direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C15⋊8M4(2), C30⋊8M4(2), C23.4(C3⋊F5), (C22×C6).7F5, C15⋊21(C2×M4(2)), (C22×C30).7C4, C6⋊2(C22.F5), C15⋊C8⋊13C22, C6.43(C22×F5), C30.81(C22×C4), C10⋊2(C4.Dic3), (C6×Dic5).23C4, (C2×Dic5).210D6, (C22×C10).9Dic3, Dic5.19(C2×Dic3), (C2×Dic5).14Dic3, (C3×Dic5).68C23, Dic5.54(C22×S3), (C22×Dic5).12S3, C10.12(C22×Dic3), (C6×Dic5).269C22, C5⋊3(C2×C4.Dic3), C22.8(C2×C3⋊F5), C3⋊3(C2×C22.F5), (C2×C15⋊C8)⋊12C2, (C2×C6).50(C2×F5), (C2×C30).44(C2×C4), C2.12(C22×C3⋊F5), (C2×C6×Dic5).17C2, (C3×Dic5).69(C2×C4), (C2×C10).20(C2×Dic3), SmallGroup(480,1071)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C15⋊8M4(2)
G = < a,b,c,d | a2=b15=c8=d2=1, ab=ba, ac=ca, ad=da, cbc-1=b2, bd=db, dcd=c5 >
Subgroups: 460 in 136 conjugacy classes, 65 normal (27 characteristic)
C1, C2, C2, C2, C3, C4, C22, C22, C22, C5, C6, C6, C6, C8, C2×C4, C23, C10, C10, C10, C12, C2×C6, C2×C6, C2×C6, C15, C2×C8, M4(2), C22×C4, Dic5, Dic5, C2×C10, C2×C10, C2×C10, C3⋊C8, C2×C12, C22×C6, C30, C30, C30, C2×M4(2), C5⋊C8, C2×Dic5, C2×Dic5, C22×C10, C2×C3⋊C8, C4.Dic3, C22×C12, C3×Dic5, C3×Dic5, C2×C30, C2×C30, C2×C30, C2×C5⋊C8, C22.F5, C22×Dic5, C2×C4.Dic3, C15⋊C8, C6×Dic5, C6×Dic5, C22×C30, C2×C22.F5, C2×C15⋊C8, C15⋊8M4(2), C2×C6×Dic5, C2×C15⋊8M4(2)
Quotients: C1, C2, C4, C22, S3, C2×C4, C23, Dic3, D6, M4(2), C22×C4, F5, C2×Dic3, C22×S3, C2×M4(2), C2×F5, C4.Dic3, C22×Dic3, C3⋊F5, C22.F5, C22×F5, C2×C4.Dic3, C2×C3⋊F5, C2×C22.F5, C15⋊8M4(2), C22×C3⋊F5, C2×C15⋊8M4(2)
►On 240 points
Generators in S240
(1 70)(2 71)(3 72)(4 73)(5 74)(6 75)(7 61)(8 62)(9 63)(10 64)(11 65)(12 66)(13 67)(14 68)(15 69)(16 80)(17 81)(18 82)(19 83)(20 84)(21 85)(22 86)(23 87)(24 88)(25 89)(26 90)(27 76)(28 77)(29 78)(30 79)(31 100)(32 101)(33 102)(34 103)(35 104)(36 105)(37 91)(38 92)(39 93)(40 94)(41 95)(42 96)(43 97)(44 98)(45 99)(46 120)(47 106)(48 107)(49 108)(50 109)(51 110)(52 111)(53 112)(54 113)(55 114)(56 115)(57 116)(58 117)(59 118)(60 119)(121 191)(122 192)(123 193)(124 194)(125 195)(126 181)(127 182)(128 183)(129 184)(130 185)(131 186)(132 187)(133 188)(134 189)(135 190)(136 196)(137 197)(138 198)(139 199)(140 200)(141 201)(142 202)(143 203)(144 204)(145 205)(146 206)(147 207)(148 208)(149 209)(150 210)(151 211)(152 212)(153 213)(154 214)(155 215)(156 216)(157 217)(158 218)(159 219)(160 220)(161 221)(162 222)(163 223)(164 224)(165 225)(166 227)(167 228)(168 229)(169 230)(170 231)(171 232)(172 233)(173 234)(174 235)(175 236)(176 237)(177 238)(178 239)(179 240)(180 226)
(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)
(1 233 52 196 19 211 32 181)(2 226 56 198 20 219 36 183)(3 234 60 200 21 212 40 185)(4 227 49 202 22 220 44 187)(5 235 53 204 23 213 33 189)(6 228 57 206 24 221 37 191)(7 236 46 208 25 214 41 193)(8 229 50 210 26 222 45 195)(9 237 54 197 27 215 34 182)(10 230 58 199 28 223 38 184)(11 238 47 201 29 216 42 186)(12 231 51 203 30 224 31 188)(13 239 55 205 16 217 35 190)(14 232 59 207 17 225 39 192)(15 240 48 209 18 218 43 194)(61 175 120 148 89 154 95 123)(62 168 109 150 90 162 99 125)(63 176 113 137 76 155 103 127)(64 169 117 139 77 163 92 129)(65 177 106 141 78 156 96 131)(66 170 110 143 79 164 100 133)(67 178 114 145 80 157 104 135)(68 171 118 147 81 165 93 122)(69 179 107 149 82 158 97 124)(70 172 111 136 83 151 101 126)(71 180 115 138 84 159 105 128)(72 173 119 140 85 152 94 130)(73 166 108 142 86 160 98 132)(74 174 112 144 87 153 102 134)(75 167 116 146 88 161 91 121)
(1 70)(2 71)(3 72)(4 73)(5 74)(6 75)(7 61)(8 62)(9 63)(10 64)(11 65)(12 66)(13 67)(14 68)(15 69)(16 80)(17 81)(18 82)(19 83)(20 84)(21 85)(22 86)(23 87)(24 88)(25 89)(26 90)(27 76)(28 77)(29 78)(30 79)(31 100)(32 101)(33 102)(34 103)(35 104)(36 105)(37 91)(38 92)(39 93)(40 94)(41 95)(42 96)(43 97)(44 98)(45 99)(46 120)(47 106)(48 107)(49 108)(50 109)(51 110)(52 111)(53 112)(54 113)(55 114)(56 115)(57 116)(58 117)(59 118)(60 119)(121 206)(122 207)(123 208)(124 209)(125 210)(126 196)(127 197)(128 198)(129 199)(130 200)(131 201)(132 202)(133 203)(134 204)(135 205)(136 181)(137 182)(138 183)(139 184)(140 185)(141 186)(142 187)(143 188)(144 189)(145 190)(146 191)(147 192)(148 193)(149 194)(150 195)(151 233)(152 234)(153 235)(154 236)(155 237)(156 238)(157 239)(158 240)(159 226)(160 227)(161 228)(162 229)(163 230)(164 231)(165 232)(166 220)(167 221)(168 222)(169 223)(170 224)(171 225)(172 211)(173 212)(174 213)(175 214)(176 215)(177 216)(178 217)(179 218)(180 219)
G:=sub<Sym(240)| (1,70)(2,71)(3,72)(4,73)(5,74)(6,75)(7,61)(8,62)(9,63)(10,64)(11,65)(12,66)(13,67)(14,68)(15,69)(16,80)(17,81)(18,82)(19,83)(20,84)(21,85)(22,86)(23,87)(24,88)(25,89)(26,90)(27,76)(28,77)(29,78)(30,79)(31,100)(32,101)(33,102)(34,103)(35,104)(36,105)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,99)(46,120)(47,106)(48,107)(49,108)(50,109)(51,110)(52,111)(53,112)(54,113)(55,114)(56,115)(57,116)(58,117)(59,118)(60,119)(121,191)(122,192)(123,193)(124,194)(125,195)(126,181)(127,182)(128,183)(129,184)(130,185)(131,186)(132,187)(133,188)(134,189)(135,190)(136,196)(137,197)(138,198)(139,199)(140,200)(141,201)(142,202)(143,203)(144,204)(145,205)(146,206)(147,207)(148,208)(149,209)(150,210)(151,211)(152,212)(153,213)(154,214)(155,215)(156,216)(157,217)(158,218)(159,219)(160,220)(161,221)(162,222)(163,223)(164,224)(165,225)(166,227)(167,228)(168,229)(169,230)(170,231)(171,232)(172,233)(173,234)(174,235)(175,236)(176,237)(177,238)(178,239)(179,240)(180,226), (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), (1,233,52,196,19,211,32,181)(2,226,56,198,20,219,36,183)(3,234,60,200,21,212,40,185)(4,227,49,202,22,220,44,187)(5,235,53,204,23,213,33,189)(6,228,57,206,24,221,37,191)(7,236,46,208,25,214,41,193)(8,229,50,210,26,222,45,195)(9,237,54,197,27,215,34,182)(10,230,58,199,28,223,38,184)(11,238,47,201,29,216,42,186)(12,231,51,203,30,224,31,188)(13,239,55,205,16,217,35,190)(14,232,59,207,17,225,39,192)(15,240,48,209,18,218,43,194)(61,175,120,148,89,154,95,123)(62,168,109,150,90,162,99,125)(63,176,113,137,76,155,103,127)(64,169,117,139,77,163,92,129)(65,177,106,141,78,156,96,131)(66,170,110,143,79,164,100,133)(67,178,114,145,80,157,104,135)(68,171,118,147,81,165,93,122)(69,179,107,149,82,158,97,124)(70,172,111,136,83,151,101,126)(71,180,115,138,84,159,105,128)(72,173,119,140,85,152,94,130)(73,166,108,142,86,160,98,132)(74,174,112,144,87,153,102,134)(75,167,116,146,88,161,91,121), (1,70)(2,71)(3,72)(4,73)(5,74)(6,75)(7,61)(8,62)(9,63)(10,64)(11,65)(12,66)(13,67)(14,68)(15,69)(16,80)(17,81)(18,82)(19,83)(20,84)(21,85)(22,86)(23,87)(24,88)(25,89)(26,90)(27,76)(28,77)(29,78)(30,79)(31,100)(32,101)(33,102)(34,103)(35,104)(36,105)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,99)(46,120)(47,106)(48,107)(49,108)(50,109)(51,110)(52,111)(53,112)(54,113)(55,114)(56,115)(57,116)(58,117)(59,118)(60,119)(121,206)(122,207)(123,208)(124,209)(125,210)(126,196)(127,197)(128,198)(129,199)(130,200)(131,201)(132,202)(133,203)(134,204)(135,205)(136,181)(137,182)(138,183)(139,184)(140,185)(141,186)(142,187)(143,188)(144,189)(145,190)(146,191)(147,192)(148,193)(149,194)(150,195)(151,233)(152,234)(153,235)(154,236)(155,237)(156,238)(157,239)(158,240)(159,226)(160,227)(161,228)(162,229)(163,230)(164,231)(165,232)(166,220)(167,221)(168,222)(169,223)(170,224)(171,225)(172,211)(173,212)(174,213)(175,214)(176,215)(177,216)(178,217)(179,218)(180,219)>;
G:=Group( (1,70)(2,71)(3,72)(4,73)(5,74)(6,75)(7,61)(8,62)(9,63)(10,64)(11,65)(12,66)(13,67)(14,68)(15,69)(16,80)(17,81)(18,82)(19,83)(20,84)(21,85)(22,86)(23,87)(24,88)(25,89)(26,90)(27,76)(28,77)(29,78)(30,79)(31,100)(32,101)(33,102)(34,103)(35,104)(36,105)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,99)(46,120)(47,106)(48,107)(49,108)(50,109)(51,110)(52,111)(53,112)(54,113)(55,114)(56,115)(57,116)(58,117)(59,118)(60,119)(121,191)(122,192)(123,193)(124,194)(125,195)(126,181)(127,182)(128,183)(129,184)(130,185)(131,186)(132,187)(133,188)(134,189)(135,190)(136,196)(137,197)(138,198)(139,199)(140,200)(141,201)(142,202)(143,203)(144,204)(145,205)(146,206)(147,207)(148,208)(149,209)(150,210)(151,211)(152,212)(153,213)(154,214)(155,215)(156,216)(157,217)(158,218)(159,219)(160,220)(161,221)(162,222)(163,223)(164,224)(165,225)(166,227)(167,228)(168,229)(169,230)(170,231)(171,232)(172,233)(173,234)(174,235)(175,236)(176,237)(177,238)(178,239)(179,240)(180,226), (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), (1,233,52,196,19,211,32,181)(2,226,56,198,20,219,36,183)(3,234,60,200,21,212,40,185)(4,227,49,202,22,220,44,187)(5,235,53,204,23,213,33,189)(6,228,57,206,24,221,37,191)(7,236,46,208,25,214,41,193)(8,229,50,210,26,222,45,195)(9,237,54,197,27,215,34,182)(10,230,58,199,28,223,38,184)(11,238,47,201,29,216,42,186)(12,231,51,203,30,224,31,188)(13,239,55,205,16,217,35,190)(14,232,59,207,17,225,39,192)(15,240,48,209,18,218,43,194)(61,175,120,148,89,154,95,123)(62,168,109,150,90,162,99,125)(63,176,113,137,76,155,103,127)(64,169,117,139,77,163,92,129)(65,177,106,141,78,156,96,131)(66,170,110,143,79,164,100,133)(67,178,114,145,80,157,104,135)(68,171,118,147,81,165,93,122)(69,179,107,149,82,158,97,124)(70,172,111,136,83,151,101,126)(71,180,115,138,84,159,105,128)(72,173,119,140,85,152,94,130)(73,166,108,142,86,160,98,132)(74,174,112,144,87,153,102,134)(75,167,116,146,88,161,91,121), (1,70)(2,71)(3,72)(4,73)(5,74)(6,75)(7,61)(8,62)(9,63)(10,64)(11,65)(12,66)(13,67)(14,68)(15,69)(16,80)(17,81)(18,82)(19,83)(20,84)(21,85)(22,86)(23,87)(24,88)(25,89)(26,90)(27,76)(28,77)(29,78)(30,79)(31,100)(32,101)(33,102)(34,103)(35,104)(36,105)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,99)(46,120)(47,106)(48,107)(49,108)(50,109)(51,110)(52,111)(53,112)(54,113)(55,114)(56,115)(57,116)(58,117)(59,118)(60,119)(121,206)(122,207)(123,208)(124,209)(125,210)(126,196)(127,197)(128,198)(129,199)(130,200)(131,201)(132,202)(133,203)(134,204)(135,205)(136,181)(137,182)(138,183)(139,184)(140,185)(141,186)(142,187)(143,188)(144,189)(145,190)(146,191)(147,192)(148,193)(149,194)(150,195)(151,233)(152,234)(153,235)(154,236)(155,237)(156,238)(157,239)(158,240)(159,226)(160,227)(161,228)(162,229)(163,230)(164,231)(165,232)(166,220)(167,221)(168,222)(169,223)(170,224)(171,225)(172,211)(173,212)(174,213)(175,214)(176,215)(177,216)(178,217)(179,218)(180,219) );
G=PermutationGroup([[(1,70),(2,71),(3,72),(4,73),(5,74),(6,75),(7,61),(8,62),(9,63),(10,64),(11,65),(12,66),(13,67),(14,68),(15,69),(16,80),(17,81),(18,82),(19,83),(20,84),(21,85),(22,86),(23,87),(24,88),(25,89),(26,90),(27,76),(28,77),(29,78),(30,79),(31,100),(32,101),(33,102),(34,103),(35,104),(36,105),(37,91),(38,92),(39,93),(40,94),(41,95),(42,96),(43,97),(44,98),(45,99),(46,120),(47,106),(48,107),(49,108),(50,109),(51,110),(52,111),(53,112),(54,113),(55,114),(56,115),(57,116),(58,117),(59,118),(60,119),(121,191),(122,192),(123,193),(124,194),(125,195),(126,181),(127,182),(128,183),(129,184),(130,185),(131,186),(132,187),(133,188),(134,189),(135,190),(136,196),(137,197),(138,198),(139,199),(140,200),(141,201),(142,202),(143,203),(144,204),(145,205),(146,206),(147,207),(148,208),(149,209),(150,210),(151,211),(152,212),(153,213),(154,214),(155,215),(156,216),(157,217),(158,218),(159,219),(160,220),(161,221),(162,222),(163,223),(164,224),(165,225),(166,227),(167,228),(168,229),(169,230),(170,231),(171,232),(172,233),(173,234),(174,235),(175,236),(176,237),(177,238),(178,239),(179,240),(180,226)], [(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)], [(1,233,52,196,19,211,32,181),(2,226,56,198,20,219,36,183),(3,234,60,200,21,212,40,185),(4,227,49,202,22,220,44,187),(5,235,53,204,23,213,33,189),(6,228,57,206,24,221,37,191),(7,236,46,208,25,214,41,193),(8,229,50,210,26,222,45,195),(9,237,54,197,27,215,34,182),(10,230,58,199,28,223,38,184),(11,238,47,201,29,216,42,186),(12,231,51,203,30,224,31,188),(13,239,55,205,16,217,35,190),(14,232,59,207,17,225,39,192),(15,240,48,209,18,218,43,194),(61,175,120,148,89,154,95,123),(62,168,109,150,90,162,99,125),(63,176,113,137,76,155,103,127),(64,169,117,139,77,163,92,129),(65,177,106,141,78,156,96,131),(66,170,110,143,79,164,100,133),(67,178,114,145,80,157,104,135),(68,171,118,147,81,165,93,122),(69,179,107,149,82,158,97,124),(70,172,111,136,83,151,101,126),(71,180,115,138,84,159,105,128),(72,173,119,140,85,152,94,130),(73,166,108,142,86,160,98,132),(74,174,112,144,87,153,102,134),(75,167,116,146,88,161,91,121)], [(1,70),(2,71),(3,72),(4,73),(5,74),(6,75),(7,61),(8,62),(9,63),(10,64),(11,65),(12,66),(13,67),(14,68),(15,69),(16,80),(17,81),(18,82),(19,83),(20,84),(21,85),(22,86),(23,87),(24,88),(25,89),(26,90),(27,76),(28,77),(29,78),(30,79),(31,100),(32,101),(33,102),(34,103),(35,104),(36,105),(37,91),(38,92),(39,93),(40,94),(41,95),(42,96),(43,97),(44,98),(45,99),(46,120),(47,106),(48,107),(49,108),(50,109),(51,110),(52,111),(53,112),(54,113),(55,114),(56,115),(57,116),(58,117),(59,118),(60,119),(121,206),(122,207),(123,208),(124,209),(125,210),(126,196),(127,197),(128,198),(129,199),(130,200),(131,201),(132,202),(133,203),(134,204),(135,205),(136,181),(137,182),(138,183),(139,184),(140,185),(141,186),(142,187),(143,188),(144,189),(145,190),(146,191),(147,192),(148,193),(149,194),(150,195),(151,233),(152,234),(153,235),(154,236),(155,237),(156,238),(157,239),(158,240),(159,226),(160,227),(161,228),(162,229),(163,230),(164,231),(165,232),(166,220),(167,221),(168,222),(169,223),(170,224),(171,225),(172,211),(173,212),(174,213),(175,214),(176,215),(177,216),(178,217),(179,218),(180,219)]])
60 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 5 | 6A | ··· | 6G | 8A | ··· | 8H | 10A | ··· | 10G | 12A | ··· | 12H | 15A | 15B | 30A | ··· | 30N |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 6 | ··· | 6 | 8 | ··· | 8 | 10 | ··· | 10 | 12 | ··· | 12 | 15 | 15 | 30 | ··· | 30 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 5 | 5 | 5 | 5 | 10 | 10 | 4 | 2 | ··· | 2 | 30 | ··· | 30 | 4 | ··· | 4 | 10 | ··· | 10 | 4 | 4 | 4 | ··· | 4 |
60 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | - | + | - | + | + | - | |||||||
| image | C1 | C2 | C2 | C2 | C4 | C4 | S3 | Dic3 | D6 | Dic3 | M4(2) | C4.Dic3 | F5 | C2×F5 | C3⋊F5 | C22.F5 | C2×C3⋊F5 | C15⋊8M4(2) |
| kernel | C2×C15⋊8M4(2) | C2×C15⋊C8 | C15⋊8M4(2) | C2×C6×Dic5 | C6×Dic5 | C22×C30 | C22×Dic5 | C2×Dic5 | C2×Dic5 | C22×C10 | C30 | C10 | C22×C6 | C2×C6 | C23 | C6 | C22 | C2 |
| # reps | 1 | 2 | 4 | 1 | 6 | 2 | 1 | 3 | 3 | 1 | 4 | 8 | 1 | 3 | 2 | 4 | 6 | 8 |
Matrix representation of C2×C15⋊8M4(2) ►in GL6(𝔽241)
| 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 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 15 | 0 | 0 | 0 | 0 | 0 |
| 71 | 225 | 0 | 0 | 0 | 0 |
| 0 | 0 | 51 | 52 | 0 | 0 |
| 0 | 0 | 190 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 240 | 240 |
| 0 | 0 | 0 | 0 | 191 | 190 |
| 40 | 64 | 0 | 0 | 0 | 0 |
| 39 | 201 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 150 | 106 | 0 | 0 |
| 0 | 0 | 31 | 91 | 0 | 0 |
| 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 |
G:=sub<GL(6,GF(241))| [240,0,0,0,0,0,0,240,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[15,71,0,0,0,0,0,225,0,0,0,0,0,0,51,190,0,0,0,0,52,0,0,0,0,0,0,0,240,191,0,0,0,0,240,190],[40,39,0,0,0,0,64,201,0,0,0,0,0,0,0,0,150,31,0,0,0,0,106,91,0,0,1,0,0,0,0,0,0,1,0,0],[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] >;
C2×C15⋊8M4(2) in GAP, Magma, Sage, TeX
C_2\times C_{15}\rtimes_8M_4(2) % in TeX
G:=Group("C2xC15:8M4(2)"); // GroupNames label
G:=SmallGroup(480,1071);
// by ID
G=gap.SmallGroup(480,1071);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,422,80,2693,14118,2379]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^15=c^8=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^2,b*d=d*b,d*c*d=c^5>;
// generators/relations