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G = C60.10C23order 480 = 25·3·5

10th non-split extension by C60 of C23 acting faithfully

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C60.10C23, Dic6.6D10, Dic10.23D6, Dic30.2C22, D4.D51S3, D42S3.D5, D4.2(S3×D5), C52C8.5D6, D4.D154C2, (C5×D4).19D6, (C4×S3).6D10, C15⋊Q162C2, C5⋊Dic121C2, (S3×C10).9D4, (C3×D4).2D10, C56(D4.D6), (S3×Dic10)⋊2C2, C30.172(C2×D4), C10.142(S3×D4), D6.7(C5⋊D4), D6.Dic52C2, C32(D4.9D10), C1514(C8.C22), (S3×C20).4C22, C20.10(C22×S3), C153C8.2C22, (C5×Dic3).35D4, (D4×C15).4C22, C12.10(C22×D5), (C5×Dic6).2C22, Dic3.16(C5⋊D4), (C3×Dic10).2C22, C4.10(C2×S3×D5), (C3×D4.D5)⋊2C2, C2.23(S3×C5⋊D4), C6.45(C2×C5⋊D4), (C5×D42S3).1C2, (C3×C52C8).1C22, SmallGroup(480,562)

Series: Derived Chief Lower central Upper central

C1C60 — C60.10C23
C1C5C15C30C60C3×Dic10S3×Dic10 — C60.10C23
C15C30C60 — C60.10C23
C1C2C4D4

Generators and relations for C60.10C23
 G = < a,b,c,d | a60=c2=d2=1, b2=a30, bab-1=a19, cac=a41, dad=a31, bc=cb, dbd=a45b, dcd=a30c >

Subgroups: 540 in 120 conjugacy classes, 40 normal (all characteristic)
C1, C2, C2 [×2], C3, C4, C4 [×4], C22 [×2], C5, S3, C6, C6, C8 [×2], C2×C4 [×3], D4, D4, Q8 [×4], C10, C10 [×2], Dic3, Dic3 [×2], C12, C12, D6, C2×C6, C15, M4(2), SD16 [×2], Q16 [×2], C2×Q8, C4○D4, Dic5 [×2], C20, C20 [×2], C2×C10 [×2], C3⋊C8, C24, Dic6, Dic6 [×2], C4×S3, C4×S3, C2×Dic3, C3⋊D4, C3×D4, C3×Q8, C5×S3, C30, C30, C8.C22, C52C8, C52C8, Dic10, Dic10 [×2], C2×Dic5, C2×C20 [×2], C5×D4, C5×D4, C5×Q8, C8⋊S3, Dic12, D4.S3, C3⋊Q16, C3×SD16, D42S3, S3×Q8, C5×Dic3, C5×Dic3, C3×Dic5, Dic15, C60, S3×C10, C2×C30, C4.Dic5, D4.D5, D4.D5, C5⋊Q16 [×2], C2×Dic10, C5×C4○D4, D4.D6, C3×C52C8, C153C8, S3×Dic5, C15⋊Q8, C3×Dic10, C5×Dic6, S3×C20, C10×Dic3, C5×C3⋊D4, Dic30, D4×C15, D4.9D10, D6.Dic5, C15⋊Q16, C5⋊Dic12, C3×D4.D5, D4.D15, S3×Dic10, C5×D42S3, C60.10C23
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], C22×S3, C8.C22, C5⋊D4 [×2], C22×D5, S3×D4, S3×D5, C2×C5⋊D4, D4.D6, C2×S3×D5, D4.9D10, S3×C5⋊D4, C60.10C23

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

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

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

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

48 conjugacy classes

class 1 2A2B2C 3 4A4B4C4D4E5A5B6A6B8A8B10A10B10C10D10E10F10G10H12A12B15A15B20A20B20C20D20E20F20G20H20I20J24A24B30A30B30C30D30E30F60A60B
order12223444445566881010101010101010121215152020202020202020202024243030303030306060
size11462261220602228206022444412124404444666612121212202044888888

48 irreducible representations

dim1111111122222222222244444448
type++++++++++++++++++-++-+--
imageC1C2C2C2C2C2C2C2S3D4D4D5D6D6D6D10D10D10C5⋊D4C5⋊D4C8.C22S3×D4S3×D5D4.D6C2×S3×D5D4.9D10S3×C5⋊D4C60.10C23
kernelC60.10C23D6.Dic5C15⋊Q16C5⋊Dic12C3×D4.D5D4.D15S3×Dic10C5×D42S3D4.D5C5×Dic3S3×C10D42S3C52C8Dic10C5×D4Dic6C4×S3C3×D4Dic3D6C15C10D4C5C4C3C2C1
# reps1111111111121112224411222442

Matrix representation of C60.10C23 in GL8(𝔽241)

21371921030000
1041370540000
177640520000
670190510000
0000116000
0000324000
000032391238
0000016081240
,
220166000000
3821000000
00592030000
001551820000
00002219100
00008221900
000022511321982
00001284519122
,
24001031380000
024010300000
00100000
00010000
00001000
00000100
0000302400
000021600240
,
2400000000
0240000000
0024000000
0002400000
0000101600
0000012393
0000002400
0000000240

G:=sub<GL(8,GF(241))| [2,104,177,67,0,0,0,0,137,137,64,0,0,0,0,0,192,0,0,190,0,0,0,0,103,54,52,51,0,0,0,0,0,0,0,0,1,3,3,0,0,0,0,0,160,240,239,160,0,0,0,0,0,0,1,81,0,0,0,0,0,0,238,240],[220,38,0,0,0,0,0,0,166,21,0,0,0,0,0,0,0,0,59,155,0,0,0,0,0,0,203,182,0,0,0,0,0,0,0,0,22,82,225,128,0,0,0,0,191,219,113,45,0,0,0,0,0,0,219,191,0,0,0,0,0,0,82,22],[240,0,0,0,0,0,0,0,0,240,0,0,0,0,0,0,103,103,1,0,0,0,0,0,138,0,0,1,0,0,0,0,0,0,0,0,1,0,3,2,0,0,0,0,0,1,0,160,0,0,0,0,0,0,240,0,0,0,0,0,0,0,0,240],[240,0,0,0,0,0,0,0,0,240,0,0,0,0,0,0,0,0,240,0,0,0,0,0,0,0,0,240,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,160,239,240,0,0,0,0,0,0,3,0,240] >;

C60.10C23 in GAP, Magma, Sage, TeX

C_{60}._{10}C_2^3
% in TeX

G:=Group("C60.10C2^3");
// GroupNames label

G:=SmallGroup(480,562);
// by ID

G=gap.SmallGroup(480,562);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,254,219,675,185,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^60=c^2=d^2=1,b^2=a^30,b*a*b^-1=a^19,c*a*c=a^41,d*a*d=a^31,b*c=c*b,d*b*d=a^45*b,d*c*d=a^30*c>;
// generators/relations

׿
×
𝔽