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G = C15×C4.10D4order 480 = 25·3·5

Direct product of C15 and C4.10D4

direct product, metabelian, nilpotent (class 3), monomial, 2-elementary

Aliases: C15×C4.10D4, C60.244D4, M4(2).1C30, (C2×C4).C60, (C2×C60).26C4, (C2×C12).2C20, C4.10(D4×C15), C20.59(C3×D4), C12.59(C5×D4), (C6×Q8).6C10, (C2×Q8).3C30, (C2×C20).13C12, C22.4(C2×C60), (Q8×C10).10C6, (Q8×C30).16C2, (C5×M4(2)).3C6, (C2×C60).419C22, (C15×M4(2)).7C2, (C3×M4(2)).3C10, C30.127(C22⋊C4), (C2×C4).2(C2×C30), (C2×C20).60(C2×C6), (C2×C6).21(C2×C20), C2.5(C15×C22⋊C4), C6.23(C5×C22⋊C4), (C2×C10).41(C2×C12), (C2×C30).166(C2×C4), (C2×C12).60(C2×C10), C10.34(C3×C22⋊C4), SmallGroup(480,204)

Series: Derived Chief Lower central Upper central

C1C22 — C15×C4.10D4
C1C2C4C2×C4C2×C20C2×C60C15×M4(2) — C15×C4.10D4
C1C2C22 — C15×C4.10D4
C1C30C2×C60 — C15×C4.10D4

Generators and relations for C15×C4.10D4
 G = < a,b,c,d | a15=b4=1, c4=b2, d2=cbc-1=b-1, ab=ba, ac=ca, ad=da, bd=db, dcd-1=b-1c3 >

Subgroups: 104 in 76 conjugacy classes, 48 normal (24 characteristic)
C1, C2, C2, C3, C4 [×2], C4 [×2], C22, C5, C6, C6, C8 [×2], C2×C4, C2×C4 [×2], Q8 [×2], C10, C10, C12 [×2], C12 [×2], C2×C6, C15, M4(2) [×2], C2×Q8, C20 [×2], C20 [×2], C2×C10, C24 [×2], C2×C12, C2×C12 [×2], C3×Q8 [×2], C30, C30, C4.10D4, C40 [×2], C2×C20, C2×C20 [×2], C5×Q8 [×2], C3×M4(2) [×2], C6×Q8, C60 [×2], C60 [×2], C2×C30, C5×M4(2) [×2], Q8×C10, C3×C4.10D4, C120 [×2], C2×C60, C2×C60 [×2], Q8×C15 [×2], C5×C4.10D4, C15×M4(2) [×2], Q8×C30, C15×C4.10D4
Quotients: C1, C2 [×3], C3, C4 [×2], C22, C5, C6 [×3], C2×C4, D4 [×2], C10 [×3], C12 [×2], C2×C6, C15, C22⋊C4, C20 [×2], C2×C10, C2×C12, C3×D4 [×2], C30 [×3], C4.10D4, C2×C20, C5×D4 [×2], C3×C22⋊C4, C60 [×2], C2×C30, C5×C22⋊C4, C3×C4.10D4, C2×C60, D4×C15 [×2], C5×C4.10D4, C15×C22⋊C4, C15×C4.10D4

Smallest permutation representation of C15×C4.10D4
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)
(1 104 144 69)(2 105 145 70)(3 91 146 71)(4 92 147 72)(5 93 148 73)(6 94 149 74)(7 95 150 75)(8 96 136 61)(9 97 137 62)(10 98 138 63)(11 99 139 64)(12 100 140 65)(13 101 141 66)(14 102 142 67)(15 103 143 68)(16 206 178 157)(17 207 179 158)(18 208 180 159)(19 209 166 160)(20 210 167 161)(21 196 168 162)(22 197 169 163)(23 198 170 164)(24 199 171 165)(25 200 172 151)(26 201 173 152)(27 202 174 153)(28 203 175 154)(29 204 176 155)(30 205 177 156)(31 133 211 185)(32 134 212 186)(33 135 213 187)(34 121 214 188)(35 122 215 189)(36 123 216 190)(37 124 217 191)(38 125 218 192)(39 126 219 193)(40 127 220 194)(41 128 221 195)(42 129 222 181)(43 130 223 182)(44 131 224 183)(45 132 225 184)(46 112 235 84)(47 113 236 85)(48 114 237 86)(49 115 238 87)(50 116 239 88)(51 117 240 89)(52 118 226 90)(53 119 227 76)(54 120 228 77)(55 106 229 78)(56 107 230 79)(57 108 231 80)(58 109 232 81)(59 110 233 82)(60 111 234 83)
(1 17 104 158 144 179 69 207)(2 18 105 159 145 180 70 208)(3 19 91 160 146 166 71 209)(4 20 92 161 147 167 72 210)(5 21 93 162 148 168 73 196)(6 22 94 163 149 169 74 197)(7 23 95 164 150 170 75 198)(8 24 96 165 136 171 61 199)(9 25 97 151 137 172 62 200)(10 26 98 152 138 173 63 201)(11 27 99 153 139 174 64 202)(12 28 100 154 140 175 65 203)(13 29 101 155 141 176 66 204)(14 30 102 156 142 177 67 205)(15 16 103 157 143 178 68 206)(31 78 133 229 211 106 185 55)(32 79 134 230 212 107 186 56)(33 80 135 231 213 108 187 57)(34 81 121 232 214 109 188 58)(35 82 122 233 215 110 189 59)(36 83 123 234 216 111 190 60)(37 84 124 235 217 112 191 46)(38 85 125 236 218 113 192 47)(39 86 126 237 219 114 193 48)(40 87 127 238 220 115 194 49)(41 88 128 239 221 116 195 50)(42 89 129 240 222 117 181 51)(43 90 130 226 223 118 182 52)(44 76 131 227 224 119 183 53)(45 77 132 228 225 120 184 54)
(1 84 69 235 144 112 104 46)(2 85 70 236 145 113 105 47)(3 86 71 237 146 114 91 48)(4 87 72 238 147 115 92 49)(5 88 73 239 148 116 93 50)(6 89 74 240 149 117 94 51)(7 90 75 226 150 118 95 52)(8 76 61 227 136 119 96 53)(9 77 62 228 137 120 97 54)(10 78 63 229 138 106 98 55)(11 79 64 230 139 107 99 56)(12 80 65 231 140 108 100 57)(13 81 66 232 141 109 101 58)(14 82 67 233 142 110 102 59)(15 83 68 234 143 111 103 60)(16 123 157 36 178 190 206 216)(17 124 158 37 179 191 207 217)(18 125 159 38 180 192 208 218)(19 126 160 39 166 193 209 219)(20 127 161 40 167 194 210 220)(21 128 162 41 168 195 196 221)(22 129 163 42 169 181 197 222)(23 130 164 43 170 182 198 223)(24 131 165 44 171 183 199 224)(25 132 151 45 172 184 200 225)(26 133 152 31 173 185 201 211)(27 134 153 32 174 186 202 212)(28 135 154 33 175 187 203 213)(29 121 155 34 176 188 204 214)(30 122 156 35 177 189 205 215)

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

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

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

165 conjugacy classes

class 1 2A2B3A3B4A4B4C4D5A5B5C5D6A6B6C6D8A8B8C8D10A10B10C10D10E10F10G10H12A12B12C12D12E12F12G12H15A···15H20A···20H20I···20P24A···24H30A···30H30I···30P40A···40P60A···60P60Q···60AF120A···120AF
order1223344445555666688881010101010101010121212121212121215···1520···2020···2024···2430···3030···3040···4060···6060···60120···120
size11211224411111122444411112222222244441···12···24···44···41···12···24···42···24···44···4

165 irreducible representations

dim111111111111111122224444
type++++-
imageC1C2C2C3C4C5C6C6C10C10C12C15C20C30C30C60D4C3×D4C5×D4D4×C15C4.10D4C3×C4.10D4C5×C4.10D4C15×C4.10D4
kernelC15×C4.10D4C15×M4(2)Q8×C30C5×C4.10D4C2×C60C3×C4.10D4C5×M4(2)Q8×C10C3×M4(2)C6×Q8C2×C20C4.10D4C2×C12M4(2)C2×Q8C2×C4C60C20C12C4C15C5C3C1
# reps1212444284881616832248161248

Matrix representation of C15×C4.10D4 in GL6(𝔽241)

22500000
02250000
0098000
0009800
0000980
0000098
,
100000
010000
0001740
00240074167
00002401
00002391
,
02400000
100000
001670133
001670033
0011074
0020074
,
02400000
24000000
0021835291
002183513430
00781360206
001832140229

G:=sub<GL(6,GF(241))| [225,0,0,0,0,0,0,225,0,0,0,0,0,0,98,0,0,0,0,0,0,98,0,0,0,0,0,0,98,0,0,0,0,0,0,98],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,240,0,0,0,0,1,0,0,0,0,0,74,74,240,239,0,0,0,167,1,1],[0,1,0,0,0,0,240,0,0,0,0,0,0,0,167,167,1,2,0,0,0,0,1,0,0,0,1,0,0,0,0,0,33,33,74,74],[0,240,0,0,0,0,240,0,0,0,0,0,0,0,218,218,78,183,0,0,35,35,136,214,0,0,29,134,0,0,0,0,1,30,206,229] >;

C15×C4.10D4 in GAP, Magma, Sage, TeX

C_{15}\times C_4._{10}D_4
% in TeX

G:=Group("C15xC4.10D4");
// GroupNames label

G:=SmallGroup(480,204);
// by ID

G=gap.SmallGroup(480,204);
# by ID

G:=PCGroup([7,-2,-2,-3,-5,-2,-2,-2,840,869,1688,10504,7572,124]);
// Polycyclic

G:=Group<a,b,c,d|a^15=b^4=1,c^4=b^2,d^2=c*b*c^-1=b^-1,a*b=b*a,a*c=c*a,a*d=d*a,b*d=d*b,d*c*d^-1=b^-1*c^3>;
// generators/relations

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