direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C3×D10⋊C8, D10⋊2C24, C30.10M4(2), (C6×D5)⋊6C8, (C2×C60).8C4, (C2×C12).4F5, C15⋊4(C22⋊C8), (C2×C20).3C12, C30.17(C2×C8), C10.3(C2×C24), C6.9(C4.F5), C6.14(D5⋊C8), C22.11(C6×F5), Dic5.20(C3×D4), (C3×Dic5).85D4, (C22×D5).6C12, C10.2(C3×M4(2)), C6.28(C22⋊F5), C30.28(C22⋊C4), (C6×Dic5).273C22, (C6×C5⋊C8)⋊8C2, (C2×C5⋊C8)⋊1C6, C5⋊1(C3×C22⋊C8), (C2×C4×D5).7C6, C2.4(C3×D5⋊C8), (D5×C2×C6).16C4, (C2×C4).3(C3×F5), C2.3(C3×C4.F5), (D5×C2×C12).22C2, (C2×C6).54(C2×F5), (C2×C10).6(C2×C12), (C2×C30).49(C2×C4), C2.1(C3×C22⋊F5), C10.2(C3×C22⋊C4), (C2×Dic5).50(C2×C6), SmallGroup(480,283)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3×D10⋊C8
G = < a,b,c,d | a3=b10=c2=d8=1, ab=ba, ac=ca, ad=da, cbc=b-1, dbd-1=b3, dcd-1=b7c >
Subgroups: 344 in 100 conjugacy classes, 44 normal (32 characteristic)
C1, C2, C2, C3, C4, C22, C22, C5, C6, C6, C8, C2×C4, C2×C4, C23, D5, C10, C12, C2×C6, C2×C6, C15, C2×C8, C22×C4, Dic5, C20, D10, D10, C2×C10, C24, C2×C12, C2×C12, C22×C6, C3×D5, C30, C22⋊C8, C5⋊C8, C4×D5, C2×Dic5, C2×C20, C22×D5, C2×C24, C22×C12, C3×Dic5, C60, C6×D5, C6×D5, C2×C30, C2×C5⋊C8, C2×C4×D5, C3×C22⋊C8, C3×C5⋊C8, D5×C12, C6×Dic5, C2×C60, D5×C2×C6, D10⋊C8, C6×C5⋊C8, D5×C2×C12, C3×D10⋊C8
Quotients: C1, C2, C3, C4, C22, C6, C8, C2×C4, D4, C12, C2×C6, C22⋊C4, C2×C8, M4(2), F5, C24, C2×C12, C3×D4, C22⋊C8, C2×F5, C3×C22⋊C4, C2×C24, C3×M4(2), C3×F5, D5⋊C8, C4.F5, C22⋊F5, C3×C22⋊C8, C6×F5, D10⋊C8, C3×D5⋊C8, C3×C4.F5, C3×C22⋊F5, C3×D10⋊C8
►On 240 points
Generators in S240
(1 92 52)(2 93 53)(3 94 54)(4 95 55)(5 96 56)(6 97 57)(7 98 58)(8 99 59)(9 100 60)(10 91 51)(11 203 163)(12 204 164)(13 205 165)(14 206 166)(15 207 167)(16 208 168)(17 209 169)(18 210 170)(19 201 161)(20 202 162)(21 101 61)(22 102 62)(23 103 63)(24 104 64)(25 105 65)(26 106 66)(27 107 67)(28 108 68)(29 109 69)(30 110 70)(31 111 71)(32 112 72)(33 113 73)(34 114 74)(35 115 75)(36 116 76)(37 117 77)(38 118 78)(39 119 79)(40 120 80)(41 129 81)(42 130 82)(43 121 83)(44 122 84)(45 123 85)(46 124 86)(47 125 87)(48 126 88)(49 127 89)(50 128 90)(131 211 171)(132 212 172)(133 213 173)(134 214 174)(135 215 175)(136 216 176)(137 217 177)(138 218 178)(139 219 179)(140 220 180)(141 221 181)(142 222 182)(143 223 183)(144 224 184)(145 225 185)(146 226 186)(147 227 187)(148 228 188)(149 229 189)(150 230 190)(151 231 191)(152 232 192)(153 233 193)(154 234 194)(155 235 195)(156 236 196)(157 237 197)(158 238 198)(159 239 199)(160 240 200)
(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 10)(2 9)(3 8)(4 7)(5 6)(11 19)(12 18)(13 17)(14 16)(21 26)(22 25)(23 24)(27 30)(28 29)(31 38)(32 37)(33 36)(34 35)(39 40)(41 50)(42 49)(43 48)(44 47)(45 46)(51 52)(53 60)(54 59)(55 58)(56 57)(61 66)(62 65)(63 64)(67 70)(68 69)(71 78)(72 77)(73 76)(74 75)(79 80)(81 90)(82 89)(83 88)(84 87)(85 86)(91 92)(93 100)(94 99)(95 98)(96 97)(101 106)(102 105)(103 104)(107 110)(108 109)(111 118)(112 117)(113 116)(114 115)(119 120)(121 126)(122 125)(123 124)(127 130)(128 129)(131 135)(132 134)(136 140)(137 139)(141 143)(144 150)(145 149)(146 148)(151 159)(152 158)(153 157)(154 156)(161 163)(164 170)(165 169)(166 168)(171 175)(172 174)(176 180)(177 179)(181 183)(184 190)(185 189)(186 188)(191 199)(192 198)(193 197)(194 196)(201 203)(204 210)(205 209)(206 208)(211 215)(212 214)(216 220)(217 219)(221 223)(224 230)(225 229)(226 228)(231 239)(232 238)(233 237)(234 236)
(1 165 41 150 24 158 40 136)(2 162 50 143 25 155 39 139)(3 169 49 146 26 152 38 132)(4 166 48 149 27 159 37 135)(5 163 47 142 28 156 36 138)(6 170 46 145 29 153 35 131)(7 167 45 148 30 160 34 134)(8 164 44 141 21 157 33 137)(9 161 43 144 22 154 32 140)(10 168 42 147 23 151 31 133)(11 125 222 108 236 116 218 96)(12 122 221 101 237 113 217 99)(13 129 230 104 238 120 216 92)(14 126 229 107 239 117 215 95)(15 123 228 110 240 114 214 98)(16 130 227 103 231 111 213 91)(17 127 226 106 232 118 212 94)(18 124 225 109 233 115 211 97)(19 121 224 102 234 112 220 100)(20 128 223 105 235 119 219 93)(51 208 82 187 63 191 71 173)(52 205 81 190 64 198 80 176)(53 202 90 183 65 195 79 179)(54 209 89 186 66 192 78 172)(55 206 88 189 67 199 77 175)(56 203 87 182 68 196 76 178)(57 210 86 185 69 193 75 171)(58 207 85 188 70 200 74 174)(59 204 84 181 61 197 73 177)(60 201 83 184 62 194 72 180)
G:=sub<Sym(240)| (1,92,52)(2,93,53)(3,94,54)(4,95,55)(5,96,56)(6,97,57)(7,98,58)(8,99,59)(9,100,60)(10,91,51)(11,203,163)(12,204,164)(13,205,165)(14,206,166)(15,207,167)(16,208,168)(17,209,169)(18,210,170)(19,201,161)(20,202,162)(21,101,61)(22,102,62)(23,103,63)(24,104,64)(25,105,65)(26,106,66)(27,107,67)(28,108,68)(29,109,69)(30,110,70)(31,111,71)(32,112,72)(33,113,73)(34,114,74)(35,115,75)(36,116,76)(37,117,77)(38,118,78)(39,119,79)(40,120,80)(41,129,81)(42,130,82)(43,121,83)(44,122,84)(45,123,85)(46,124,86)(47,125,87)(48,126,88)(49,127,89)(50,128,90)(131,211,171)(132,212,172)(133,213,173)(134,214,174)(135,215,175)(136,216,176)(137,217,177)(138,218,178)(139,219,179)(140,220,180)(141,221,181)(142,222,182)(143,223,183)(144,224,184)(145,225,185)(146,226,186)(147,227,187)(148,228,188)(149,229,189)(150,230,190)(151,231,191)(152,232,192)(153,233,193)(154,234,194)(155,235,195)(156,236,196)(157,237,197)(158,238,198)(159,239,199)(160,240,200), (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), (1,10)(2,9)(3,8)(4,7)(5,6)(11,19)(12,18)(13,17)(14,16)(21,26)(22,25)(23,24)(27,30)(28,29)(31,38)(32,37)(33,36)(34,35)(39,40)(41,50)(42,49)(43,48)(44,47)(45,46)(51,52)(53,60)(54,59)(55,58)(56,57)(61,66)(62,65)(63,64)(67,70)(68,69)(71,78)(72,77)(73,76)(74,75)(79,80)(81,90)(82,89)(83,88)(84,87)(85,86)(91,92)(93,100)(94,99)(95,98)(96,97)(101,106)(102,105)(103,104)(107,110)(108,109)(111,118)(112,117)(113,116)(114,115)(119,120)(121,126)(122,125)(123,124)(127,130)(128,129)(131,135)(132,134)(136,140)(137,139)(141,143)(144,150)(145,149)(146,148)(151,159)(152,158)(153,157)(154,156)(161,163)(164,170)(165,169)(166,168)(171,175)(172,174)(176,180)(177,179)(181,183)(184,190)(185,189)(186,188)(191,199)(192,198)(193,197)(194,196)(201,203)(204,210)(205,209)(206,208)(211,215)(212,214)(216,220)(217,219)(221,223)(224,230)(225,229)(226,228)(231,239)(232,238)(233,237)(234,236), (1,165,41,150,24,158,40,136)(2,162,50,143,25,155,39,139)(3,169,49,146,26,152,38,132)(4,166,48,149,27,159,37,135)(5,163,47,142,28,156,36,138)(6,170,46,145,29,153,35,131)(7,167,45,148,30,160,34,134)(8,164,44,141,21,157,33,137)(9,161,43,144,22,154,32,140)(10,168,42,147,23,151,31,133)(11,125,222,108,236,116,218,96)(12,122,221,101,237,113,217,99)(13,129,230,104,238,120,216,92)(14,126,229,107,239,117,215,95)(15,123,228,110,240,114,214,98)(16,130,227,103,231,111,213,91)(17,127,226,106,232,118,212,94)(18,124,225,109,233,115,211,97)(19,121,224,102,234,112,220,100)(20,128,223,105,235,119,219,93)(51,208,82,187,63,191,71,173)(52,205,81,190,64,198,80,176)(53,202,90,183,65,195,79,179)(54,209,89,186,66,192,78,172)(55,206,88,189,67,199,77,175)(56,203,87,182,68,196,76,178)(57,210,86,185,69,193,75,171)(58,207,85,188,70,200,74,174)(59,204,84,181,61,197,73,177)(60,201,83,184,62,194,72,180)>;
G:=Group( (1,92,52)(2,93,53)(3,94,54)(4,95,55)(5,96,56)(6,97,57)(7,98,58)(8,99,59)(9,100,60)(10,91,51)(11,203,163)(12,204,164)(13,205,165)(14,206,166)(15,207,167)(16,208,168)(17,209,169)(18,210,170)(19,201,161)(20,202,162)(21,101,61)(22,102,62)(23,103,63)(24,104,64)(25,105,65)(26,106,66)(27,107,67)(28,108,68)(29,109,69)(30,110,70)(31,111,71)(32,112,72)(33,113,73)(34,114,74)(35,115,75)(36,116,76)(37,117,77)(38,118,78)(39,119,79)(40,120,80)(41,129,81)(42,130,82)(43,121,83)(44,122,84)(45,123,85)(46,124,86)(47,125,87)(48,126,88)(49,127,89)(50,128,90)(131,211,171)(132,212,172)(133,213,173)(134,214,174)(135,215,175)(136,216,176)(137,217,177)(138,218,178)(139,219,179)(140,220,180)(141,221,181)(142,222,182)(143,223,183)(144,224,184)(145,225,185)(146,226,186)(147,227,187)(148,228,188)(149,229,189)(150,230,190)(151,231,191)(152,232,192)(153,233,193)(154,234,194)(155,235,195)(156,236,196)(157,237,197)(158,238,198)(159,239,199)(160,240,200), (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), (1,10)(2,9)(3,8)(4,7)(5,6)(11,19)(12,18)(13,17)(14,16)(21,26)(22,25)(23,24)(27,30)(28,29)(31,38)(32,37)(33,36)(34,35)(39,40)(41,50)(42,49)(43,48)(44,47)(45,46)(51,52)(53,60)(54,59)(55,58)(56,57)(61,66)(62,65)(63,64)(67,70)(68,69)(71,78)(72,77)(73,76)(74,75)(79,80)(81,90)(82,89)(83,88)(84,87)(85,86)(91,92)(93,100)(94,99)(95,98)(96,97)(101,106)(102,105)(103,104)(107,110)(108,109)(111,118)(112,117)(113,116)(114,115)(119,120)(121,126)(122,125)(123,124)(127,130)(128,129)(131,135)(132,134)(136,140)(137,139)(141,143)(144,150)(145,149)(146,148)(151,159)(152,158)(153,157)(154,156)(161,163)(164,170)(165,169)(166,168)(171,175)(172,174)(176,180)(177,179)(181,183)(184,190)(185,189)(186,188)(191,199)(192,198)(193,197)(194,196)(201,203)(204,210)(205,209)(206,208)(211,215)(212,214)(216,220)(217,219)(221,223)(224,230)(225,229)(226,228)(231,239)(232,238)(233,237)(234,236), (1,165,41,150,24,158,40,136)(2,162,50,143,25,155,39,139)(3,169,49,146,26,152,38,132)(4,166,48,149,27,159,37,135)(5,163,47,142,28,156,36,138)(6,170,46,145,29,153,35,131)(7,167,45,148,30,160,34,134)(8,164,44,141,21,157,33,137)(9,161,43,144,22,154,32,140)(10,168,42,147,23,151,31,133)(11,125,222,108,236,116,218,96)(12,122,221,101,237,113,217,99)(13,129,230,104,238,120,216,92)(14,126,229,107,239,117,215,95)(15,123,228,110,240,114,214,98)(16,130,227,103,231,111,213,91)(17,127,226,106,232,118,212,94)(18,124,225,109,233,115,211,97)(19,121,224,102,234,112,220,100)(20,128,223,105,235,119,219,93)(51,208,82,187,63,191,71,173)(52,205,81,190,64,198,80,176)(53,202,90,183,65,195,79,179)(54,209,89,186,66,192,78,172)(55,206,88,189,67,199,77,175)(56,203,87,182,68,196,76,178)(57,210,86,185,69,193,75,171)(58,207,85,188,70,200,74,174)(59,204,84,181,61,197,73,177)(60,201,83,184,62,194,72,180) );
G=PermutationGroup([[(1,92,52),(2,93,53),(3,94,54),(4,95,55),(5,96,56),(6,97,57),(7,98,58),(8,99,59),(9,100,60),(10,91,51),(11,203,163),(12,204,164),(13,205,165),(14,206,166),(15,207,167),(16,208,168),(17,209,169),(18,210,170),(19,201,161),(20,202,162),(21,101,61),(22,102,62),(23,103,63),(24,104,64),(25,105,65),(26,106,66),(27,107,67),(28,108,68),(29,109,69),(30,110,70),(31,111,71),(32,112,72),(33,113,73),(34,114,74),(35,115,75),(36,116,76),(37,117,77),(38,118,78),(39,119,79),(40,120,80),(41,129,81),(42,130,82),(43,121,83),(44,122,84),(45,123,85),(46,124,86),(47,125,87),(48,126,88),(49,127,89),(50,128,90),(131,211,171),(132,212,172),(133,213,173),(134,214,174),(135,215,175),(136,216,176),(137,217,177),(138,218,178),(139,219,179),(140,220,180),(141,221,181),(142,222,182),(143,223,183),(144,224,184),(145,225,185),(146,226,186),(147,227,187),(148,228,188),(149,229,189),(150,230,190),(151,231,191),(152,232,192),(153,233,193),(154,234,194),(155,235,195),(156,236,196),(157,237,197),(158,238,198),(159,239,199),(160,240,200)], [(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)], [(1,10),(2,9),(3,8),(4,7),(5,6),(11,19),(12,18),(13,17),(14,16),(21,26),(22,25),(23,24),(27,30),(28,29),(31,38),(32,37),(33,36),(34,35),(39,40),(41,50),(42,49),(43,48),(44,47),(45,46),(51,52),(53,60),(54,59),(55,58),(56,57),(61,66),(62,65),(63,64),(67,70),(68,69),(71,78),(72,77),(73,76),(74,75),(79,80),(81,90),(82,89),(83,88),(84,87),(85,86),(91,92),(93,100),(94,99),(95,98),(96,97),(101,106),(102,105),(103,104),(107,110),(108,109),(111,118),(112,117),(113,116),(114,115),(119,120),(121,126),(122,125),(123,124),(127,130),(128,129),(131,135),(132,134),(136,140),(137,139),(141,143),(144,150),(145,149),(146,148),(151,159),(152,158),(153,157),(154,156),(161,163),(164,170),(165,169),(166,168),(171,175),(172,174),(176,180),(177,179),(181,183),(184,190),(185,189),(186,188),(191,199),(192,198),(193,197),(194,196),(201,203),(204,210),(205,209),(206,208),(211,215),(212,214),(216,220),(217,219),(221,223),(224,230),(225,229),(226,228),(231,239),(232,238),(233,237),(234,236)], [(1,165,41,150,24,158,40,136),(2,162,50,143,25,155,39,139),(3,169,49,146,26,152,38,132),(4,166,48,149,27,159,37,135),(5,163,47,142,28,156,36,138),(6,170,46,145,29,153,35,131),(7,167,45,148,30,160,34,134),(8,164,44,141,21,157,33,137),(9,161,43,144,22,154,32,140),(10,168,42,147,23,151,31,133),(11,125,222,108,236,116,218,96),(12,122,221,101,237,113,217,99),(13,129,230,104,238,120,216,92),(14,126,229,107,239,117,215,95),(15,123,228,110,240,114,214,98),(16,130,227,103,231,111,213,91),(17,127,226,106,232,118,212,94),(18,124,225,109,233,115,211,97),(19,121,224,102,234,112,220,100),(20,128,223,105,235,119,219,93),(51,208,82,187,63,191,71,173),(52,205,81,190,64,198,80,176),(53,202,90,183,65,195,79,179),(54,209,89,186,66,192,78,172),(55,206,88,189,67,199,77,175),(56,203,87,182,68,196,76,178),(57,210,86,185,69,193,75,171),(58,207,85,188,70,200,74,174),(59,204,84,181,61,197,73,177),(60,201,83,184,62,194,72,180)]])
84 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 3A | 3B | 4A | 4B | 4C | 4D | 4E | 4F | 5 | 6A | ··· | 6F | 6G | 6H | 6I | 6J | 8A | ··· | 8H | 10A | 10B | 10C | 12A | 12B | 12C | 12D | 12E | ··· | 12L | 15A | 15B | 20A | 20B | 20C | 20D | 24A | ··· | 24P | 30A | ··· | 30F | 60A | ··· | 60H |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 6 | ··· | 6 | 6 | 6 | 6 | 6 | 8 | ··· | 8 | 10 | 10 | 10 | 12 | 12 | 12 | 12 | 12 | ··· | 12 | 15 | 15 | 20 | 20 | 20 | 20 | 24 | ··· | 24 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 10 | 10 | 1 | 1 | 2 | 2 | 5 | 5 | 5 | 5 | 4 | 1 | ··· | 1 | 10 | 10 | 10 | 10 | 10 | ··· | 10 | 4 | 4 | 4 | 2 | 2 | 2 | 2 | 5 | ··· | 5 | 4 | 4 | 4 | 4 | 4 | 4 | 10 | ··· | 10 | 4 | ··· | 4 | 4 | ··· | 4 |
84 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | |||||||||||||||||||
| image | C1 | C2 | C2 | C3 | C4 | C4 | C6 | C6 | C8 | C12 | C12 | C24 | D4 | M4(2) | C3×D4 | C3×M4(2) | F5 | C2×F5 | C3×F5 | D5⋊C8 | C4.F5 | C22⋊F5 | C6×F5 | C3×D5⋊C8 | C3×C4.F5 | C3×C22⋊F5 |
| kernel | C3×D10⋊C8 | C6×C5⋊C8 | D5×C2×C12 | D10⋊C8 | C2×C60 | D5×C2×C6 | C2×C5⋊C8 | C2×C4×D5 | C6×D5 | C2×C20 | C22×D5 | D10 | C3×Dic5 | C30 | Dic5 | C10 | C2×C12 | C2×C6 | C2×C4 | C6 | C6 | C6 | C22 | C2 | C2 | C2 |
| # reps | 1 | 2 | 1 | 2 | 2 | 2 | 4 | 2 | 8 | 4 | 4 | 16 | 2 | 2 | 4 | 4 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
Matrix representation of C3×D10⋊C8 ►in GL6(𝔽241)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 225 | 0 | 0 | 0 |
| 0 | 0 | 0 | 225 | 0 | 0 |
| 0 | 0 | 0 | 0 | 225 | 0 |
| 0 | 0 | 0 | 0 | 0 | 225 |
| 240 | 0 | 0 | 0 | 0 | 0 |
| 0 | 240 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 240 | 0 |
| 0 | 0 | 0 | 1 | 0 | 240 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 240 | 1 | 0 | 0 |
| 240 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 240 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 240 |
| 0 | 0 | 0 | 1 | 240 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 177 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 82 | 82 | 142 | 34 |
| 0 | 0 | 224 | 116 | 43 | 116 |
| 0 | 0 | 125 | 198 | 125 | 17 |
| 0 | 0 | 207 | 99 | 159 | 159 |
G:=sub<GL(6,GF(241))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,225,0,0,0,0,0,0,225,0,0,0,0,0,0,225,0,0,0,0,0,0,225],[240,0,0,0,0,0,0,240,0,0,0,0,0,0,0,0,0,240,0,0,1,1,1,1,0,0,240,0,0,0,0,0,0,240,0,0],[240,0,0,0,0,0,0,1,0,0,0,0,0,0,240,0,0,0,0,0,1,1,1,1,0,0,0,0,0,240,0,0,0,0,240,0],[0,177,0,0,0,0,1,0,0,0,0,0,0,0,82,224,125,207,0,0,82,116,198,99,0,0,142,43,125,159,0,0,34,116,17,159] >;
C3×D10⋊C8 in GAP, Magma, Sage, TeX
C_3\times D_{10}\rtimes C_8 % in TeX
G:=Group("C3xD10:C8"); // GroupNames label
G:=SmallGroup(480,283);
// by ID
G=gap.SmallGroup(480,283);
# by ID
G:=PCGroup([7,-2,-2,-3,-2,-2,-2,-5,84,365,344,136,9414,1595]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^10=c^2=d^8=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c=b^-1,d*b*d^-1=b^3,d*c*d^-1=b^7*c>;
// generators/relations