Copied to
clipboard

G = C60.16C23order 480 = 25·3·5

16th non-split extension by C60 of C23 acting faithfully

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C60.16C23, Dic10.9D6, D60.4C22, Dic6.24D10, D4⋊D156C2, D4.S37D5, C3⋊C8.14D10, (C5×D4).8D6, D42D53S3, C1514(C4○D8), (C6×D5).11D4, D4.12(S3×D5), (C4×D5).46D6, C15⋊Q163C2, C6.145(D4×D5), C12.28D102C2, (C3×D4).23D10, C30.178(C2×D4), C15⋊SD163C2, C53(Q8.13D6), C36(SD163D5), C20.16(C22×S3), C153C8.4C22, (C3×Dic5).69D4, (D5×C12).8C22, C12.16(C22×D5), D10.10(C3⋊D4), (D4×C15).10C22, (C5×Dic6).4C22, Dic5.41(C3⋊D4), (C3×Dic10).5C22, (D5×C3⋊C8)⋊4C2, C4.16(C2×S3×D5), (C5×D4.S3)⋊6C2, C2.27(D5×C3⋊D4), (C5×C3⋊C8).4C22, (C3×D42D5)⋊3C2, C10.48(C2×C3⋊D4), SmallGroup(480,568)

Series: Derived Chief Lower central Upper central

C1C60 — C60.16C23
C1C5C15C30C60D5×C12C12.28D10 — C60.16C23
C15C30C60 — C60.16C23
C1C2C4D4

Generators and relations for C60.16C23
 G = < a,b,c,d | a60=b2=d2=1, c2=a30, bab=a49, cac-1=a11, dad=a31, cbc-1=dbd=a30b, dcd=a45c >

Subgroups: 668 in 124 conjugacy classes, 40 normal (all characteristic)
C1, C2, C2 [×3], C3, C4, C4 [×3], C22 [×3], C5, S3, C6, C6 [×2], C8 [×2], C2×C4 [×3], D4, D4 [×3], Q8 [×2], D5 [×2], C10, C10, Dic3, C12, C12 [×2], D6, C2×C6 [×2], C15, C2×C8, D8, SD16 [×2], Q16, C4○D4 [×2], Dic5, Dic5, C20, C20, D10, D10, C2×C10, C3⋊C8, C3⋊C8, Dic6, C4×S3, D12, C3⋊D4, C2×C12 [×2], C3×D4, C3×D4, C3×Q8, C3×D5, D15, C30, C30, C4○D8, C52C8, C40, Dic10, C4×D5, C4×D5, D20 [×2], C2×Dic5, C5⋊D4, C5×D4, C5×Q8, C2×C3⋊C8, D4⋊S3, D4.S3, Q82S3, C3⋊Q16, C4○D12, C3×C4○D4, C5×Dic3, C3×Dic5, C3×Dic5, C60, C6×D5, D30, C2×C30, C8×D5, C40⋊C2, D4⋊D5, C5⋊Q16, C5×SD16, D42D5, Q82D5, Q8.13D6, C5×C3⋊C8, C153C8, D30.C2, C3⋊D20, C3×Dic10, D5×C12, C6×Dic5, C3×C5⋊D4, C5×Dic6, D60, D4×C15, SD163D5, D5×C3⋊C8, C15⋊SD16, C15⋊Q16, C5×D4.S3, D4⋊D15, C12.28D10, C3×D42D5, C60.16C23
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], C3⋊D4 [×2], C22×S3, C4○D8, C22×D5, C2×C3⋊D4, S3×D5, D4×D5, Q8.13D6, C2×S3×D5, SD163D5, D5×C3⋊D4, C60.16C23

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

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

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

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

48 conjugacy classes

class 1 2A2B2C2D 3 4A4B4C4D4E5A5B6A6B6C6D8A8B8C8D10A10B10C10D12A12B12C12D12E15A15B20A20B20C20D30A30B30C30D30E30F40A40B40C40D60A60B
order122223444445566668888101010101212121212151520202020303030303030404040406060
size11410602255122022244206630302288410102020444424244488881212121288

48 irreducible representations

dim1111111122222222222224444448
type++++++++++++++++++++++
imageC1C2C2C2C2C2C2C2S3D4D4D5D6D6D6D10D10D10C3⋊D4C3⋊D4C4○D8S3×D5D4×D5Q8.13D6C2×S3×D5SD163D5D5×C3⋊D4C60.16C23
kernelC60.16C23D5×C3⋊C8C15⋊SD16C15⋊Q16C5×D4.S3D4⋊D15C12.28D10C3×D42D5D42D5C3×Dic5C6×D5D4.S3Dic10C4×D5C5×D4C3⋊C8Dic6C3×D4Dic5D10C15D4C6C5C4C3C2C1
# reps1111111111121112222242222442

Matrix representation of C60.16C23 in GL6(𝔽241)

1901900000
512400000
000100
0024024000
0000640
0000101177
,
100000
512400000
001000
000100
000010
000043240
,
100000
010000
00735500
0022316800
00007151
0000188234
,
24000000
02400000
001000
000100
0000563
0000160185

G:=sub<GL(6,GF(241))| [190,51,0,0,0,0,190,240,0,0,0,0,0,0,0,240,0,0,0,0,1,240,0,0,0,0,0,0,64,101,0,0,0,0,0,177],[1,51,0,0,0,0,0,240,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,43,0,0,0,0,0,240],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,73,223,0,0,0,0,55,168,0,0,0,0,0,0,7,188,0,0,0,0,151,234],[240,0,0,0,0,0,0,240,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,56,160,0,0,0,0,3,185] >;

C60.16C23 in GAP, Magma, Sage, TeX

C_{60}._{16}C_2^3
% in TeX

G:=Group("C60.16C2^3");
// GroupNames label

G:=SmallGroup(480,568);
// by ID

G=gap.SmallGroup(480,568);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,253,120,422,135,346,185,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^60=b^2=d^2=1,c^2=a^30,b*a*b=a^49,c*a*c^-1=a^11,d*a*d=a^31,c*b*c^-1=d*b*d=a^30*b,d*c*d=a^45*c>;
// generators/relations

׿
×
𝔽