metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C22.4D60, C23.20D30, (C2×C4).9D30, C2.8(C2×D60), (C2×C30).4D4, (C2×C6).9D20, C22⋊C4⋊6D15, C60⋊5C4⋊11C2, C6.34(C2×D20), (C2×C20).35D6, (C2×C10).9D12, D30⋊3C4⋊7C2, C10.35(C2×D12), (C2×C12).35D10, C30.262(C2×D4), (C2×C60).18C22, (C22×C10).76D6, (C22×C6).61D10, C30.217(C4○D4), C6.94(D4⋊2D5), (C2×C30).283C23, (C22×Dic15)⋊2C2, C3⋊3(C22.D20), C5⋊3(C23.21D6), C2.10(D4⋊2D15), C10.94(D4⋊2S3), C15⋊26(C22.D4), (C22×C30).17C22, (C22×D15).6C22, C22.45(C22×D15), (C2×Dic15).159C22, (C5×C22⋊C4)⋊4S3, (C3×C22⋊C4)⋊4D5, (C15×C22⋊C4)⋊6C2, (C2×C15⋊7D4).5C2, (C2×C6).279(C22×D5), (C2×C10).278(C22×S3), SmallGroup(480,851)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C22.D60
G = < a,b,c,d | a2=b2=c60=1, d2=b, cac-1=ab=ba, ad=da, bc=cb, bd=db, dcd-1=bc-1 >
Subgroups: 932 in 156 conjugacy classes, 55 normal (25 characteristic)
C1, C2, C2 [×2], C2 [×3], C3, C4 [×5], C22, C22 [×2], C22 [×5], C5, S3, C6, C6 [×2], C6 [×2], C2×C4 [×2], C2×C4 [×5], D4 [×2], C23, C23, D5, C10, C10 [×2], C10 [×2], Dic3 [×3], C12 [×2], D6 [×3], C2×C6, C2×C6 [×2], C2×C6 [×2], C15, C22⋊C4, C22⋊C4 [×2], C4⋊C4 [×2], C22×C4, C2×D4, Dic5 [×3], C20 [×2], D10 [×3], C2×C10, C2×C10 [×2], C2×C10 [×2], C2×Dic3 [×5], C3⋊D4 [×2], C2×C12 [×2], C22×S3, C22×C6, D15, C30, C30 [×2], C30 [×2], C22.D4, C2×Dic5 [×5], C5⋊D4 [×2], C2×C20 [×2], C22×D5, C22×C10, C4⋊Dic3 [×2], D6⋊C4 [×2], C3×C22⋊C4, C22×Dic3, C2×C3⋊D4, Dic15 [×3], C60 [×2], D30 [×3], C2×C30, C2×C30 [×2], C2×C30 [×2], C4⋊Dic5 [×2], D10⋊C4 [×2], C5×C22⋊C4, C22×Dic5, C2×C5⋊D4, C23.21D6, C2×Dic15, C2×Dic15 [×2], C2×Dic15 [×2], C15⋊7D4 [×2], C2×C60 [×2], C22×D15, C22×C30, C22.D20, C60⋊5C4 [×2], D30⋊3C4 [×2], C15×C22⋊C4, C22×Dic15, C2×C15⋊7D4, C22.D60
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, C4○D4 [×2], D10 [×3], D12 [×2], C22×S3, D15, C22.D4, D20 [×2], C22×D5, C2×D12, D4⋊2S3 [×2], D30 [×3], C2×D20, D4⋊2D5 [×2], C23.21D6, D60 [×2], C22×D15, C22.D20, C2×D60, D4⋊2D15 [×2], C22.D60
►On 240 points
Generators in S240
(2 148)(4 150)(6 152)(8 154)(10 156)(12 158)(14 160)(16 162)(18 164)(20 166)(22 168)(24 170)(26 172)(28 174)(30 176)(32 178)(34 180)(36 122)(38 124)(40 126)(42 128)(44 130)(46 132)(48 134)(50 136)(52 138)(54 140)(56 142)(58 144)(60 146)(62 236)(64 238)(66 240)(68 182)(70 184)(72 186)(74 188)(76 190)(78 192)(80 194)(82 196)(84 198)(86 200)(88 202)(90 204)(92 206)(94 208)(96 210)(98 212)(100 214)(102 216)(104 218)(106 220)(108 222)(110 224)(112 226)(114 228)(116 230)(118 232)(120 234)
(1 147)(2 148)(3 149)(4 150)(5 151)(6 152)(7 153)(8 154)(9 155)(10 156)(11 157)(12 158)(13 159)(14 160)(15 161)(16 162)(17 163)(18 164)(19 165)(20 166)(21 167)(22 168)(23 169)(24 170)(25 171)(26 172)(27 173)(28 174)(29 175)(30 176)(31 177)(32 178)(33 179)(34 180)(35 121)(36 122)(37 123)(38 124)(39 125)(40 126)(41 127)(42 128)(43 129)(44 130)(45 131)(46 132)(47 133)(48 134)(49 135)(50 136)(51 137)(52 138)(53 139)(54 140)(55 141)(56 142)(57 143)(58 144)(59 145)(60 146)(61 235)(62 236)(63 237)(64 238)(65 239)(66 240)(67 181)(68 182)(69 183)(70 184)(71 185)(72 186)(73 187)(74 188)(75 189)(76 190)(77 191)(78 192)(79 193)(80 194)(81 195)(82 196)(83 197)(84 198)(85 199)(86 200)(87 201)(88 202)(89 203)(90 204)(91 205)(92 206)(93 207)(94 208)(95 209)(96 210)(97 211)(98 212)(99 213)(100 214)(101 215)(102 216)(103 217)(104 218)(105 219)(106 220)(107 221)(108 222)(109 223)(110 224)(111 225)(112 226)(113 227)(114 228)(115 229)(116 230)(117 231)(118 232)(119 233)(120 234)
(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)
(1 119 147 233)(2 232 148 118)(3 117 149 231)(4 230 150 116)(5 115 151 229)(6 228 152 114)(7 113 153 227)(8 226 154 112)(9 111 155 225)(10 224 156 110)(11 109 157 223)(12 222 158 108)(13 107 159 221)(14 220 160 106)(15 105 161 219)(16 218 162 104)(17 103 163 217)(18 216 164 102)(19 101 165 215)(20 214 166 100)(21 99 167 213)(22 212 168 98)(23 97 169 211)(24 210 170 96)(25 95 171 209)(26 208 172 94)(27 93 173 207)(28 206 174 92)(29 91 175 205)(30 204 176 90)(31 89 177 203)(32 202 178 88)(33 87 179 201)(34 200 180 86)(35 85 121 199)(36 198 122 84)(37 83 123 197)(38 196 124 82)(39 81 125 195)(40 194 126 80)(41 79 127 193)(42 192 128 78)(43 77 129 191)(44 190 130 76)(45 75 131 189)(46 188 132 74)(47 73 133 187)(48 186 134 72)(49 71 135 185)(50 184 136 70)(51 69 137 183)(52 182 138 68)(53 67 139 181)(54 240 140 66)(55 65 141 239)(56 238 142 64)(57 63 143 237)(58 236 144 62)(59 61 145 235)(60 234 146 120)
G:=sub<Sym(240)| (2,148)(4,150)(6,152)(8,154)(10,156)(12,158)(14,160)(16,162)(18,164)(20,166)(22,168)(24,170)(26,172)(28,174)(30,176)(32,178)(34,180)(36,122)(38,124)(40,126)(42,128)(44,130)(46,132)(48,134)(50,136)(52,138)(54,140)(56,142)(58,144)(60,146)(62,236)(64,238)(66,240)(68,182)(70,184)(72,186)(74,188)(76,190)(78,192)(80,194)(82,196)(84,198)(86,200)(88,202)(90,204)(92,206)(94,208)(96,210)(98,212)(100,214)(102,216)(104,218)(106,220)(108,222)(110,224)(112,226)(114,228)(116,230)(118,232)(120,234), (1,147)(2,148)(3,149)(4,150)(5,151)(6,152)(7,153)(8,154)(9,155)(10,156)(11,157)(12,158)(13,159)(14,160)(15,161)(16,162)(17,163)(18,164)(19,165)(20,166)(21,167)(22,168)(23,169)(24,170)(25,171)(26,172)(27,173)(28,174)(29,175)(30,176)(31,177)(32,178)(33,179)(34,180)(35,121)(36,122)(37,123)(38,124)(39,125)(40,126)(41,127)(42,128)(43,129)(44,130)(45,131)(46,132)(47,133)(48,134)(49,135)(50,136)(51,137)(52,138)(53,139)(54,140)(55,141)(56,142)(57,143)(58,144)(59,145)(60,146)(61,235)(62,236)(63,237)(64,238)(65,239)(66,240)(67,181)(68,182)(69,183)(70,184)(71,185)(72,186)(73,187)(74,188)(75,189)(76,190)(77,191)(78,192)(79,193)(80,194)(81,195)(82,196)(83,197)(84,198)(85,199)(86,200)(87,201)(88,202)(89,203)(90,204)(91,205)(92,206)(93,207)(94,208)(95,209)(96,210)(97,211)(98,212)(99,213)(100,214)(101,215)(102,216)(103,217)(104,218)(105,219)(106,220)(107,221)(108,222)(109,223)(110,224)(111,225)(112,226)(113,227)(114,228)(115,229)(116,230)(117,231)(118,232)(119,233)(120,234), (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), (1,119,147,233)(2,232,148,118)(3,117,149,231)(4,230,150,116)(5,115,151,229)(6,228,152,114)(7,113,153,227)(8,226,154,112)(9,111,155,225)(10,224,156,110)(11,109,157,223)(12,222,158,108)(13,107,159,221)(14,220,160,106)(15,105,161,219)(16,218,162,104)(17,103,163,217)(18,216,164,102)(19,101,165,215)(20,214,166,100)(21,99,167,213)(22,212,168,98)(23,97,169,211)(24,210,170,96)(25,95,171,209)(26,208,172,94)(27,93,173,207)(28,206,174,92)(29,91,175,205)(30,204,176,90)(31,89,177,203)(32,202,178,88)(33,87,179,201)(34,200,180,86)(35,85,121,199)(36,198,122,84)(37,83,123,197)(38,196,124,82)(39,81,125,195)(40,194,126,80)(41,79,127,193)(42,192,128,78)(43,77,129,191)(44,190,130,76)(45,75,131,189)(46,188,132,74)(47,73,133,187)(48,186,134,72)(49,71,135,185)(50,184,136,70)(51,69,137,183)(52,182,138,68)(53,67,139,181)(54,240,140,66)(55,65,141,239)(56,238,142,64)(57,63,143,237)(58,236,144,62)(59,61,145,235)(60,234,146,120)>;
G:=Group( (2,148)(4,150)(6,152)(8,154)(10,156)(12,158)(14,160)(16,162)(18,164)(20,166)(22,168)(24,170)(26,172)(28,174)(30,176)(32,178)(34,180)(36,122)(38,124)(40,126)(42,128)(44,130)(46,132)(48,134)(50,136)(52,138)(54,140)(56,142)(58,144)(60,146)(62,236)(64,238)(66,240)(68,182)(70,184)(72,186)(74,188)(76,190)(78,192)(80,194)(82,196)(84,198)(86,200)(88,202)(90,204)(92,206)(94,208)(96,210)(98,212)(100,214)(102,216)(104,218)(106,220)(108,222)(110,224)(112,226)(114,228)(116,230)(118,232)(120,234), (1,147)(2,148)(3,149)(4,150)(5,151)(6,152)(7,153)(8,154)(9,155)(10,156)(11,157)(12,158)(13,159)(14,160)(15,161)(16,162)(17,163)(18,164)(19,165)(20,166)(21,167)(22,168)(23,169)(24,170)(25,171)(26,172)(27,173)(28,174)(29,175)(30,176)(31,177)(32,178)(33,179)(34,180)(35,121)(36,122)(37,123)(38,124)(39,125)(40,126)(41,127)(42,128)(43,129)(44,130)(45,131)(46,132)(47,133)(48,134)(49,135)(50,136)(51,137)(52,138)(53,139)(54,140)(55,141)(56,142)(57,143)(58,144)(59,145)(60,146)(61,235)(62,236)(63,237)(64,238)(65,239)(66,240)(67,181)(68,182)(69,183)(70,184)(71,185)(72,186)(73,187)(74,188)(75,189)(76,190)(77,191)(78,192)(79,193)(80,194)(81,195)(82,196)(83,197)(84,198)(85,199)(86,200)(87,201)(88,202)(89,203)(90,204)(91,205)(92,206)(93,207)(94,208)(95,209)(96,210)(97,211)(98,212)(99,213)(100,214)(101,215)(102,216)(103,217)(104,218)(105,219)(106,220)(107,221)(108,222)(109,223)(110,224)(111,225)(112,226)(113,227)(114,228)(115,229)(116,230)(117,231)(118,232)(119,233)(120,234), (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), (1,119,147,233)(2,232,148,118)(3,117,149,231)(4,230,150,116)(5,115,151,229)(6,228,152,114)(7,113,153,227)(8,226,154,112)(9,111,155,225)(10,224,156,110)(11,109,157,223)(12,222,158,108)(13,107,159,221)(14,220,160,106)(15,105,161,219)(16,218,162,104)(17,103,163,217)(18,216,164,102)(19,101,165,215)(20,214,166,100)(21,99,167,213)(22,212,168,98)(23,97,169,211)(24,210,170,96)(25,95,171,209)(26,208,172,94)(27,93,173,207)(28,206,174,92)(29,91,175,205)(30,204,176,90)(31,89,177,203)(32,202,178,88)(33,87,179,201)(34,200,180,86)(35,85,121,199)(36,198,122,84)(37,83,123,197)(38,196,124,82)(39,81,125,195)(40,194,126,80)(41,79,127,193)(42,192,128,78)(43,77,129,191)(44,190,130,76)(45,75,131,189)(46,188,132,74)(47,73,133,187)(48,186,134,72)(49,71,135,185)(50,184,136,70)(51,69,137,183)(52,182,138,68)(53,67,139,181)(54,240,140,66)(55,65,141,239)(56,238,142,64)(57,63,143,237)(58,236,144,62)(59,61,145,235)(60,234,146,120) );
G=PermutationGroup([(2,148),(4,150),(6,152),(8,154),(10,156),(12,158),(14,160),(16,162),(18,164),(20,166),(22,168),(24,170),(26,172),(28,174),(30,176),(32,178),(34,180),(36,122),(38,124),(40,126),(42,128),(44,130),(46,132),(48,134),(50,136),(52,138),(54,140),(56,142),(58,144),(60,146),(62,236),(64,238),(66,240),(68,182),(70,184),(72,186),(74,188),(76,190),(78,192),(80,194),(82,196),(84,198),(86,200),(88,202),(90,204),(92,206),(94,208),(96,210),(98,212),(100,214),(102,216),(104,218),(106,220),(108,222),(110,224),(112,226),(114,228),(116,230),(118,232),(120,234)], [(1,147),(2,148),(3,149),(4,150),(5,151),(6,152),(7,153),(8,154),(9,155),(10,156),(11,157),(12,158),(13,159),(14,160),(15,161),(16,162),(17,163),(18,164),(19,165),(20,166),(21,167),(22,168),(23,169),(24,170),(25,171),(26,172),(27,173),(28,174),(29,175),(30,176),(31,177),(32,178),(33,179),(34,180),(35,121),(36,122),(37,123),(38,124),(39,125),(40,126),(41,127),(42,128),(43,129),(44,130),(45,131),(46,132),(47,133),(48,134),(49,135),(50,136),(51,137),(52,138),(53,139),(54,140),(55,141),(56,142),(57,143),(58,144),(59,145),(60,146),(61,235),(62,236),(63,237),(64,238),(65,239),(66,240),(67,181),(68,182),(69,183),(70,184),(71,185),(72,186),(73,187),(74,188),(75,189),(76,190),(77,191),(78,192),(79,193),(80,194),(81,195),(82,196),(83,197),(84,198),(85,199),(86,200),(87,201),(88,202),(89,203),(90,204),(91,205),(92,206),(93,207),(94,208),(95,209),(96,210),(97,211),(98,212),(99,213),(100,214),(101,215),(102,216),(103,217),(104,218),(105,219),(106,220),(107,221),(108,222),(109,223),(110,224),(111,225),(112,226),(113,227),(114,228),(115,229),(116,230),(117,231),(118,232),(119,233),(120,234)], [(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)], [(1,119,147,233),(2,232,148,118),(3,117,149,231),(4,230,150,116),(5,115,151,229),(6,228,152,114),(7,113,153,227),(8,226,154,112),(9,111,155,225),(10,224,156,110),(11,109,157,223),(12,222,158,108),(13,107,159,221),(14,220,160,106),(15,105,161,219),(16,218,162,104),(17,103,163,217),(18,216,164,102),(19,101,165,215),(20,214,166,100),(21,99,167,213),(22,212,168,98),(23,97,169,211),(24,210,170,96),(25,95,171,209),(26,208,172,94),(27,93,173,207),(28,206,174,92),(29,91,175,205),(30,204,176,90),(31,89,177,203),(32,202,178,88),(33,87,179,201),(34,200,180,86),(35,85,121,199),(36,198,122,84),(37,83,123,197),(38,196,124,82),(39,81,125,195),(40,194,126,80),(41,79,127,193),(42,192,128,78),(43,77,129,191),(44,190,130,76),(45,75,131,189),(46,188,132,74),(47,73,133,187),(48,186,134,72),(49,71,135,185),(50,184,136,70),(51,69,137,183),(52,182,138,68),(53,67,139,181),(54,240,140,66),(55,65,141,239),(56,238,142,64),(57,63,143,237),(58,236,144,62),(59,61,145,235),(60,234,146,120)])
84 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 5A | 5B | 6A | 6B | 6C | 6D | 6E | 10A | ··· | 10F | 10G | 10H | 10I | 10J | 12A | 12B | 12C | 12D | 15A | 15B | 15C | 15D | 20A | ··· | 20H | 30A | ··· | 30L | 30M | ··· | 30T | 60A | ··· | 60P |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 6 | 6 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 12 | 12 | 12 | 12 | 15 | 15 | 15 | 15 | 20 | ··· | 20 | 30 | ··· | 30 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 60 | 2 | 4 | 4 | 30 | 30 | 30 | 30 | 60 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
84 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | S3 | D4 | D5 | D6 | D6 | C4○D4 | D10 | D10 | D12 | D15 | D20 | D30 | D30 | D60 | D4⋊2S3 | D4⋊2D5 | D4⋊2D15 |
| kernel | C22.D60 | C60⋊5C4 | D30⋊3C4 | C15×C22⋊C4 | C22×Dic15 | C2×C15⋊7D4 | C5×C22⋊C4 | C2×C30 | C3×C22⋊C4 | C2×C20 | C22×C10 | C30 | C2×C12 | C22×C6 | C2×C10 | C22⋊C4 | C2×C6 | C2×C4 | C23 | C22 | C10 | C6 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 1 | 4 | 4 | 2 | 4 | 4 | 8 | 8 | 4 | 16 | 2 | 4 | 8 |
Matrix representation of C22.D60 ►in GL6(𝔽61)
| 1 | 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 | 0 |
| 0 | 0 | 0 | 0 | 23 | 60 |
| 1 | 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 | 60 | 0 |
| 0 | 0 | 0 | 0 | 0 | 60 |
| 25 | 27 | 0 | 0 | 0 | 0 |
| 34 | 27 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 23 | 0 | 0 |
| 0 | 0 | 2 | 30 | 0 | 0 |
| 0 | 0 | 0 | 0 | 57 | 3 |
| 0 | 0 | 0 | 0 | 35 | 4 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 43 | 60 | 0 | 0 | 0 | 0 |
| 0 | 0 | 41 | 39 | 0 | 0 |
| 0 | 0 | 32 | 20 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 0 |
| 0 | 0 | 0 | 0 | 0 | 11 |
G:=sub<GL(6,GF(61))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,23,0,0,0,0,0,60],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,60,0,0,0,0,0,0,60],[25,34,0,0,0,0,27,27,0,0,0,0,0,0,28,2,0,0,0,0,23,30,0,0,0,0,0,0,57,35,0,0,0,0,3,4],[1,43,0,0,0,0,0,60,0,0,0,0,0,0,41,32,0,0,0,0,39,20,0,0,0,0,0,0,11,0,0,0,0,0,0,11] >;
C22.D60 in GAP, Magma, Sage, TeX
C_2^2.D_{60} % in TeX
G:=Group("C2^2.D60"); // GroupNames label
G:=SmallGroup(480,851);
// by ID
G=gap.SmallGroup(480,851);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,253,254,219,142,2693,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^2=c^60=1,d^2=b,c*a*c^-1=a*b=b*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=b*c^-1>;
// generators/relations