(5 148 213 68)(6 129 214 79)(7 140 215 90)(8 121 216 71)(9 132 217 82)(10 143 218 63)(11 124 219 74)(12 135 220 85)(13 146 221 66)(14 127 222 77)(15 138 223 88)(16 149 224 69)(17 130 225 80)(18 141 226 61)(19 122 227 72)(20 133 228 83)(21 144 229 64)(22 125 230 75)(23 136 231 86)(24 147 232 67)(25 128 233 78)(26 139 234 89)(27 150 235 70)(28 131 236 81)(29 142 237 62)(30 123 238 73)(31 189 158 110)(32 200 159 91)(33 181 160 102)(34 192 161 113)(35 203 162 94)(36 184 163 105)(37 195 164 116)(38 206 165 97)(39 187 166 108)(40 198 167 119)(41 209 168 100)(42 190 169 111)(43 201 170 92)(44 182 171 103)(45 193 172 114)(46 204 173 95)(47 185 174 106)(48 196 175 117)(49 207 176 98)(50 188 177 109)(51 199 178 120)(52 210 179 101)(53 191 180 112)(54 202 151 93)(55 183 152 104)(56 194 153 115)(57 205 154 96)(58 186 155 107)(59 197 156 118)(60 208 157 99)
(2 12)(3 23)(5 15)(6 26)(8 18)(9 29)(11 21)(14 24)(17 27)(20 30)(31 178)(32 159)(33 170)(34 151)(35 162)(36 173)(37 154)(38 165)(39 176)(40 157)(41 168)(42 179)(43 160)(44 171)(45 152)(46 163)(47 174)(48 155)(49 166)(50 177)(51 158)(52 169)(53 180)(54 161)(55 172)(56 153)(57 164)(58 175)(59 156)(60 167)(61 121)(62 132)(63 143)(64 124)(65 135)(66 146)(67 127)(68 138)(69 149)(70 130)(71 141)(72 122)(73 133)(74 144)(75 125)(76 136)(77 147)(78 128)(79 139)(80 150)(81 131)(82 142)(83 123)(84 134)(85 145)(86 126)(87 137)(88 148)(89 129)(90 140)(92 102)(93 113)(95 105)(96 116)(98 108)(99 119)(101 111)(104 114)(107 117)(110 120)(181 201)(183 193)(184 204)(186 196)(187 207)(189 199)(190 210)(192 202)(195 205)(198 208)(211 231)(213 223)(214 234)(216 226)(217 237)(219 229)(220 240)(222 232)(225 235)(228 238)

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

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

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

60 conjugacy classes

class 1 2A2B2C2D2E2F2G 3 4A4B4C4D4E4F5A5B6A6B6C6D6E10A···10F10G10H10I10J10K10L10M10N12A12B12C12D15A15B20A20B20C20D30A···30N
order122222223444444556666610···1010101010101010101212121215152020202030···30
size111146660210101220303022222442···24444121212122020202044121212124···4

60 irreducible representations

dim1111111122222222222244444444
type++++++++++++++++++++-++
imageC1C2C2C2C2C2C2C2S3D4D4D5D6D6C4○D4D10D10D10C5⋊D4C4○D12S3×D4S3×D5D4×D5D42D5C2×S3×D5Dic3.D10S3×C5⋊D4D10⋊D6
kernelDic154D4D304C4Dic155C4C3×C23.D5C2×S3×Dic5C2×C5⋊D12C10×C3⋊D4C2×C157D4C23.D5Dic15S3×C10C2×C3⋊D4C2×Dic5C22×C10C30C2×Dic3C22×S3C22×C6D6C10C10C23C6C6C22C2C2C2
# reps1111111112222122228422222444

Matrix representation of Dic154D4 in GL4(𝔽61) generated by

16000
1000
00060
00144
,
01100
11000
003630
003225
,
43900
521800
004716
004514
,
0100
1000
0010
0001
G:=sub<GL(4,GF(61))| [1,1,0,0,60,0,0,0,0,0,0,1,0,0,60,44],[0,11,0,0,11,0,0,0,0,0,36,32,0,0,30,25],[43,52,0,0,9,18,0,0,0,0,47,45,0,0,16,14],[0,1,0,0,1,0,0,0,0,0,1,0,0,0,0,1] >;

Dic154D4 in GAP, Magma, Sage, TeX

{\rm Dic}_{15}\rtimes_4D_4
% in TeX

G:=Group("Dic15:4D4");
// GroupNames label

G:=SmallGroup(480,634);
// by ID

G=gap.SmallGroup(480,634);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,422,303,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^30=c^4=d^2=1,b^2=a^15,b*a*b^-1=a^-1,c*a*c^-1=d*a*d=a^11,c*b*c^-1=a^15*b,b*d=d*b,d*c*d=c^-1>;
// generators/relations

׿
×
𝔽