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G = C60.44C23order 480 = 25·3·5

44th non-split extension by C60 of C23 acting faithfully

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C60.44C23, Dic6.15D10, Dic10.28D6, D60.16C22, (S3×Q8)⋊3D5, C5⋊Q164S3, C15⋊Q168C2, C52C8.10D6, C56(Q16⋊S3), (C3×Q8).8D10, (C5×Q8).40D6, Q8.13(S3×D5), Q82D158C2, (S3×C10).38D4, (C4×S3).12D10, C10.154(S3×D4), C30.206(C2×D4), Dic6⋊D57C2, D6.Dic58C2, D60⋊C2.1C2, D6.16(C5⋊D4), C33(C20.C23), C1522(C8.C22), C20.44(C22×S3), (C5×Dic3).18D4, C12.44(C22×D5), (S3×C20).16C22, C153C8.18C22, (Q8×C15).14C22, Dic3.13(C5⋊D4), (C5×Dic6).16C22, (C3×Dic10).16C22, (C5×S3×Q8)⋊3C2, C4.44(C2×S3×D5), (C3×C5⋊Q16)⋊6C2, C6.57(C2×C5⋊D4), C2.35(S3×C5⋊D4), (C3×C52C8).14C22, SmallGroup(480,596)

Series: Derived Chief Lower central Upper central

C1C60 — C60.44C23
C1C5C15C30C60C3×Dic10D60⋊C2 — C60.44C23
C15C30C60 — C60.44C23
C1C2C4Q8

Generators and relations for C60.44C23
 G = < a,b,c,d | a60=1, b2=c2=d2=a30, bab-1=a19, cac-1=a41, dad-1=a31, bc=cb, dbd-1=a45b, dcd-1=a30c >

Subgroups: 620 in 120 conjugacy classes, 40 normal (all characteristic)
C1, C2, C2 [×2], C3, C4, C4 [×4], C22 [×2], C5, S3 [×2], C6, C8 [×2], C2×C4 [×3], D4 [×2], Q8, Q8 [×3], D5, C10, C10, Dic3, Dic3, C12, C12 [×2], D6, D6, C15, M4(2), SD16 [×2], Q16 [×2], C2×Q8, C4○D4, Dic5, C20, C20 [×3], D10, C2×C10, C3⋊C8, C24, Dic6, Dic6, C4×S3, C4×S3 [×2], D12 [×2], C3×Q8, C3×Q8, C5×S3, D15, C30, C8.C22, C52C8, C52C8, Dic10, C4×D5, D20, C5⋊D4, C2×C20 [×2], C5×Q8, C5×Q8 [×2], C8⋊S3, C24⋊C2, Q82S3, C3⋊Q16, C3×Q16, S3×Q8, Q83S3, C5×Dic3, C5×Dic3, C3×Dic5, C60, C60, S3×C10, D30, C4.Dic5, Q8⋊D5 [×2], C5⋊Q16, C5⋊Q16, C4○D20, Q8×C10, Q16⋊S3, C3×C52C8, C153C8, D30.C2, C5⋊D12, C3×Dic10, C5×Dic6, C5×Dic6, S3×C20, S3×C20, D60, Q8×C15, C20.C23, D6.Dic5, Dic6⋊D5, C15⋊Q16, C3×C5⋊Q16, Q82D15, D60⋊C2, C5×S3×Q8, C60.44C23
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, Q16⋊S3, C2×S3×D5, C20.C23, S3×C5⋊D4, C60.44C23

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

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

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

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

48 conjugacy classes

class 1 2A2B2C 3 4A4B4C4D4E5A5B 6 8A8B10A10B10C10D10E10F12A12B12C15A15B20A···20F20G···20L24A24B30A30B60A···60F
order122234444455688101010101010121212151520···2020···202424303060···60
size116602246122022220602266664840444···412···122020448···8

48 irreducible representations

dim1111111122222222222244444448
type++++++++++++++++++-++++
imageC1C2C2C2C2C2C2C2S3D4D4D5D6D6D6D10D10D10C5⋊D4C5⋊D4C8.C22S3×D4S3×D5Q16⋊S3C2×S3×D5C20.C23S3×C5⋊D4C60.44C23
kernelC60.44C23D6.Dic5Dic6⋊D5C15⋊Q16C3×C5⋊Q16Q82D15D60⋊C2C5×S3×Q8C5⋊Q16C5×Dic3S3×C10S3×Q8C52C8Dic10C5×Q8Dic6C4×S3C3×Q8Dic3D6C15C10Q8C5C4C3C2C1
# reps1111111111121112224411222442

Matrix representation of C60.44C23 in GL8(𝔽241)

001510000
00190510000
2401902401900000
51190511900000
0000010239
000024024022
0000010240
000024024011
,
127170000000
200114000000
001271700000
002001140000
0000265215059
000018921518291
0000101202215189
0000391405226
,
2400000000
0240000000
10100000
01010000
0000240020
000011239239
0000240010
000011240240
,
16549000000
19276000000
00165490000
00192760000
00004401390
00000440139
000023401970
000002340197

G:=sub<GL(8,GF(241))| [0,0,240,51,0,0,0,0,0,0,190,190,0,0,0,0,1,190,240,51,0,0,0,0,51,51,190,190,0,0,0,0,0,0,0,0,0,240,0,240,0,0,0,0,1,240,1,240,0,0,0,0,0,2,0,1,0,0,0,0,239,2,240,1],[127,200,0,0,0,0,0,0,170,114,0,0,0,0,0,0,0,0,127,200,0,0,0,0,0,0,170,114,0,0,0,0,0,0,0,0,26,189,101,39,0,0,0,0,52,215,202,140,0,0,0,0,150,182,215,52,0,0,0,0,59,91,189,26],[240,0,1,0,0,0,0,0,0,240,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,240,1,240,1,0,0,0,0,0,1,0,1,0,0,0,0,2,239,1,240,0,0,0,0,0,239,0,240],[165,192,0,0,0,0,0,0,49,76,0,0,0,0,0,0,0,0,165,192,0,0,0,0,0,0,49,76,0,0,0,0,0,0,0,0,44,0,234,0,0,0,0,0,0,44,0,234,0,0,0,0,139,0,197,0,0,0,0,0,0,139,0,197] >;

C60.44C23 in GAP, Magma, Sage, TeX

C_{60}._{44}C_2^3
% in TeX

G:=Group("C60.44C2^3");
// GroupNames label

G:=SmallGroup(480,596);
// by ID

G=gap.SmallGroup(480,596);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,120,254,219,100,675,185,80,1356,18822]);
// Polycyclic

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

׿
×
𝔽