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## G = Dic15⋊2D4order 480 = 25·3·5

### 2nd semidirect product of Dic15 and D4 acting via D4/C2=C22

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C30 — Dic15⋊2D4
 Chief series C1 — C5 — C15 — C30 — C2×C30 — D5×C2×C6 — C2×C15⋊D4 — Dic15⋊2D4
 Lower central C15 — C2×C30 — Dic15⋊2D4
 Upper central C1 — C22 — C2×C4

Generators and relations for Dic152D4
G = < a,b,c,d | a30=c4=d2=1, b2=a15, bab-1=a-1, ac=ca, dad=a11, cbc-1=dbd=a15b, dcd=c-1 >

Subgroups: 1004 in 188 conjugacy classes, 50 normal (44 characteristic)
C1, C2, C2, C3, C4, C22, C22, C5, S3, C6, C6, C2×C4, C2×C4, D4, C23, D5, C10, C10, Dic3, C12, D6, D6, C2×C6, C2×C6, C15, C22⋊C4, C4⋊C4, C22×C4, C2×D4, Dic5, C20, D10, C2×C10, C2×C10, C4×S3, D12, C2×Dic3, C3⋊D4, C2×C12, C2×C12, C22×S3, C22×C6, C5×S3, C3×D5, C30, C4⋊D4, C2×Dic5, C2×Dic5, C5⋊D4, C2×C20, C5×D4, C22×D5, C22×C10, Dic3⋊C4, D6⋊C4, C3×C22⋊C4, S3×C2×C4, C2×D12, C2×C3⋊D4, C3×Dic5, Dic15, Dic15, C60, C6×D5, S3×C10, S3×C10, C2×C30, C10.D4, D10⋊C4, C23.D5, C22×Dic5, C2×C5⋊D4, D4×C10, Dic3⋊D4, S3×Dic5, C15⋊D4, C6×Dic5, C5×D12, C2×Dic15, C2×C60, D5×C2×C6, S3×C2×C10, Dic5⋊D4, D6⋊Dic5, C3×D10⋊C4, C30.4Q8, C2×S3×Dic5, C2×C15⋊D4, C10×D12, Dic152D4
Quotients: C1, C2, C22, S3, D4, C23, D5, D6, C2×D4, C4○D4, D10, C22×S3, C4⋊D4, C5⋊D4, C22×D5, C4○D12, S3×D4, S3×D5, D4×D5, D42D5, C2×C5⋊D4, Dic3⋊D4, C2×S3×D5, Dic5⋊D4, D125D5, C20⋊D6, S3×C5⋊D4, Dic152D4

Smallest permutation representation of Dic152D4
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)
(1 238 16 223)(2 237 17 222)(3 236 18 221)(4 235 19 220)(5 234 20 219)(6 233 21 218)(7 232 22 217)(8 231 23 216)(9 230 24 215)(10 229 25 214)(11 228 26 213)(12 227 27 212)(13 226 28 211)(14 225 29 240)(15 224 30 239)(31 187 46 202)(32 186 47 201)(33 185 48 200)(34 184 49 199)(35 183 50 198)(36 182 51 197)(37 181 52 196)(38 210 53 195)(39 209 54 194)(40 208 55 193)(41 207 56 192)(42 206 57 191)(43 205 58 190)(44 204 59 189)(45 203 60 188)(61 112 76 97)(62 111 77 96)(63 110 78 95)(64 109 79 94)(65 108 80 93)(66 107 81 92)(67 106 82 91)(68 105 83 120)(69 104 84 119)(70 103 85 118)(71 102 86 117)(72 101 87 116)(73 100 88 115)(74 99 89 114)(75 98 90 113)(121 152 136 167)(122 151 137 166)(123 180 138 165)(124 179 139 164)(125 178 140 163)(126 177 141 162)(127 176 142 161)(128 175 143 160)(129 174 144 159)(130 173 145 158)(131 172 146 157)(132 171 147 156)(133 170 148 155)(134 169 149 154)(135 168 150 153)
(1 58 70 152)(2 59 71 153)(3 60 72 154)(4 31 73 155)(5 32 74 156)(6 33 75 157)(7 34 76 158)(8 35 77 159)(9 36 78 160)(10 37 79 161)(11 38 80 162)(12 39 81 163)(13 40 82 164)(14 41 83 165)(15 42 84 166)(16 43 85 167)(17 44 86 168)(18 45 87 169)(19 46 88 170)(20 47 89 171)(21 48 90 172)(22 49 61 173)(23 50 62 174)(24 51 63 175)(25 52 64 176)(26 53 65 177)(27 54 66 178)(28 55 67 179)(29 56 68 180)(30 57 69 151)(91 139 226 193)(92 140 227 194)(93 141 228 195)(94 142 229 196)(95 143 230 197)(96 144 231 198)(97 145 232 199)(98 146 233 200)(99 147 234 201)(100 148 235 202)(101 149 236 203)(102 150 237 204)(103 121 238 205)(104 122 239 206)(105 123 240 207)(106 124 211 208)(107 125 212 209)(108 126 213 210)(109 127 214 181)(110 128 215 182)(111 129 216 183)(112 130 217 184)(113 131 218 185)(114 132 219 186)(115 133 220 187)(116 134 221 188)(117 135 222 189)(118 136 223 190)(119 137 224 191)(120 138 225 192)
(1 152)(2 163)(3 174)(4 155)(5 166)(6 177)(7 158)(8 169)(9 180)(10 161)(11 172)(12 153)(13 164)(14 175)(15 156)(16 167)(17 178)(18 159)(19 170)(20 151)(21 162)(22 173)(23 154)(24 165)(25 176)(26 157)(27 168)(28 179)(29 160)(30 171)(31 73)(32 84)(33 65)(34 76)(35 87)(36 68)(37 79)(38 90)(39 71)(40 82)(41 63)(42 74)(43 85)(44 66)(45 77)(46 88)(47 69)(48 80)(49 61)(50 72)(51 83)(52 64)(53 75)(54 86)(55 67)(56 78)(57 89)(58 70)(59 81)(60 62)(91 193)(92 204)(93 185)(94 196)(95 207)(96 188)(97 199)(98 210)(99 191)(100 202)(101 183)(102 194)(103 205)(104 186)(105 197)(106 208)(107 189)(108 200)(109 181)(110 192)(111 203)(112 184)(113 195)(114 206)(115 187)(116 198)(117 209)(118 190)(119 201)(120 182)(121 238)(122 219)(123 230)(124 211)(125 222)(126 233)(127 214)(128 225)(129 236)(130 217)(131 228)(132 239)(133 220)(134 231)(135 212)(136 223)(137 234)(138 215)(139 226)(140 237)(141 218)(142 229)(143 240)(144 221)(145 232)(146 213)(147 224)(148 235)(149 216)(150 227)

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

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

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

60 conjugacy classes

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

60 irreducible representations

 dim 1 1 1 1 1 1 1 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 C2 S3 D4 D4 D5 D6 D6 D6 C4○D4 D10 D10 C5⋊D4 C4○D12 S3×D4 S3×D5 D4×D5 D4⋊2D5 C2×S3×D5 D12⋊5D5 C20⋊D6 S3×C5⋊D4 kernel Dic15⋊2D4 D6⋊Dic5 C3×D10⋊C4 C30.4Q8 C2×S3×Dic5 C2×C15⋊D4 C10×D12 D10⋊C4 Dic15 S3×C10 C2×D12 C2×Dic5 C2×C20 C22×D5 C30 C2×C12 C22×S3 D6 C10 C10 C2×C4 C6 C6 C22 C2 C2 C2 # reps 1 1 1 1 1 2 1 1 2 2 2 1 1 1 2 2 4 8 4 2 2 2 2 2 4 4 4

Matrix representation of Dic152D4 in GL6(𝔽61)

 0 60 0 0 0 0 1 1 0 0 0 0 0 0 60 1 0 0 0 0 16 44 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 11 0 0 0 0 0 50 50 0 0 0 0 0 0 0 18 0 0 0 0 17 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 38 15 0 0 0 0 46 23 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 15 20 0 0 0 0 7 46
,
 38 15 0 0 0 0 38 23 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 15 20 0 0 0 0 1 46

G:=sub<GL(6,GF(61))| [0,1,0,0,0,0,60,1,0,0,0,0,0,0,60,16,0,0,0,0,1,44,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[11,50,0,0,0,0,0,50,0,0,0,0,0,0,0,17,0,0,0,0,18,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[38,46,0,0,0,0,15,23,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,15,7,0,0,0,0,20,46],[38,38,0,0,0,0,15,23,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,15,1,0,0,0,0,20,46] >;

Dic152D4 in GAP, Magma, Sage, TeX

{\rm Dic}_{15}\rtimes_2D_4
% in TeX

G:=Group("Dic15:2D4");
// GroupNames label

G:=SmallGroup(480,529);
// by ID

G=gap.SmallGroup(480,529);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,253,254,219,100,1356,18822]);
// Polycyclic

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

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