metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D30.43D4, D20.17D6, C60.46C23, Dic15.17D4, Dic6.17D10, Dic30.17C22, Q8⋊D5⋊6S3, C3⋊C8.11D10, (Q8×D15)⋊2C2, C3⋊Q16⋊6D5, C6.80(D4×D5), C5⋊Dic12⋊8C2, C10.81(S3×D4), C5⋊2C8.11D6, C5⋊4(D4.D6), (C5×Q8).27D6, Q8.23(S3×D5), C3⋊3(Q16⋊D5), C6.D20⋊8C2, C30.208(C2×D4), (C3×Q8).10D10, D20⋊S3.1C2, D30.5C4⋊7C2, C15⋊23(C8.C22), C20.46(C22×S3), C12.46(C22×D5), (C4×D15).14C22, (C3×D20).18C22, (Q8×C15).16C22, C2.33(D10⋊D6), (C5×Dic6).18C22, C4.46(C2×S3×D5), (C3×Q8⋊D5)⋊8C2, (C5×C3⋊Q16)⋊8C2, (C5×C3⋊C8).16C22, (C3×C5⋊2C8).16C22, SmallGroup(480,598)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D30.43D4
G = < a,b,c,d | a30=b2=d2=1, c4=a15, bab=a-1, cac-1=dad=a19, cbc-1=dbd=a3b, dcd=c3 >
Subgroups: 700 in 120 conjugacy classes, 38 normal (all characteristic)
C1, C2, C2 [×2], C3, C4, C4 [×4], C22 [×2], C5, S3, C6, C6, C8 [×2], C2×C4 [×3], D4 [×2], Q8, Q8 [×3], D5 [×2], C10, Dic3 [×3], C12, C12, D6, C2×C6, C15, M4(2), SD16 [×2], Q16 [×2], C2×Q8, C4○D4, Dic5 [×2], C20, C20 [×2], D10 [×2], C3⋊C8, C24, Dic6, Dic6 [×2], C4×S3 [×2], C2×Dic3, C3⋊D4, C3×D4, C3×Q8, C3×D5, D15, C30, C8.C22, C5⋊2C8, C40, Dic10 [×2], C4×D5 [×3], D20, D20, C5×Q8, C5×Q8, C8⋊S3, Dic12, D4.S3, C3⋊Q16, C3×SD16, D4⋊2S3, S3×Q8, C5×Dic3, Dic15, Dic15, C60, C60, C6×D5, D30, C8⋊D5, C40⋊C2, Q8⋊D5, C5⋊Q16, C5×Q16, Q8×D5, Q8⋊2D5, D4.D6, C5×C3⋊C8, C3×C5⋊2C8, D5×Dic3, C3⋊D20, C3×D20, C5×Dic6, Dic30, Dic30, C4×D15, C4×D15, Q8×C15, Q16⋊D5, D30.5C4, C6.D20, C5⋊Dic12, C3×Q8⋊D5, C5×C3⋊Q16, D20⋊S3, Q8×D15, D30.43D4
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, D10 [×3], C22×S3, C8.C22, C22×D5, S3×D4, S3×D5, D4×D5, D4.D6, C2×S3×D5, Q16⋊D5, D10⋊D6, D30.43D4
►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 30)(2 29)(3 28)(4 27)(5 26)(6 25)(7 24)(8 23)(9 22)(10 21)(11 20)(12 19)(13 18)(14 17)(15 16)(31 60)(32 59)(33 58)(34 57)(35 56)(36 55)(37 54)(38 53)(39 52)(40 51)(41 50)(42 49)(43 48)(44 47)(45 46)(61 70)(62 69)(63 68)(64 67)(65 66)(71 90)(72 89)(73 88)(74 87)(75 86)(76 85)(77 84)(78 83)(79 82)(80 81)(91 110)(92 109)(93 108)(94 107)(95 106)(96 105)(97 104)(98 103)(99 102)(100 101)(111 120)(112 119)(113 118)(114 117)(115 116)(121 145)(122 144)(123 143)(124 142)(125 141)(126 140)(127 139)(128 138)(129 137)(130 136)(131 135)(132 134)(146 150)(147 149)(151 175)(152 174)(153 173)(154 172)(155 171)(156 170)(157 169)(158 168)(159 167)(160 166)(161 165)(162 164)(176 180)(177 179)(181 185)(182 184)(186 210)(187 209)(188 208)(189 207)(190 206)(191 205)(192 204)(193 203)(194 202)(195 201)(196 200)(197 199)(211 215)(212 214)(216 240)(217 239)(218 238)(219 237)(220 236)(221 235)(222 234)(223 233)(224 232)(225 231)(226 230)(227 229)
(1 221 46 206 16 236 31 191)(2 240 47 195 17 225 32 210)(3 229 48 184 18 214 33 199)(4 218 49 203 19 233 34 188)(5 237 50 192 20 222 35 207)(6 226 51 181 21 211 36 196)(7 215 52 200 22 230 37 185)(8 234 53 189 23 219 38 204)(9 223 54 208 24 238 39 193)(10 212 55 197 25 227 40 182)(11 231 56 186 26 216 41 201)(12 220 57 205 27 235 42 190)(13 239 58 194 28 224 43 209)(14 228 59 183 29 213 44 198)(15 217 60 202 30 232 45 187)(61 166 111 121 76 151 96 136)(62 155 112 140 77 170 97 125)(63 174 113 129 78 159 98 144)(64 163 114 148 79 178 99 133)(65 152 115 137 80 167 100 122)(66 171 116 126 81 156 101 141)(67 160 117 145 82 175 102 130)(68 179 118 134 83 164 103 149)(69 168 119 123 84 153 104 138)(70 157 120 142 85 172 105 127)(71 176 91 131 86 161 106 146)(72 165 92 150 87 180 107 135)(73 154 93 139 88 169 108 124)(74 173 94 128 89 158 109 143)(75 162 95 147 90 177 110 132)
(1 126)(2 145)(3 134)(4 123)(5 142)(6 131)(7 150)(8 139)(9 128)(10 147)(11 136)(12 125)(13 144)(14 133)(15 122)(16 141)(17 130)(18 149)(19 138)(20 127)(21 146)(22 135)(23 124)(24 143)(25 132)(26 121)(27 140)(28 129)(29 148)(30 137)(31 156)(32 175)(33 164)(34 153)(35 172)(36 161)(37 180)(38 169)(39 158)(40 177)(41 166)(42 155)(43 174)(44 163)(45 152)(46 171)(47 160)(48 179)(49 168)(50 157)(51 176)(52 165)(53 154)(54 173)(55 162)(56 151)(57 170)(58 159)(59 178)(60 167)(61 186)(62 205)(63 194)(64 183)(65 202)(66 191)(67 210)(68 199)(69 188)(70 207)(71 196)(72 185)(73 204)(74 193)(75 182)(76 201)(77 190)(78 209)(79 198)(80 187)(81 206)(82 195)(83 184)(84 203)(85 192)(86 181)(87 200)(88 189)(89 208)(90 197)(91 211)(92 230)(93 219)(94 238)(95 227)(96 216)(97 235)(98 224)(99 213)(100 232)(101 221)(102 240)(103 229)(104 218)(105 237)(106 226)(107 215)(108 234)(109 223)(110 212)(111 231)(112 220)(113 239)(114 228)(115 217)(116 236)(117 225)(118 214)(119 233)(120 222)
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), (1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(31,60)(32,59)(33,58)(34,57)(35,56)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(45,46)(61,70)(62,69)(63,68)(64,67)(65,66)(71,90)(72,89)(73,88)(74,87)(75,86)(76,85)(77,84)(78,83)(79,82)(80,81)(91,110)(92,109)(93,108)(94,107)(95,106)(96,105)(97,104)(98,103)(99,102)(100,101)(111,120)(112,119)(113,118)(114,117)(115,116)(121,145)(122,144)(123,143)(124,142)(125,141)(126,140)(127,139)(128,138)(129,137)(130,136)(131,135)(132,134)(146,150)(147,149)(151,175)(152,174)(153,173)(154,172)(155,171)(156,170)(157,169)(158,168)(159,167)(160,166)(161,165)(162,164)(176,180)(177,179)(181,185)(182,184)(186,210)(187,209)(188,208)(189,207)(190,206)(191,205)(192,204)(193,203)(194,202)(195,201)(196,200)(197,199)(211,215)(212,214)(216,240)(217,239)(218,238)(219,237)(220,236)(221,235)(222,234)(223,233)(224,232)(225,231)(226,230)(227,229), (1,221,46,206,16,236,31,191)(2,240,47,195,17,225,32,210)(3,229,48,184,18,214,33,199)(4,218,49,203,19,233,34,188)(5,237,50,192,20,222,35,207)(6,226,51,181,21,211,36,196)(7,215,52,200,22,230,37,185)(8,234,53,189,23,219,38,204)(9,223,54,208,24,238,39,193)(10,212,55,197,25,227,40,182)(11,231,56,186,26,216,41,201)(12,220,57,205,27,235,42,190)(13,239,58,194,28,224,43,209)(14,228,59,183,29,213,44,198)(15,217,60,202,30,232,45,187)(61,166,111,121,76,151,96,136)(62,155,112,140,77,170,97,125)(63,174,113,129,78,159,98,144)(64,163,114,148,79,178,99,133)(65,152,115,137,80,167,100,122)(66,171,116,126,81,156,101,141)(67,160,117,145,82,175,102,130)(68,179,118,134,83,164,103,149)(69,168,119,123,84,153,104,138)(70,157,120,142,85,172,105,127)(71,176,91,131,86,161,106,146)(72,165,92,150,87,180,107,135)(73,154,93,139,88,169,108,124)(74,173,94,128,89,158,109,143)(75,162,95,147,90,177,110,132), (1,126)(2,145)(3,134)(4,123)(5,142)(6,131)(7,150)(8,139)(9,128)(10,147)(11,136)(12,125)(13,144)(14,133)(15,122)(16,141)(17,130)(18,149)(19,138)(20,127)(21,146)(22,135)(23,124)(24,143)(25,132)(26,121)(27,140)(28,129)(29,148)(30,137)(31,156)(32,175)(33,164)(34,153)(35,172)(36,161)(37,180)(38,169)(39,158)(40,177)(41,166)(42,155)(43,174)(44,163)(45,152)(46,171)(47,160)(48,179)(49,168)(50,157)(51,176)(52,165)(53,154)(54,173)(55,162)(56,151)(57,170)(58,159)(59,178)(60,167)(61,186)(62,205)(63,194)(64,183)(65,202)(66,191)(67,210)(68,199)(69,188)(70,207)(71,196)(72,185)(73,204)(74,193)(75,182)(76,201)(77,190)(78,209)(79,198)(80,187)(81,206)(82,195)(83,184)(84,203)(85,192)(86,181)(87,200)(88,189)(89,208)(90,197)(91,211)(92,230)(93,219)(94,238)(95,227)(96,216)(97,235)(98,224)(99,213)(100,232)(101,221)(102,240)(103,229)(104,218)(105,237)(106,226)(107,215)(108,234)(109,223)(110,212)(111,231)(112,220)(113,239)(114,228)(115,217)(116,236)(117,225)(118,214)(119,233)(120,222)>;
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), (1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(31,60)(32,59)(33,58)(34,57)(35,56)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(45,46)(61,70)(62,69)(63,68)(64,67)(65,66)(71,90)(72,89)(73,88)(74,87)(75,86)(76,85)(77,84)(78,83)(79,82)(80,81)(91,110)(92,109)(93,108)(94,107)(95,106)(96,105)(97,104)(98,103)(99,102)(100,101)(111,120)(112,119)(113,118)(114,117)(115,116)(121,145)(122,144)(123,143)(124,142)(125,141)(126,140)(127,139)(128,138)(129,137)(130,136)(131,135)(132,134)(146,150)(147,149)(151,175)(152,174)(153,173)(154,172)(155,171)(156,170)(157,169)(158,168)(159,167)(160,166)(161,165)(162,164)(176,180)(177,179)(181,185)(182,184)(186,210)(187,209)(188,208)(189,207)(190,206)(191,205)(192,204)(193,203)(194,202)(195,201)(196,200)(197,199)(211,215)(212,214)(216,240)(217,239)(218,238)(219,237)(220,236)(221,235)(222,234)(223,233)(224,232)(225,231)(226,230)(227,229), (1,221,46,206,16,236,31,191)(2,240,47,195,17,225,32,210)(3,229,48,184,18,214,33,199)(4,218,49,203,19,233,34,188)(5,237,50,192,20,222,35,207)(6,226,51,181,21,211,36,196)(7,215,52,200,22,230,37,185)(8,234,53,189,23,219,38,204)(9,223,54,208,24,238,39,193)(10,212,55,197,25,227,40,182)(11,231,56,186,26,216,41,201)(12,220,57,205,27,235,42,190)(13,239,58,194,28,224,43,209)(14,228,59,183,29,213,44,198)(15,217,60,202,30,232,45,187)(61,166,111,121,76,151,96,136)(62,155,112,140,77,170,97,125)(63,174,113,129,78,159,98,144)(64,163,114,148,79,178,99,133)(65,152,115,137,80,167,100,122)(66,171,116,126,81,156,101,141)(67,160,117,145,82,175,102,130)(68,179,118,134,83,164,103,149)(69,168,119,123,84,153,104,138)(70,157,120,142,85,172,105,127)(71,176,91,131,86,161,106,146)(72,165,92,150,87,180,107,135)(73,154,93,139,88,169,108,124)(74,173,94,128,89,158,109,143)(75,162,95,147,90,177,110,132), (1,126)(2,145)(3,134)(4,123)(5,142)(6,131)(7,150)(8,139)(9,128)(10,147)(11,136)(12,125)(13,144)(14,133)(15,122)(16,141)(17,130)(18,149)(19,138)(20,127)(21,146)(22,135)(23,124)(24,143)(25,132)(26,121)(27,140)(28,129)(29,148)(30,137)(31,156)(32,175)(33,164)(34,153)(35,172)(36,161)(37,180)(38,169)(39,158)(40,177)(41,166)(42,155)(43,174)(44,163)(45,152)(46,171)(47,160)(48,179)(49,168)(50,157)(51,176)(52,165)(53,154)(54,173)(55,162)(56,151)(57,170)(58,159)(59,178)(60,167)(61,186)(62,205)(63,194)(64,183)(65,202)(66,191)(67,210)(68,199)(69,188)(70,207)(71,196)(72,185)(73,204)(74,193)(75,182)(76,201)(77,190)(78,209)(79,198)(80,187)(81,206)(82,195)(83,184)(84,203)(85,192)(86,181)(87,200)(88,189)(89,208)(90,197)(91,211)(92,230)(93,219)(94,238)(95,227)(96,216)(97,235)(98,224)(99,213)(100,232)(101,221)(102,240)(103,229)(104,218)(105,237)(106,226)(107,215)(108,234)(109,223)(110,212)(111,231)(112,220)(113,239)(114,228)(115,217)(116,236)(117,225)(118,214)(119,233)(120,222) );
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)], [(1,30),(2,29),(3,28),(4,27),(5,26),(6,25),(7,24),(8,23),(9,22),(10,21),(11,20),(12,19),(13,18),(14,17),(15,16),(31,60),(32,59),(33,58),(34,57),(35,56),(36,55),(37,54),(38,53),(39,52),(40,51),(41,50),(42,49),(43,48),(44,47),(45,46),(61,70),(62,69),(63,68),(64,67),(65,66),(71,90),(72,89),(73,88),(74,87),(75,86),(76,85),(77,84),(78,83),(79,82),(80,81),(91,110),(92,109),(93,108),(94,107),(95,106),(96,105),(97,104),(98,103),(99,102),(100,101),(111,120),(112,119),(113,118),(114,117),(115,116),(121,145),(122,144),(123,143),(124,142),(125,141),(126,140),(127,139),(128,138),(129,137),(130,136),(131,135),(132,134),(146,150),(147,149),(151,175),(152,174),(153,173),(154,172),(155,171),(156,170),(157,169),(158,168),(159,167),(160,166),(161,165),(162,164),(176,180),(177,179),(181,185),(182,184),(186,210),(187,209),(188,208),(189,207),(190,206),(191,205),(192,204),(193,203),(194,202),(195,201),(196,200),(197,199),(211,215),(212,214),(216,240),(217,239),(218,238),(219,237),(220,236),(221,235),(222,234),(223,233),(224,232),(225,231),(226,230),(227,229)], [(1,221,46,206,16,236,31,191),(2,240,47,195,17,225,32,210),(3,229,48,184,18,214,33,199),(4,218,49,203,19,233,34,188),(5,237,50,192,20,222,35,207),(6,226,51,181,21,211,36,196),(7,215,52,200,22,230,37,185),(8,234,53,189,23,219,38,204),(9,223,54,208,24,238,39,193),(10,212,55,197,25,227,40,182),(11,231,56,186,26,216,41,201),(12,220,57,205,27,235,42,190),(13,239,58,194,28,224,43,209),(14,228,59,183,29,213,44,198),(15,217,60,202,30,232,45,187),(61,166,111,121,76,151,96,136),(62,155,112,140,77,170,97,125),(63,174,113,129,78,159,98,144),(64,163,114,148,79,178,99,133),(65,152,115,137,80,167,100,122),(66,171,116,126,81,156,101,141),(67,160,117,145,82,175,102,130),(68,179,118,134,83,164,103,149),(69,168,119,123,84,153,104,138),(70,157,120,142,85,172,105,127),(71,176,91,131,86,161,106,146),(72,165,92,150,87,180,107,135),(73,154,93,139,88,169,108,124),(74,173,94,128,89,158,109,143),(75,162,95,147,90,177,110,132)], [(1,126),(2,145),(3,134),(4,123),(5,142),(6,131),(7,150),(8,139),(9,128),(10,147),(11,136),(12,125),(13,144),(14,133),(15,122),(16,141),(17,130),(18,149),(19,138),(20,127),(21,146),(22,135),(23,124),(24,143),(25,132),(26,121),(27,140),(28,129),(29,148),(30,137),(31,156),(32,175),(33,164),(34,153),(35,172),(36,161),(37,180),(38,169),(39,158),(40,177),(41,166),(42,155),(43,174),(44,163),(45,152),(46,171),(47,160),(48,179),(49,168),(50,157),(51,176),(52,165),(53,154),(54,173),(55,162),(56,151),(57,170),(58,159),(59,178),(60,167),(61,186),(62,205),(63,194),(64,183),(65,202),(66,191),(67,210),(68,199),(69,188),(70,207),(71,196),(72,185),(73,204),(74,193),(75,182),(76,201),(77,190),(78,209),(79,198),(80,187),(81,206),(82,195),(83,184),(84,203),(85,192),(86,181),(87,200),(88,189),(89,208),(90,197),(91,211),(92,230),(93,219),(94,238),(95,227),(96,216),(97,235),(98,224),(99,213),(100,232),(101,221),(102,240),(103,229),(104,218),(105,237),(106,226),(107,215),(108,234),(109,223),(110,212),(111,231),(112,220),(113,239),(114,228),(115,217),(116,236),(117,225),(118,214),(119,233),(120,222)])
42 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 4E | 5A | 5B | 6A | 6B | 8A | 8B | 10A | 10B | 12A | 12B | 15A | 15B | 20A | 20B | 20C | 20D | 20E | 20F | 24A | 24B | 30A | 30B | 40A | 40B | 40C | 40D | 60A | ··· | 60F |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 8 | 8 | 10 | 10 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 20 | 20 | 20 | 24 | 24 | 30 | 30 | 40 | 40 | 40 | 40 | 60 | ··· | 60 |
| size | 1 | 1 | 20 | 30 | 2 | 2 | 4 | 12 | 30 | 60 | 2 | 2 | 2 | 40 | 12 | 20 | 2 | 2 | 4 | 8 | 4 | 4 | 4 | 4 | 8 | 8 | 24 | 24 | 20 | 20 | 4 | 4 | 12 | 12 | 12 | 12 | 8 | ··· | 8 |
42 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 8 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | + | - | + | + | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | S3 | D4 | D4 | D5 | D6 | D6 | D6 | D10 | D10 | D10 | C8.C22 | S3×D4 | S3×D5 | D4×D5 | D4.D6 | C2×S3×D5 | Q16⋊D5 | D10⋊D6 | D30.43D4 |
| kernel | D30.43D4 | D30.5C4 | C6.D20 | C5⋊Dic12 | C3×Q8⋊D5 | C5×C3⋊Q16 | D20⋊S3 | Q8×D15 | Q8⋊D5 | Dic15 | D30 | C3⋊Q16 | C5⋊2C8 | D20 | C5×Q8 | C3⋊C8 | Dic6 | C3×Q8 | C15 | C10 | Q8 | C6 | C5 | C4 | C3 | C2 | C1 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 2 | 2 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 2 |
Matrix representation of D30.43D4 ►in GL8(𝔽241)
| 0 | 0 | 0 | 240 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 51 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 |
| 240 | 190 | 240 | 190 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 240 | 52 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 51 | 191 |
| 0 | 0 | 0 | 0 | 0 | 0 | 240 | 1 |
| 0 | 0 | 190 | 240 | 0 | 0 | 0 | 0 |
| 0 | 0 | 190 | 51 | 0 | 0 | 0 | 0 |
| 190 | 240 | 0 | 0 | 0 | 0 | 0 | 0 |
| 190 | 51 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 52 | 189 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 189 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 51 |
| 0 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
| 11 | 20 | 31 | 31 | 0 | 0 | 0 | 0 |
| 182 | 230 | 137 | 210 | 0 | 0 | 0 | 0 |
| 210 | 210 | 221 | 230 | 0 | 0 | 0 | 0 |
| 104 | 31 | 45 | 20 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 77 | 148 |
| 0 | 0 | 0 | 0 | 0 | 0 | 225 | 71 |
| 0 | 0 | 0 | 0 | 173 | 230 | 169 | 57 |
| 0 | 0 | 0 | 0 | 151 | 79 | 57 | 72 |
| 104 | 238 | 101 | 101 | 0 | 0 | 0 | 0 |
| 236 | 137 | 11 | 140 | 0 | 0 | 0 | 0 |
| 140 | 140 | 3 | 137 | 0 | 0 | 0 | 0 |
| 230 | 101 | 225 | 238 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 202 | 219 | 76 | 96 |
| 0 | 0 | 0 | 0 | 119 | 39 | 172 | 20 |
| 0 | 0 | 0 | 0 | 91 | 238 | 180 | 219 |
| 0 | 0 | 0 | 0 | 85 | 153 | 219 | 61 |
G:=sub<GL(8,GF(241))| [0,0,0,240,0,0,0,0,0,0,1,190,0,0,0,0,0,1,0,240,0,0,0,0,240,51,1,190,0,0,0,0,0,0,0,0,0,240,0,0,0,0,0,0,1,52,0,0,0,0,0,0,0,0,51,240,0,0,0,0,0,0,191,1],[0,0,190,190,0,0,0,0,0,0,240,51,0,0,0,0,190,190,0,0,0,0,0,0,240,51,0,0,0,0,0,0,0,0,0,0,52,1,0,0,0,0,0,0,189,189,0,0,0,0,0,0,0,0,0,52,0,0,0,0,0,0,51,0],[11,182,210,104,0,0,0,0,20,230,210,31,0,0,0,0,31,137,221,45,0,0,0,0,31,210,230,20,0,0,0,0,0,0,0,0,0,0,173,151,0,0,0,0,0,0,230,79,0,0,0,0,77,225,169,57,0,0,0,0,148,71,57,72],[104,236,140,230,0,0,0,0,238,137,140,101,0,0,0,0,101,11,3,225,0,0,0,0,101,140,137,238,0,0,0,0,0,0,0,0,202,119,91,85,0,0,0,0,219,39,238,153,0,0,0,0,76,172,180,219,0,0,0,0,96,20,219,61] >;
D30.43D4 in GAP, Magma, Sage, TeX
D_{30}._{43}D_4 % in TeX
G:=Group("D30.43D4"); // GroupNames label
G:=SmallGroup(480,598);
// by ID
G=gap.SmallGroup(480,598);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,120,254,303,100,675,346,185,80,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^30=b^2=d^2=1,c^4=a^15,b*a*b=a^-1,c*a*c^-1=d*a*d=a^19,c*b*c^-1=d*b*d=a^3*b,d*c*d=c^3>;
// generators/relations