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G = C3×D101C8order 480 = 25·3·5

Direct product of C3 and D101C8

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

Aliases: C3×D101C8, D101C24, C60.230D4, C12.71D20, C30.30M4(2), (C2×C40)⋊1C6, (C6×D5)⋊3C8, (C2×C24)⋊1D5, (C2×C120)⋊1C2, C2.5(D5×C24), C6.20(C8×D5), C30.52(C2×C8), C4.19(C3×D20), C20.52(C3×D4), C1511(C22⋊C8), C10.14(C2×C24), (C2×C12).444D10, C6.12(C8⋊D5), (C6×Dic5).14C4, (C2×Dic5).5C12, (C22×D5).3C12, C22.11(D5×C12), C10.8(C3×M4(2)), C12.120(C5⋊D4), C30.85(C22⋊C4), (C2×C60).544C22, C6.38(D10⋊C4), (C2×C8)⋊1(C3×D5), C53(C3×C22⋊C8), (D5×C2×C6).9C4, (C2×C4×D5).6C6, (C2×C52C8)⋊9C6, (C6×C52C8)⋊23C2, (D5×C2×C12).21C2, (C2×C4).94(C6×D5), (C2×C6).60(C4×D5), C2.3(C3×C8⋊D5), C4.27(C3×C5⋊D4), (C2×C10).32(C2×C12), (C2×C20).110(C2×C6), (C2×C30).146(C2×C4), C2.1(C3×D10⋊C4), C10.17(C3×C22⋊C4), SmallGroup(480,98)

Series: Derived Chief Lower central Upper central

C1C10 — C3×D101C8
C1C5C10C2×C10C2×C20C2×C60D5×C2×C12 — C3×D101C8
C5C10 — C3×D101C8
C1C2×C12C2×C24

Generators and relations for C3×D101C8
 G = < a,b,c,d | a3=b10=c2=d8=1, ab=ba, ac=ca, ad=da, cbc=b-1, bd=db, dcd-1=b5c >

Subgroups: 320 in 100 conjugacy classes, 50 normal (46 characteristic)
C1, C2 [×3], C2 [×2], C3, C4 [×2], C4, C22, C22 [×4], C5, C6 [×3], C6 [×2], C8 [×2], C2×C4, C2×C4 [×3], C23, D5 [×2], C10 [×3], C12 [×2], C12, C2×C6, C2×C6 [×4], C15, C2×C8, C2×C8, C22×C4, Dic5, C20 [×2], D10 [×2], D10 [×2], C2×C10, C24 [×2], C2×C12, C2×C12 [×3], C22×C6, C3×D5 [×2], C30 [×3], C22⋊C8, C52C8, C40, C4×D5 [×2], C2×Dic5, C2×C20, C22×D5, C2×C24, C2×C24, C22×C12, C3×Dic5, C60 [×2], C6×D5 [×2], C6×D5 [×2], C2×C30, C2×C52C8, C2×C40, C2×C4×D5, C3×C22⋊C8, C3×C52C8, C120, D5×C12 [×2], C6×Dic5, C2×C60, D5×C2×C6, D101C8, C6×C52C8, C2×C120, D5×C2×C12, C3×D101C8
Quotients: C1, C2 [×3], C3, C4 [×2], C22, C6 [×3], C8 [×2], C2×C4, D4 [×2], D5, C12 [×2], C2×C6, C22⋊C4, C2×C8, M4(2), D10, C24 [×2], C2×C12, C3×D4 [×2], C3×D5, C22⋊C8, C4×D5, D20, C5⋊D4, C3×C22⋊C4, C2×C24, C3×M4(2), C6×D5, C8×D5, C8⋊D5, D10⋊C4, C3×C22⋊C8, D5×C12, C3×D20, C3×C5⋊D4, D101C8, D5×C24, C3×C8⋊D5, C3×D10⋊C4, C3×D101C8

Smallest permutation representation of C3×D101C8
On 240 points
Generators in S240
(1 100 60)(2 91 51)(3 92 52)(4 93 53)(5 94 54)(6 95 55)(7 96 56)(8 97 57)(9 98 58)(10 99 59)(11 205 165)(12 206 166)(13 207 167)(14 208 168)(15 209 169)(16 210 170)(17 201 161)(18 202 162)(19 203 163)(20 204 164)(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)(41 121 81)(42 122 82)(43 123 83)(44 124 84)(45 125 85)(46 126 86)(47 127 87)(48 128 88)(49 129 89)(50 130 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 15)(12 14)(16 20)(17 19)(21 28)(22 27)(23 26)(24 25)(29 30)(31 38)(32 37)(33 36)(34 35)(39 40)(41 48)(42 47)(43 46)(44 45)(49 50)(51 58)(52 57)(53 56)(54 55)(59 60)(61 68)(62 67)(63 66)(64 65)(69 70)(71 78)(72 77)(73 76)(74 75)(79 80)(81 88)(82 87)(83 86)(84 85)(89 90)(91 98)(92 97)(93 96)(94 95)(99 100)(101 108)(102 107)(103 106)(104 105)(109 110)(111 118)(112 117)(113 116)(114 115)(119 120)(121 128)(122 127)(123 126)(124 125)(129 130)(131 133)(134 140)(135 139)(136 138)(141 143)(144 150)(145 149)(146 148)(151 153)(154 160)(155 159)(156 158)(161 163)(164 170)(165 169)(166 168)(171 173)(174 180)(175 179)(176 178)(181 183)(184 190)(185 189)(186 188)(191 193)(194 200)(195 199)(196 198)(201 203)(204 210)(205 209)(206 208)(211 213)(214 220)(215 219)(216 218)(221 223)(224 230)(225 229)(226 228)(231 233)(234 240)(235 239)(236 238)
(1 165 45 145 25 160 40 140)(2 166 46 146 26 151 31 131)(3 167 47 147 27 152 32 132)(4 168 48 148 28 153 33 133)(5 169 49 149 29 154 34 134)(6 170 50 150 30 155 35 135)(7 161 41 141 21 156 36 136)(8 162 42 142 22 157 37 137)(9 163 43 143 23 158 38 138)(10 164 44 144 24 159 39 139)(11 125 225 105 240 120 220 100)(12 126 226 106 231 111 211 91)(13 127 227 107 232 112 212 92)(14 128 228 108 233 113 213 93)(15 129 229 109 234 114 214 94)(16 130 230 110 235 115 215 95)(17 121 221 101 236 116 216 96)(18 122 222 102 237 117 217 97)(19 123 223 103 238 118 218 98)(20 124 224 104 239 119 219 99)(51 206 86 186 66 191 71 171)(52 207 87 187 67 192 72 172)(53 208 88 188 68 193 73 173)(54 209 89 189 69 194 74 174)(55 210 90 190 70 195 75 175)(56 201 81 181 61 196 76 176)(57 202 82 182 62 197 77 177)(58 203 83 183 63 198 78 178)(59 204 84 184 64 199 79 179)(60 205 85 185 65 200 80 180)

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

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

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

156 conjugacy classes

class 1 2A2B2C2D2E3A3B4A4B4C4D4E4F5A5B6A···6F6G6H6I6J8A8B8C8D8E8F8G8H10A···10F12A···12H12I12J12K12L15A15B15C15D20A···20H24A···24H24I···24P30A···30L40A···40P60A···60P120A···120AF
order12222233444444556···666668888888810···1012···12121212121515151520···2024···2424···2430···3040···4060···60120···120
size111110101111111010221···1101010102222101010102···21···11010101022222···22···210···102···22···22···22···2

156 irreducible representations

dim11111111111111222222222222222222
type++++++++
imageC1C2C2C2C3C4C4C6C6C6C8C12C12C24D4D5M4(2)D10C3×D4C3×D5D20C5⋊D4C4×D5C3×M4(2)C6×D5C8×D5C8⋊D5C3×D20C3×C5⋊D4D5×C12D5×C24C3×C8⋊D5
kernelC3×D101C8C6×C52C8C2×C120D5×C2×C12D101C8C6×Dic5D5×C2×C6C2×C52C8C2×C40C2×C4×D5C6×D5C2×Dic5C22×D5D10C60C2×C24C30C2×C12C20C2×C8C12C12C2×C6C10C2×C4C6C6C4C4C22C2C2
# reps11112222228441622224444444888881616

Matrix representation of C3×D101C8 in GL4(𝔽241) generated by

225000
022500
002250
000225
,
2405100
19019000
002400
000240
,
2405100
0100
002400
00711
,
211000
021100
0068192
0076173
G:=sub<GL(4,GF(241))| [225,0,0,0,0,225,0,0,0,0,225,0,0,0,0,225],[240,190,0,0,51,190,0,0,0,0,240,0,0,0,0,240],[240,0,0,0,51,1,0,0,0,0,240,71,0,0,0,1],[211,0,0,0,0,211,0,0,0,0,68,76,0,0,192,173] >;

C3×D101C8 in GAP, Magma, Sage, TeX

C_3\times D_{10}\rtimes_1C_8
% in TeX

G:=Group("C3xD10:1C8");
// GroupNames label

G:=SmallGroup(480,98);
// by ID

G=gap.SmallGroup(480,98);
# by ID

G:=PCGroup([7,-2,-2,-3,-2,-2,-2,-5,365,92,136,18822]);
// 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,b*d=d*b,d*c*d^-1=b^5*c>;
// generators/relations

׿
×
𝔽