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, C2, C3, C4, C22, C22, C22, C5, S3, C6, C6, C6, C2×C4, C2×C4, D4, C23, C23, D5, C10, C10, C10, Dic3, C12, D6, C2×C6, C2×C6, C2×C6, C15, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C2×D4, Dic5, C20, D10, C2×C10, C2×C10, C2×C10, C2×Dic3, C3⋊D4, C2×C12, C22×S3, C22×C6, D15, C30, C30, C30, C22.D4, C2×Dic5, C5⋊D4, C2×C20, C22×D5, C22×C10, C4⋊Dic3, D6⋊C4, C3×C22⋊C4, C22×Dic3, C2×C3⋊D4, Dic15, C60, D30, C2×C30, C2×C30, C2×C30, C4⋊Dic5, D10⋊C4, C5×C22⋊C4, C22×Dic5, C2×C5⋊D4, C23.21D6, C2×Dic15, C2×Dic15, C2×Dic15, C15⋊7D4, C2×C60, C22×D15, C22×C30, C22.D20, C60⋊5C4, D30⋊3C4, C15×C22⋊C4, C22×Dic15, C2×C15⋊7D4, C22.D60
Quotients: C1, C2, C22, S3, D4, C23, D5, D6, C2×D4, C4○D4, D10, D12, C22×S3, D15, C22.D4, D20, C22×D5, C2×D12, D4⋊2S3, D30, C2×D20, D4⋊2D5, C23.21D6, D60, C22×D15, C22.D20, C2×D60, D4⋊2D15, C22.D60
►On 240 points
Generators in S240
(2 99)(4 101)(6 103)(8 105)(10 107)(12 109)(14 111)(16 113)(18 115)(20 117)(22 119)(24 61)(26 63)(28 65)(30 67)(32 69)(34 71)(36 73)(38 75)(40 77)(42 79)(44 81)(46 83)(48 85)(50 87)(52 89)(54 91)(56 93)(58 95)(60 97)(121 211)(123 213)(125 215)(127 217)(129 219)(131 221)(133 223)(135 225)(137 227)(139 229)(141 231)(143 233)(145 235)(147 237)(149 239)(151 181)(153 183)(155 185)(157 187)(159 189)(161 191)(163 193)(165 195)(167 197)(169 199)(171 201)(173 203)(175 205)(177 207)(179 209)
(1 98)(2 99)(3 100)(4 101)(5 102)(6 103)(7 104)(8 105)(9 106)(10 107)(11 108)(12 109)(13 110)(14 111)(15 112)(16 113)(17 114)(18 115)(19 116)(20 117)(21 118)(22 119)(23 120)(24 61)(25 62)(26 63)(27 64)(28 65)(29 66)(30 67)(31 68)(32 69)(33 70)(34 71)(35 72)(36 73)(37 74)(38 75)(39 76)(40 77)(41 78)(42 79)(43 80)(44 81)(45 82)(46 83)(47 84)(48 85)(49 86)(50 87)(51 88)(52 89)(53 90)(54 91)(55 92)(56 93)(57 94)(58 95)(59 96)(60 97)(121 211)(122 212)(123 213)(124 214)(125 215)(126 216)(127 217)(128 218)(129 219)(130 220)(131 221)(132 222)(133 223)(134 224)(135 225)(136 226)(137 227)(138 228)(139 229)(140 230)(141 231)(142 232)(143 233)(144 234)(145 235)(146 236)(147 237)(148 238)(149 239)(150 240)(151 181)(152 182)(153 183)(154 184)(155 185)(156 186)(157 187)(158 188)(159 189)(160 190)(161 191)(162 192)(163 193)(164 194)(165 195)(166 196)(167 197)(168 198)(169 199)(170 200)(171 201)(172 202)(173 203)(174 204)(175 205)(176 206)(177 207)(178 208)(179 209)(180 210)
(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)
(1 208 98 178)(2 177 99 207)(3 206 100 176)(4 175 101 205)(5 204 102 174)(6 173 103 203)(7 202 104 172)(8 171 105 201)(9 200 106 170)(10 169 107 199)(11 198 108 168)(12 167 109 197)(13 196 110 166)(14 165 111 195)(15 194 112 164)(16 163 113 193)(17 192 114 162)(18 161 115 191)(19 190 116 160)(20 159 117 189)(21 188 118 158)(22 157 119 187)(23 186 120 156)(24 155 61 185)(25 184 62 154)(26 153 63 183)(27 182 64 152)(28 151 65 181)(29 240 66 150)(30 149 67 239)(31 238 68 148)(32 147 69 237)(33 236 70 146)(34 145 71 235)(35 234 72 144)(36 143 73 233)(37 232 74 142)(38 141 75 231)(39 230 76 140)(40 139 77 229)(41 228 78 138)(42 137 79 227)(43 226 80 136)(44 135 81 225)(45 224 82 134)(46 133 83 223)(47 222 84 132)(48 131 85 221)(49 220 86 130)(50 129 87 219)(51 218 88 128)(52 127 89 217)(53 216 90 126)(54 125 91 215)(55 214 92 124)(56 123 93 213)(57 212 94 122)(58 121 95 211)(59 210 96 180)(60 179 97 209)
G:=sub<Sym(240)| (2,99)(4,101)(6,103)(8,105)(10,107)(12,109)(14,111)(16,113)(18,115)(20,117)(22,119)(24,61)(26,63)(28,65)(30,67)(32,69)(34,71)(36,73)(38,75)(40,77)(42,79)(44,81)(46,83)(48,85)(50,87)(52,89)(54,91)(56,93)(58,95)(60,97)(121,211)(123,213)(125,215)(127,217)(129,219)(131,221)(133,223)(135,225)(137,227)(139,229)(141,231)(143,233)(145,235)(147,237)(149,239)(151,181)(153,183)(155,185)(157,187)(159,189)(161,191)(163,193)(165,195)(167,197)(169,199)(171,201)(173,203)(175,205)(177,207)(179,209), (1,98)(2,99)(3,100)(4,101)(5,102)(6,103)(7,104)(8,105)(9,106)(10,107)(11,108)(12,109)(13,110)(14,111)(15,112)(16,113)(17,114)(18,115)(19,116)(20,117)(21,118)(22,119)(23,120)(24,61)(25,62)(26,63)(27,64)(28,65)(29,66)(30,67)(31,68)(32,69)(33,70)(34,71)(35,72)(36,73)(37,74)(38,75)(39,76)(40,77)(41,78)(42,79)(43,80)(44,81)(45,82)(46,83)(47,84)(48,85)(49,86)(50,87)(51,88)(52,89)(53,90)(54,91)(55,92)(56,93)(57,94)(58,95)(59,96)(60,97)(121,211)(122,212)(123,213)(124,214)(125,215)(126,216)(127,217)(128,218)(129,219)(130,220)(131,221)(132,222)(133,223)(134,224)(135,225)(136,226)(137,227)(138,228)(139,229)(140,230)(141,231)(142,232)(143,233)(144,234)(145,235)(146,236)(147,237)(148,238)(149,239)(150,240)(151,181)(152,182)(153,183)(154,184)(155,185)(156,186)(157,187)(158,188)(159,189)(160,190)(161,191)(162,192)(163,193)(164,194)(165,195)(166,196)(167,197)(168,198)(169,199)(170,200)(171,201)(172,202)(173,203)(174,204)(175,205)(176,206)(177,207)(178,208)(179,209)(180,210), (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), (1,208,98,178)(2,177,99,207)(3,206,100,176)(4,175,101,205)(5,204,102,174)(6,173,103,203)(7,202,104,172)(8,171,105,201)(9,200,106,170)(10,169,107,199)(11,198,108,168)(12,167,109,197)(13,196,110,166)(14,165,111,195)(15,194,112,164)(16,163,113,193)(17,192,114,162)(18,161,115,191)(19,190,116,160)(20,159,117,189)(21,188,118,158)(22,157,119,187)(23,186,120,156)(24,155,61,185)(25,184,62,154)(26,153,63,183)(27,182,64,152)(28,151,65,181)(29,240,66,150)(30,149,67,239)(31,238,68,148)(32,147,69,237)(33,236,70,146)(34,145,71,235)(35,234,72,144)(36,143,73,233)(37,232,74,142)(38,141,75,231)(39,230,76,140)(40,139,77,229)(41,228,78,138)(42,137,79,227)(43,226,80,136)(44,135,81,225)(45,224,82,134)(46,133,83,223)(47,222,84,132)(48,131,85,221)(49,220,86,130)(50,129,87,219)(51,218,88,128)(52,127,89,217)(53,216,90,126)(54,125,91,215)(55,214,92,124)(56,123,93,213)(57,212,94,122)(58,121,95,211)(59,210,96,180)(60,179,97,209)>;
G:=Group( (2,99)(4,101)(6,103)(8,105)(10,107)(12,109)(14,111)(16,113)(18,115)(20,117)(22,119)(24,61)(26,63)(28,65)(30,67)(32,69)(34,71)(36,73)(38,75)(40,77)(42,79)(44,81)(46,83)(48,85)(50,87)(52,89)(54,91)(56,93)(58,95)(60,97)(121,211)(123,213)(125,215)(127,217)(129,219)(131,221)(133,223)(135,225)(137,227)(139,229)(141,231)(143,233)(145,235)(147,237)(149,239)(151,181)(153,183)(155,185)(157,187)(159,189)(161,191)(163,193)(165,195)(167,197)(169,199)(171,201)(173,203)(175,205)(177,207)(179,209), (1,98)(2,99)(3,100)(4,101)(5,102)(6,103)(7,104)(8,105)(9,106)(10,107)(11,108)(12,109)(13,110)(14,111)(15,112)(16,113)(17,114)(18,115)(19,116)(20,117)(21,118)(22,119)(23,120)(24,61)(25,62)(26,63)(27,64)(28,65)(29,66)(30,67)(31,68)(32,69)(33,70)(34,71)(35,72)(36,73)(37,74)(38,75)(39,76)(40,77)(41,78)(42,79)(43,80)(44,81)(45,82)(46,83)(47,84)(48,85)(49,86)(50,87)(51,88)(52,89)(53,90)(54,91)(55,92)(56,93)(57,94)(58,95)(59,96)(60,97)(121,211)(122,212)(123,213)(124,214)(125,215)(126,216)(127,217)(128,218)(129,219)(130,220)(131,221)(132,222)(133,223)(134,224)(135,225)(136,226)(137,227)(138,228)(139,229)(140,230)(141,231)(142,232)(143,233)(144,234)(145,235)(146,236)(147,237)(148,238)(149,239)(150,240)(151,181)(152,182)(153,183)(154,184)(155,185)(156,186)(157,187)(158,188)(159,189)(160,190)(161,191)(162,192)(163,193)(164,194)(165,195)(166,196)(167,197)(168,198)(169,199)(170,200)(171,201)(172,202)(173,203)(174,204)(175,205)(176,206)(177,207)(178,208)(179,209)(180,210), (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), (1,208,98,178)(2,177,99,207)(3,206,100,176)(4,175,101,205)(5,204,102,174)(6,173,103,203)(7,202,104,172)(8,171,105,201)(9,200,106,170)(10,169,107,199)(11,198,108,168)(12,167,109,197)(13,196,110,166)(14,165,111,195)(15,194,112,164)(16,163,113,193)(17,192,114,162)(18,161,115,191)(19,190,116,160)(20,159,117,189)(21,188,118,158)(22,157,119,187)(23,186,120,156)(24,155,61,185)(25,184,62,154)(26,153,63,183)(27,182,64,152)(28,151,65,181)(29,240,66,150)(30,149,67,239)(31,238,68,148)(32,147,69,237)(33,236,70,146)(34,145,71,235)(35,234,72,144)(36,143,73,233)(37,232,74,142)(38,141,75,231)(39,230,76,140)(40,139,77,229)(41,228,78,138)(42,137,79,227)(43,226,80,136)(44,135,81,225)(45,224,82,134)(46,133,83,223)(47,222,84,132)(48,131,85,221)(49,220,86,130)(50,129,87,219)(51,218,88,128)(52,127,89,217)(53,216,90,126)(54,125,91,215)(55,214,92,124)(56,123,93,213)(57,212,94,122)(58,121,95,211)(59,210,96,180)(60,179,97,209) );
G=PermutationGroup([[(2,99),(4,101),(6,103),(8,105),(10,107),(12,109),(14,111),(16,113),(18,115),(20,117),(22,119),(24,61),(26,63),(28,65),(30,67),(32,69),(34,71),(36,73),(38,75),(40,77),(42,79),(44,81),(46,83),(48,85),(50,87),(52,89),(54,91),(56,93),(58,95),(60,97),(121,211),(123,213),(125,215),(127,217),(129,219),(131,221),(133,223),(135,225),(137,227),(139,229),(141,231),(143,233),(145,235),(147,237),(149,239),(151,181),(153,183),(155,185),(157,187),(159,189),(161,191),(163,193),(165,195),(167,197),(169,199),(171,201),(173,203),(175,205),(177,207),(179,209)], [(1,98),(2,99),(3,100),(4,101),(5,102),(6,103),(7,104),(8,105),(9,106),(10,107),(11,108),(12,109),(13,110),(14,111),(15,112),(16,113),(17,114),(18,115),(19,116),(20,117),(21,118),(22,119),(23,120),(24,61),(25,62),(26,63),(27,64),(28,65),(29,66),(30,67),(31,68),(32,69),(33,70),(34,71),(35,72),(36,73),(37,74),(38,75),(39,76),(40,77),(41,78),(42,79),(43,80),(44,81),(45,82),(46,83),(47,84),(48,85),(49,86),(50,87),(51,88),(52,89),(53,90),(54,91),(55,92),(56,93),(57,94),(58,95),(59,96),(60,97),(121,211),(122,212),(123,213),(124,214),(125,215),(126,216),(127,217),(128,218),(129,219),(130,220),(131,221),(132,222),(133,223),(134,224),(135,225),(136,226),(137,227),(138,228),(139,229),(140,230),(141,231),(142,232),(143,233),(144,234),(145,235),(146,236),(147,237),(148,238),(149,239),(150,240),(151,181),(152,182),(153,183),(154,184),(155,185),(156,186),(157,187),(158,188),(159,189),(160,190),(161,191),(162,192),(163,193),(164,194),(165,195),(166,196),(167,197),(168,198),(169,199),(170,200),(171,201),(172,202),(173,203),(174,204),(175,205),(176,206),(177,207),(178,208),(179,209),(180,210)], [(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)], [(1,208,98,178),(2,177,99,207),(3,206,100,176),(4,175,101,205),(5,204,102,174),(6,173,103,203),(7,202,104,172),(8,171,105,201),(9,200,106,170),(10,169,107,199),(11,198,108,168),(12,167,109,197),(13,196,110,166),(14,165,111,195),(15,194,112,164),(16,163,113,193),(17,192,114,162),(18,161,115,191),(19,190,116,160),(20,159,117,189),(21,188,118,158),(22,157,119,187),(23,186,120,156),(24,155,61,185),(25,184,62,154),(26,153,63,183),(27,182,64,152),(28,151,65,181),(29,240,66,150),(30,149,67,239),(31,238,68,148),(32,147,69,237),(33,236,70,146),(34,145,71,235),(35,234,72,144),(36,143,73,233),(37,232,74,142),(38,141,75,231),(39,230,76,140),(40,139,77,229),(41,228,78,138),(42,137,79,227),(43,226,80,136),(44,135,81,225),(45,224,82,134),(46,133,83,223),(47,222,84,132),(48,131,85,221),(49,220,86,130),(50,129,87,219),(51,218,88,128),(52,127,89,217),(53,216,90,126),(54,125,91,215),(55,214,92,124),(56,123,93,213),(57,212,94,122),(58,121,95,211),(59,210,96,180),(60,179,97,209)]])
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