direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C5×C12.48D4, C60.226D4, (C2×C30)⋊13Q8, C6.8(Q8×C10), C4⋊Dic3⋊8C10, C12.48(C5×D4), C6.39(D4×C10), C30.89(C2×Q8), Dic3⋊C4⋊2C10, (C2×Dic6)⋊6C10, (C2×C10)⋊10Dic6, (C2×C20).437D6, C30.422(C2×D4), C15⋊36(C22⋊Q8), C2.9(C10×Dic6), C22⋊3(C5×Dic6), (C10×Dic6)⋊22C2, (C22×C20).19S3, C23.25(S3×C10), (C22×C60).22C2, (C22×C12).6C10, C10.48(C2×Dic6), C30.208(C4○D4), C20.116(C3⋊D4), (C2×C60).530C22, (C2×C30).421C23, C6.D4.4C10, (C22×C10).122D6, C10.122(C4○D12), (C22×C30).172C22, (C10×Dic3).147C22, (C2×C6)⋊3(C5×Q8), C3⋊4(C5×C22⋊Q8), C6.13(C5×C4○D4), C4.23(C5×C3⋊D4), C2.5(C10×C3⋊D4), (C2×C4).85(S3×C10), (C5×Dic3⋊C4)⋊2C2, (C5×C4⋊Dic3)⋊26C2, C2.17(C5×C4○D12), C22.54(S3×C2×C10), (C22×C4).7(C5×S3), (C2×C12).96(C2×C10), C10.124(C2×C3⋊D4), (C22×C6).34(C2×C10), (C2×C6).42(C22×C10), (C2×C10).355(C22×S3), (C2×Dic3).11(C2×C10), (C5×C6.D4).10C2, SmallGroup(480,803)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C5×C12.48D4
G = < a,b,c,d | a5=b12=c4=1, d2=b6, ab=ba, ac=ca, ad=da, cbc-1=dbd-1=b-1, dcd-1=b6c-1 >
Subgroups: 292 in 148 conjugacy classes, 74 normal (42 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, C22, C5, C6, C6, C2×C4, C2×C4, Q8, C23, C10, C10, Dic3, C12, C12, C2×C6, C2×C6, C2×C6, C15, C22⋊C4, C4⋊C4, C22×C4, C2×Q8, C20, C20, C2×C10, C2×C10, C2×C10, Dic6, C2×Dic3, C2×C12, C2×C12, C22×C6, C30, C30, C22⋊Q8, C2×C20, C2×C20, C5×Q8, C22×C10, Dic3⋊C4, C4⋊Dic3, C6.D4, C2×Dic6, C22×C12, C5×Dic3, C60, C60, C2×C30, C2×C30, C2×C30, C5×C22⋊C4, C5×C4⋊C4, C22×C20, Q8×C10, C12.48D4, C5×Dic6, C10×Dic3, C2×C60, C2×C60, C22×C30, C5×C22⋊Q8, C5×Dic3⋊C4, C5×C4⋊Dic3, C5×C6.D4, C10×Dic6, C22×C60, C5×C12.48D4
Quotients: C1, C2, C22, C5, S3, D4, Q8, C23, C10, D6, C2×D4, C2×Q8, C4○D4, C2×C10, Dic6, C3⋊D4, C22×S3, C5×S3, C22⋊Q8, C5×D4, C5×Q8, C22×C10, C2×Dic6, C4○D12, C2×C3⋊D4, S3×C10, D4×C10, Q8×C10, C5×C4○D4, C12.48D4, C5×Dic6, C5×C3⋊D4, S3×C2×C10, C5×C22⋊Q8, C10×Dic6, C5×C4○D12, C10×C3⋊D4, C5×C12.48D4
►On 240 points
Generators in S240
(1 233 171 25 162)(2 234 172 26 163)(3 235 173 27 164)(4 236 174 28 165)(5 237 175 29 166)(6 238 176 30 167)(7 239 177 31 168)(8 240 178 32 157)(9 229 179 33 158)(10 230 180 34 159)(11 231 169 35 160)(12 232 170 36 161)(13 225 194 152 191)(14 226 195 153 192)(15 227 196 154 181)(16 228 197 155 182)(17 217 198 156 183)(18 218 199 145 184)(19 219 200 146 185)(20 220 201 147 186)(21 221 202 148 187)(22 222 203 149 188)(23 223 204 150 189)(24 224 193 151 190)(37 74 129 104 119)(38 75 130 105 120)(39 76 131 106 109)(40 77 132 107 110)(41 78 121 108 111)(42 79 122 97 112)(43 80 123 98 113)(44 81 124 99 114)(45 82 125 100 115)(46 83 126 101 116)(47 84 127 102 117)(48 73 128 103 118)(49 139 93 66 211)(50 140 94 67 212)(51 141 95 68 213)(52 142 96 69 214)(53 143 85 70 215)(54 144 86 71 216)(55 133 87 72 205)(56 134 88 61 206)(57 135 89 62 207)(58 136 90 63 208)(59 137 91 64 209)(60 138 92 65 210)
(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 39 58 218)(2 38 59 217)(3 37 60 228)(4 48 49 227)(5 47 50 226)(6 46 51 225)(7 45 52 224)(8 44 53 223)(9 43 54 222)(10 42 55 221)(11 41 56 220)(12 40 57 219)(13 167 116 213)(14 166 117 212)(15 165 118 211)(16 164 119 210)(17 163 120 209)(18 162 109 208)(19 161 110 207)(20 160 111 206)(21 159 112 205)(22 158 113 216)(23 157 114 215)(24 168 115 214)(25 106 63 184)(26 105 64 183)(27 104 65 182)(28 103 66 181)(29 102 67 192)(30 101 68 191)(31 100 69 190)(32 99 70 189)(33 98 71 188)(34 97 72 187)(35 108 61 186)(36 107 62 185)(73 139 196 236)(74 138 197 235)(75 137 198 234)(76 136 199 233)(77 135 200 232)(78 134 201 231)(79 133 202 230)(80 144 203 229)(81 143 204 240)(82 142 193 239)(83 141 194 238)(84 140 195 237)(85 150 178 124)(86 149 179 123)(87 148 180 122)(88 147 169 121)(89 146 170 132)(90 145 171 131)(91 156 172 130)(92 155 173 129)(93 154 174 128)(94 153 175 127)(95 152 176 126)(96 151 177 125)
(1 224 7 218)(2 223 8 217)(3 222 9 228)(4 221 10 227)(5 220 11 226)(6 219 12 225)(13 167 19 161)(14 166 20 160)(15 165 21 159)(16 164 22 158)(17 163 23 157)(18 162 24 168)(25 190 31 184)(26 189 32 183)(27 188 33 182)(28 187 34 181)(29 186 35 192)(30 185 36 191)(37 60 43 54)(38 59 44 53)(39 58 45 52)(40 57 46 51)(41 56 47 50)(42 55 48 49)(61 102 67 108)(62 101 68 107)(63 100 69 106)(64 99 70 105)(65 98 71 104)(66 97 72 103)(73 139 79 133)(74 138 80 144)(75 137 81 143)(76 136 82 142)(77 135 83 141)(78 134 84 140)(85 130 91 124)(86 129 92 123)(87 128 93 122)(88 127 94 121)(89 126 95 132)(90 125 96 131)(109 208 115 214)(110 207 116 213)(111 206 117 212)(112 205 118 211)(113 216 119 210)(114 215 120 209)(145 171 151 177)(146 170 152 176)(147 169 153 175)(148 180 154 174)(149 179 155 173)(150 178 156 172)(193 239 199 233)(194 238 200 232)(195 237 201 231)(196 236 202 230)(197 235 203 229)(198 234 204 240)
G:=sub<Sym(240)| (1,233,171,25,162)(2,234,172,26,163)(3,235,173,27,164)(4,236,174,28,165)(5,237,175,29,166)(6,238,176,30,167)(7,239,177,31,168)(8,240,178,32,157)(9,229,179,33,158)(10,230,180,34,159)(11,231,169,35,160)(12,232,170,36,161)(13,225,194,152,191)(14,226,195,153,192)(15,227,196,154,181)(16,228,197,155,182)(17,217,198,156,183)(18,218,199,145,184)(19,219,200,146,185)(20,220,201,147,186)(21,221,202,148,187)(22,222,203,149,188)(23,223,204,150,189)(24,224,193,151,190)(37,74,129,104,119)(38,75,130,105,120)(39,76,131,106,109)(40,77,132,107,110)(41,78,121,108,111)(42,79,122,97,112)(43,80,123,98,113)(44,81,124,99,114)(45,82,125,100,115)(46,83,126,101,116)(47,84,127,102,117)(48,73,128,103,118)(49,139,93,66,211)(50,140,94,67,212)(51,141,95,68,213)(52,142,96,69,214)(53,143,85,70,215)(54,144,86,71,216)(55,133,87,72,205)(56,134,88,61,206)(57,135,89,62,207)(58,136,90,63,208)(59,137,91,64,209)(60,138,92,65,210), (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), (1,39,58,218)(2,38,59,217)(3,37,60,228)(4,48,49,227)(5,47,50,226)(6,46,51,225)(7,45,52,224)(8,44,53,223)(9,43,54,222)(10,42,55,221)(11,41,56,220)(12,40,57,219)(13,167,116,213)(14,166,117,212)(15,165,118,211)(16,164,119,210)(17,163,120,209)(18,162,109,208)(19,161,110,207)(20,160,111,206)(21,159,112,205)(22,158,113,216)(23,157,114,215)(24,168,115,214)(25,106,63,184)(26,105,64,183)(27,104,65,182)(28,103,66,181)(29,102,67,192)(30,101,68,191)(31,100,69,190)(32,99,70,189)(33,98,71,188)(34,97,72,187)(35,108,61,186)(36,107,62,185)(73,139,196,236)(74,138,197,235)(75,137,198,234)(76,136,199,233)(77,135,200,232)(78,134,201,231)(79,133,202,230)(80,144,203,229)(81,143,204,240)(82,142,193,239)(83,141,194,238)(84,140,195,237)(85,150,178,124)(86,149,179,123)(87,148,180,122)(88,147,169,121)(89,146,170,132)(90,145,171,131)(91,156,172,130)(92,155,173,129)(93,154,174,128)(94,153,175,127)(95,152,176,126)(96,151,177,125), (1,224,7,218)(2,223,8,217)(3,222,9,228)(4,221,10,227)(5,220,11,226)(6,219,12,225)(13,167,19,161)(14,166,20,160)(15,165,21,159)(16,164,22,158)(17,163,23,157)(18,162,24,168)(25,190,31,184)(26,189,32,183)(27,188,33,182)(28,187,34,181)(29,186,35,192)(30,185,36,191)(37,60,43,54)(38,59,44,53)(39,58,45,52)(40,57,46,51)(41,56,47,50)(42,55,48,49)(61,102,67,108)(62,101,68,107)(63,100,69,106)(64,99,70,105)(65,98,71,104)(66,97,72,103)(73,139,79,133)(74,138,80,144)(75,137,81,143)(76,136,82,142)(77,135,83,141)(78,134,84,140)(85,130,91,124)(86,129,92,123)(87,128,93,122)(88,127,94,121)(89,126,95,132)(90,125,96,131)(109,208,115,214)(110,207,116,213)(111,206,117,212)(112,205,118,211)(113,216,119,210)(114,215,120,209)(145,171,151,177)(146,170,152,176)(147,169,153,175)(148,180,154,174)(149,179,155,173)(150,178,156,172)(193,239,199,233)(194,238,200,232)(195,237,201,231)(196,236,202,230)(197,235,203,229)(198,234,204,240)>;
G:=Group( (1,233,171,25,162)(2,234,172,26,163)(3,235,173,27,164)(4,236,174,28,165)(5,237,175,29,166)(6,238,176,30,167)(7,239,177,31,168)(8,240,178,32,157)(9,229,179,33,158)(10,230,180,34,159)(11,231,169,35,160)(12,232,170,36,161)(13,225,194,152,191)(14,226,195,153,192)(15,227,196,154,181)(16,228,197,155,182)(17,217,198,156,183)(18,218,199,145,184)(19,219,200,146,185)(20,220,201,147,186)(21,221,202,148,187)(22,222,203,149,188)(23,223,204,150,189)(24,224,193,151,190)(37,74,129,104,119)(38,75,130,105,120)(39,76,131,106,109)(40,77,132,107,110)(41,78,121,108,111)(42,79,122,97,112)(43,80,123,98,113)(44,81,124,99,114)(45,82,125,100,115)(46,83,126,101,116)(47,84,127,102,117)(48,73,128,103,118)(49,139,93,66,211)(50,140,94,67,212)(51,141,95,68,213)(52,142,96,69,214)(53,143,85,70,215)(54,144,86,71,216)(55,133,87,72,205)(56,134,88,61,206)(57,135,89,62,207)(58,136,90,63,208)(59,137,91,64,209)(60,138,92,65,210), (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), (1,39,58,218)(2,38,59,217)(3,37,60,228)(4,48,49,227)(5,47,50,226)(6,46,51,225)(7,45,52,224)(8,44,53,223)(9,43,54,222)(10,42,55,221)(11,41,56,220)(12,40,57,219)(13,167,116,213)(14,166,117,212)(15,165,118,211)(16,164,119,210)(17,163,120,209)(18,162,109,208)(19,161,110,207)(20,160,111,206)(21,159,112,205)(22,158,113,216)(23,157,114,215)(24,168,115,214)(25,106,63,184)(26,105,64,183)(27,104,65,182)(28,103,66,181)(29,102,67,192)(30,101,68,191)(31,100,69,190)(32,99,70,189)(33,98,71,188)(34,97,72,187)(35,108,61,186)(36,107,62,185)(73,139,196,236)(74,138,197,235)(75,137,198,234)(76,136,199,233)(77,135,200,232)(78,134,201,231)(79,133,202,230)(80,144,203,229)(81,143,204,240)(82,142,193,239)(83,141,194,238)(84,140,195,237)(85,150,178,124)(86,149,179,123)(87,148,180,122)(88,147,169,121)(89,146,170,132)(90,145,171,131)(91,156,172,130)(92,155,173,129)(93,154,174,128)(94,153,175,127)(95,152,176,126)(96,151,177,125), (1,224,7,218)(2,223,8,217)(3,222,9,228)(4,221,10,227)(5,220,11,226)(6,219,12,225)(13,167,19,161)(14,166,20,160)(15,165,21,159)(16,164,22,158)(17,163,23,157)(18,162,24,168)(25,190,31,184)(26,189,32,183)(27,188,33,182)(28,187,34,181)(29,186,35,192)(30,185,36,191)(37,60,43,54)(38,59,44,53)(39,58,45,52)(40,57,46,51)(41,56,47,50)(42,55,48,49)(61,102,67,108)(62,101,68,107)(63,100,69,106)(64,99,70,105)(65,98,71,104)(66,97,72,103)(73,139,79,133)(74,138,80,144)(75,137,81,143)(76,136,82,142)(77,135,83,141)(78,134,84,140)(85,130,91,124)(86,129,92,123)(87,128,93,122)(88,127,94,121)(89,126,95,132)(90,125,96,131)(109,208,115,214)(110,207,116,213)(111,206,117,212)(112,205,118,211)(113,216,119,210)(114,215,120,209)(145,171,151,177)(146,170,152,176)(147,169,153,175)(148,180,154,174)(149,179,155,173)(150,178,156,172)(193,239,199,233)(194,238,200,232)(195,237,201,231)(196,236,202,230)(197,235,203,229)(198,234,204,240) );
G=PermutationGroup([[(1,233,171,25,162),(2,234,172,26,163),(3,235,173,27,164),(4,236,174,28,165),(5,237,175,29,166),(6,238,176,30,167),(7,239,177,31,168),(8,240,178,32,157),(9,229,179,33,158),(10,230,180,34,159),(11,231,169,35,160),(12,232,170,36,161),(13,225,194,152,191),(14,226,195,153,192),(15,227,196,154,181),(16,228,197,155,182),(17,217,198,156,183),(18,218,199,145,184),(19,219,200,146,185),(20,220,201,147,186),(21,221,202,148,187),(22,222,203,149,188),(23,223,204,150,189),(24,224,193,151,190),(37,74,129,104,119),(38,75,130,105,120),(39,76,131,106,109),(40,77,132,107,110),(41,78,121,108,111),(42,79,122,97,112),(43,80,123,98,113),(44,81,124,99,114),(45,82,125,100,115),(46,83,126,101,116),(47,84,127,102,117),(48,73,128,103,118),(49,139,93,66,211),(50,140,94,67,212),(51,141,95,68,213),(52,142,96,69,214),(53,143,85,70,215),(54,144,86,71,216),(55,133,87,72,205),(56,134,88,61,206),(57,135,89,62,207),(58,136,90,63,208),(59,137,91,64,209),(60,138,92,65,210)], [(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)], [(1,39,58,218),(2,38,59,217),(3,37,60,228),(4,48,49,227),(5,47,50,226),(6,46,51,225),(7,45,52,224),(8,44,53,223),(9,43,54,222),(10,42,55,221),(11,41,56,220),(12,40,57,219),(13,167,116,213),(14,166,117,212),(15,165,118,211),(16,164,119,210),(17,163,120,209),(18,162,109,208),(19,161,110,207),(20,160,111,206),(21,159,112,205),(22,158,113,216),(23,157,114,215),(24,168,115,214),(25,106,63,184),(26,105,64,183),(27,104,65,182),(28,103,66,181),(29,102,67,192),(30,101,68,191),(31,100,69,190),(32,99,70,189),(33,98,71,188),(34,97,72,187),(35,108,61,186),(36,107,62,185),(73,139,196,236),(74,138,197,235),(75,137,198,234),(76,136,199,233),(77,135,200,232),(78,134,201,231),(79,133,202,230),(80,144,203,229),(81,143,204,240),(82,142,193,239),(83,141,194,238),(84,140,195,237),(85,150,178,124),(86,149,179,123),(87,148,180,122),(88,147,169,121),(89,146,170,132),(90,145,171,131),(91,156,172,130),(92,155,173,129),(93,154,174,128),(94,153,175,127),(95,152,176,126),(96,151,177,125)], [(1,224,7,218),(2,223,8,217),(3,222,9,228),(4,221,10,227),(5,220,11,226),(6,219,12,225),(13,167,19,161),(14,166,20,160),(15,165,21,159),(16,164,22,158),(17,163,23,157),(18,162,24,168),(25,190,31,184),(26,189,32,183),(27,188,33,182),(28,187,34,181),(29,186,35,192),(30,185,36,191),(37,60,43,54),(38,59,44,53),(39,58,45,52),(40,57,46,51),(41,56,47,50),(42,55,48,49),(61,102,67,108),(62,101,68,107),(63,100,69,106),(64,99,70,105),(65,98,71,104),(66,97,72,103),(73,139,79,133),(74,138,80,144),(75,137,81,143),(76,136,82,142),(77,135,83,141),(78,134,84,140),(85,130,91,124),(86,129,92,123),(87,128,93,122),(88,127,94,121),(89,126,95,132),(90,125,96,131),(109,208,115,214),(110,207,116,213),(111,206,117,212),(112,205,118,211),(113,216,119,210),(114,215,120,209),(145,171,151,177),(146,170,152,176),(147,169,153,175),(148,180,154,174),(149,179,155,173),(150,178,156,172),(193,239,199,233),(194,238,200,232),(195,237,201,231),(196,236,202,230),(197,235,203,229),(198,234,204,240)]])
150 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 5A | 5B | 5C | 5D | 6A | ··· | 6G | 10A | ··· | 10L | 10M | ··· | 10T | 12A | ··· | 12H | 15A | 15B | 15C | 15D | 20A | ··· | 20P | 20Q | ··· | 20AF | 30A | ··· | 30AB | 60A | ··· | 60AF |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 5 | 5 | 6 | ··· | 6 | 10 | ··· | 10 | 10 | ··· | 10 | 12 | ··· | 12 | 15 | 15 | 15 | 15 | 20 | ··· | 20 | 20 | ··· | 20 | 30 | ··· | 30 | 60 | ··· | 60 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 12 | 12 | 12 | 12 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 12 | ··· | 12 | 2 | ··· | 2 | 2 | ··· | 2 |
150 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | - | + | + | - | ||||||||||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C5 | C10 | C10 | C10 | C10 | C10 | S3 | D4 | Q8 | D6 | D6 | C4○D4 | C3⋊D4 | Dic6 | C5×S3 | C5×D4 | C5×Q8 | C4○D12 | S3×C10 | S3×C10 | C5×C4○D4 | C5×C3⋊D4 | C5×Dic6 | C5×C4○D12 |
| kernel | C5×C12.48D4 | C5×Dic3⋊C4 | C5×C4⋊Dic3 | C5×C6.D4 | C10×Dic6 | C22×C60 | C12.48D4 | Dic3⋊C4 | C4⋊Dic3 | C6.D4 | C2×Dic6 | C22×C12 | C22×C20 | C60 | C2×C30 | C2×C20 | C22×C10 | C30 | C20 | C2×C10 | C22×C4 | C12 | C2×C6 | C10 | C2×C4 | C23 | C6 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 2 | 1 | 1 | 4 | 8 | 4 | 8 | 4 | 4 | 1 | 2 | 2 | 2 | 1 | 2 | 4 | 4 | 4 | 8 | 8 | 4 | 8 | 4 | 8 | 16 | 16 | 16 |
Matrix representation of C5×C12.48D4 ►in GL4(𝔽61) generated by
| 34 | 0 | 0 | 0 |
| 0 | 34 | 0 | 0 |
| 0 | 0 | 34 | 0 |
| 0 | 0 | 0 | 34 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 32 | 0 |
| 0 | 0 | 0 | 21 |
| 1 | 51 | 0 | 0 |
| 49 | 60 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 60 | 0 |
| 1 | 51 | 0 | 0 |
| 0 | 60 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 60 | 0 |
G:=sub<GL(4,GF(61))| [34,0,0,0,0,34,0,0,0,0,34,0,0,0,0,34],[1,0,0,0,0,1,0,0,0,0,32,0,0,0,0,21],[1,49,0,0,51,60,0,0,0,0,0,60,0,0,1,0],[1,0,0,0,51,60,0,0,0,0,0,60,0,0,1,0] >;
C5×C12.48D4 in GAP, Magma, Sage, TeX
C_5\times C_{12}._{48}D_4 % in TeX
G:=Group("C5xC12.48D4"); // GroupNames label
G:=SmallGroup(480,803);
// by ID
G=gap.SmallGroup(480,803);
# by ID
G:=PCGroup([7,-2,-2,-2,-5,-2,-2,-3,560,1149,568,926,15686]);
// Polycyclic
G:=Group<a,b,c,d|a^5=b^12=c^4=1,d^2=b^6,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d^-1=b^-1,d*c*d^-1=b^6*c^-1>;
// generators/relations