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G = C22.D60order 480 = 25·3·5

3rd non-split extension by C22 of D60 acting via D60/D30=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C22.4D60, C23.20D30, (C2×C4).9D30, C2.8(C2×D60), (C2×C30).4D4, (C2×C6).9D20, C22⋊C46D15, C605C411C2, C6.34(C2×D20), (C2×C20).35D6, (C2×C10).9D12, D303C47C2, 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(D42D5), (C2×C30).283C23, (C22×Dic15)⋊2C2, C33(C22.D20), C53(C23.21D6), C2.10(D42D15), C10.94(D42S3), C1526(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×C157D4).5C2, (C2×C6).279(C22×D5), (C2×C10).278(C22×S3), SmallGroup(480,851)

Series: Derived Chief Lower central Upper central

C1C2×C30 — C22.D60
C1C5C15C30C2×C30C22×D15C2×C157D4 — C22.D60
C15C2×C30 — C22.D60
C1C22C22⋊C4

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], C157D4 [×2], C2×C60 [×2], C22×D15, C22×C30, C22.D20, C605C4 [×2], D303C4 [×2], C15×C22⋊C4, C22×Dic15, C2×C157D4, 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, D42S3 [×2], D30 [×3], C2×D20, D42D5 [×2], C23.21D6, D60 [×2], C22×D15, C22.D20, C2×D60, D42D15 [×2], C22.D60

Smallest permutation representation of 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 2A2B2C2D2E2F 3 4A4B4C4D4E4F4G5A5B6A6B6C6D6E10A···10F10G10H10I10J12A12B12C12D15A15B15C15D20A···20H30A···30L30M···30T60A···60P
order122222234444444556666610···1010101010121212121515151520···2030···3030···3060···60
size11112260244303030306022222442···24444444422224···42···24···44···4

84 irreducible representations

dim11111122222222222222444
type+++++++++++++++++++---
imageC1C2C2C2C2C2S3D4D5D6D6C4○D4D10D10D12D15D20D30D30D60D42S3D42D5D42D15
kernelC22.D60C605C4D303C4C15×C22⋊C4C22×Dic15C2×C157D4C5×C22⋊C4C2×C30C3×C22⋊C4C2×C20C22×C10C30C2×C12C22×C6C2×C10C22⋊C4C2×C6C2×C4C23C22C10C6C2
# reps122111122214424488416248

Matrix representation of C22.D60 in GL6(𝔽61)

100000
010000
001000
000100
000010
00002360
,
100000
010000
001000
000100
0000600
0000060
,
25270000
34270000
00282300
0023000
0000573
0000354
,
100000
43600000
00413900
00322000
0000110
0000011

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

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