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G = C2×C30.D4order 480 = 25·3·5

Direct product of C2 and C30.D4

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C2×C30.D4, C301SD16, C60.82D4, D20.36D6, Dic619D10, C60.153C23, C62(Q8⋊D5), C154(C2×SD16), (C2×Dic6)⋊7D5, (C2×D20).8S3, (C6×D20).7C2, (C2×C30).49D4, C30.81(C2×D4), (C2×C20).92D6, C102(D4.S3), (C10×Dic6)⋊9C2, (C2×C12).92D10, C4.6(C15⋊D4), C153C838C22, C20.26(C3⋊D4), C12.29(C5⋊D4), C20.92(C22×S3), C12.90(C22×D5), (C2×C60).188C22, (C5×Dic6)⋊25C22, (C3×D20).42C22, C22.20(C15⋊D4), C33(C2×Q8⋊D5), C53(C2×D4.S3), C4.126(C2×S3×D5), (C2×C153C8)⋊16C2, C6.75(C2×C5⋊D4), C2.9(C2×C15⋊D4), (C2×C4).198(S3×D5), C10.76(C2×C3⋊D4), (C2×C6).53(C5⋊D4), (C2×C10).53(C3⋊D4), SmallGroup(480,382)

Series: Derived Chief Lower central Upper central

C1C60 — C2×C30.D4
C1C5C15C30C60C3×D20C30.D4 — C2×C30.D4
C15C30C60 — C2×C30.D4
C1C22C2×C4

Generators and relations for C2×C30.D4
 G = < a,b,c,d | a2=b20=c6=1, d2=b15, ab=ba, ac=ca, ad=da, cbc-1=b-1, dbd-1=b9, dcd-1=b5c-1 >

Subgroups: 636 in 136 conjugacy classes, 52 normal (30 characteristic)
C1, C2, C2 [×2], C2 [×2], C3, C4 [×2], C4 [×2], C22, C22 [×4], C5, C6, C6 [×2], C6 [×2], C8 [×2], C2×C4, C2×C4, D4 [×3], Q8 [×3], C23, D5 [×2], C10, C10 [×2], Dic3 [×2], C12 [×2], C2×C6, C2×C6 [×4], C15, C2×C8, SD16 [×4], C2×D4, C2×Q8, C20 [×2], C20 [×2], D10 [×4], C2×C10, C3⋊C8 [×2], Dic6 [×2], Dic6, C2×Dic3, C2×C12, C3×D4 [×3], C22×C6, C3×D5 [×2], C30, C30 [×2], C2×SD16, C52C8 [×2], D20 [×2], D20, C2×C20, C2×C20, C5×Q8 [×3], C22×D5, C2×C3⋊C8, D4.S3 [×4], C2×Dic6, C6×D4, C5×Dic3 [×2], C60 [×2], C6×D5 [×4], C2×C30, C2×C52C8, Q8⋊D5 [×4], C2×D20, Q8×C10, C2×D4.S3, C153C8 [×2], C3×D20 [×2], C3×D20, C5×Dic6 [×2], C5×Dic6, C10×Dic3, C2×C60, D5×C2×C6, C2×Q8⋊D5, C30.D4 [×4], C2×C153C8, C6×D20, C10×Dic6, C2×C30.D4
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], SD16 [×2], C2×D4, D10 [×3], C3⋊D4 [×2], C22×S3, C2×SD16, C5⋊D4 [×2], C22×D5, D4.S3 [×2], C2×C3⋊D4, S3×D5, Q8⋊D5 [×2], C2×C5⋊D4, C2×D4.S3, C15⋊D4 [×2], C2×S3×D5, C2×Q8⋊D5, C30.D4 [×2], C2×C15⋊D4, C2×C30.D4

Smallest permutation representation of C2×C30.D4
On 240 points
Generators in S240
(1 189)(2 190)(3 191)(4 192)(5 193)(6 194)(7 195)(8 196)(9 197)(10 198)(11 199)(12 200)(13 181)(14 182)(15 183)(16 184)(17 185)(18 186)(19 187)(20 188)(21 165)(22 166)(23 167)(24 168)(25 169)(26 170)(27 171)(28 172)(29 173)(30 174)(31 175)(32 176)(33 177)(34 178)(35 179)(36 180)(37 161)(38 162)(39 163)(40 164)(41 96)(42 97)(43 98)(44 99)(45 100)(46 81)(47 82)(48 83)(49 84)(50 85)(51 86)(52 87)(53 88)(54 89)(55 90)(56 91)(57 92)(58 93)(59 94)(60 95)(61 233)(62 234)(63 235)(64 236)(65 237)(66 238)(67 239)(68 240)(69 221)(70 222)(71 223)(72 224)(73 225)(74 226)(75 227)(76 228)(77 229)(78 230)(79 231)(80 232)(101 147)(102 148)(103 149)(104 150)(105 151)(106 152)(107 153)(108 154)(109 155)(110 156)(111 157)(112 158)(113 159)(114 160)(115 141)(116 142)(117 143)(118 144)(119 145)(120 146)(121 209)(122 210)(123 211)(124 212)(125 213)(126 214)(127 215)(128 216)(129 217)(130 218)(131 219)(132 220)(133 201)(134 202)(135 203)(136 204)(137 205)(138 206)(139 207)(140 208)
(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 73 125 189 225 213)(2 72 126 188 226 212)(3 71 127 187 227 211)(4 70 128 186 228 210)(5 69 129 185 229 209)(6 68 130 184 230 208)(7 67 131 183 231 207)(8 66 132 182 232 206)(9 65 133 181 233 205)(10 64 134 200 234 204)(11 63 135 199 235 203)(12 62 136 198 236 202)(13 61 137 197 237 201)(14 80 138 196 238 220)(15 79 139 195 239 219)(16 78 140 194 240 218)(17 77 121 193 221 217)(18 76 122 192 222 216)(19 75 123 191 223 215)(20 74 124 190 224 214)(21 88 147 178 60 114)(22 87 148 177 41 113)(23 86 149 176 42 112)(24 85 150 175 43 111)(25 84 151 174 44 110)(26 83 152 173 45 109)(27 82 153 172 46 108)(28 81 154 171 47 107)(29 100 155 170 48 106)(30 99 156 169 49 105)(31 98 157 168 50 104)(32 97 158 167 51 103)(33 96 159 166 52 102)(34 95 160 165 53 101)(35 94 141 164 54 120)(36 93 142 163 55 119)(37 92 143 162 56 118)(38 91 144 161 57 117)(39 90 145 180 58 116)(40 89 146 179 59 115)
(1 30 16 25 11 40 6 35)(2 39 17 34 12 29 7 24)(3 28 18 23 13 38 8 33)(4 37 19 32 14 27 9 22)(5 26 20 21 15 36 10 31)(41 128 56 123 51 138 46 133)(42 137 57 132 52 127 47 122)(43 126 58 121 53 136 48 131)(44 135 59 130 54 125 49 140)(45 124 60 139 55 134 50 129)(61 102 76 117 71 112 66 107)(62 111 77 106 72 101 67 116)(63 120 78 115 73 110 68 105)(64 109 79 104 74 119 69 114)(65 118 80 113 75 108 70 103)(81 201 96 216 91 211 86 206)(82 210 97 205 92 220 87 215)(83 219 98 214 93 209 88 204)(84 208 99 203 94 218 89 213)(85 217 100 212 95 207 90 202)(141 225 156 240 151 235 146 230)(142 234 157 229 152 224 147 239)(143 223 158 238 153 233 148 228)(144 232 159 227 154 222 149 237)(145 221 160 236 155 231 150 226)(161 187 176 182 171 197 166 192)(162 196 177 191 172 186 167 181)(163 185 178 200 173 195 168 190)(164 194 179 189 174 184 169 199)(165 183 180 198 175 193 170 188)

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

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

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

60 conjugacy classes

class 1 2A2B2C2D2E 3 4A4B4C4D5A5B6A6B6C6D6E6F6G8A8B8C8D10A···10F12A12B15A15B20A20B20C20D20E···20L30A···30F60A···60H
order12222234444556666666888810···10121215152020202020···2030···3060···60
size1111202022212122222220202020303030302···24444444412···124···44···4

60 irreducible representations

dim1111122222222222224444444
type+++++++++++++-++-+-
imageC1C2C2C2C2S3D4D4D5D6D6SD16D10D10C3⋊D4C3⋊D4C5⋊D4C5⋊D4D4.S3S3×D5Q8⋊D5C15⋊D4C2×S3×D5C15⋊D4C30.D4
kernelC2×C30.D4C30.D4C2×C153C8C6×D20C10×Dic6C2×D20C60C2×C30C2×Dic6D20C2×C20C30Dic6C2×C12C20C2×C10C12C2×C6C10C2×C4C6C4C4C22C2
# reps1411111122144222442242228

Matrix representation of C2×C30.D4 in GL6(𝔽241)

24000000
02400000
001000
000100
00002400
00000240
,
24000000
02400000
00024000
00119000
0000240239
000011
,
22600000
2022250000
001000
005124000
00002400
000011
,
311800000
1582100000
00764900
006916500
00000203
00001938

G:=sub<GL(6,GF(241))| [240,0,0,0,0,0,0,240,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,240,0,0,0,0,0,0,240],[240,0,0,0,0,0,0,240,0,0,0,0,0,0,0,1,0,0,0,0,240,190,0,0,0,0,0,0,240,1,0,0,0,0,239,1],[226,202,0,0,0,0,0,225,0,0,0,0,0,0,1,51,0,0,0,0,0,240,0,0,0,0,0,0,240,1,0,0,0,0,0,1],[31,158,0,0,0,0,180,210,0,0,0,0,0,0,76,69,0,0,0,0,49,165,0,0,0,0,0,0,0,19,0,0,0,0,203,38] >;

C2×C30.D4 in GAP, Magma, Sage, TeX

C_2\times C_{30}.D_4
% in TeX

G:=Group("C2xC30.D4");
// GroupNames label

G:=SmallGroup(480,382);
// by ID

G=gap.SmallGroup(480,382);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,141,120,675,346,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^20=c^6=1,d^2=b^15,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,d*b*d^-1=b^9,d*c*d^-1=b^5*c^-1>;
// generators/relations

׿
×
𝔽