Copied to
clipboard

G = D30.6D4order 480 = 25·3·5

6th non-split extension by D30 of D4 acting via D4/C2=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D30.6D4, C6.62(D4×D5), Dic3⋊C47D5, (C2×D60).2C2, (C2×C20).25D6, C10.64(S3×D4), C10.D48S3, C30.139(C2×D4), (C2×C12).25D10, C51(D6.D4), D304C417C2, C30.72(C4○D4), C6.11(C4○D20), (C2×C60).12C22, (C2×Dic5).41D6, C10.13(C4○D12), C31(D10.13D4), (C2×C30).123C23, C6.15(Q82D5), C2.15(D10⋊D6), C2.17(D60⋊C2), C2.16(C12.28D10), C10.16(Q83S3), (C2×Dic3).106D10, C1511(C22.D4), (C6×Dic5).76C22, (C10×Dic3).77C22, (C22×D15).42C22, (C2×C4).56(S3×D5), (C5×Dic3⋊C4)⋊7C2, (C2×D30.C2)⋊7C2, C22.186(C2×S3×D5), (C3×C10.D4)⋊8C2, (C2×C6).135(C22×D5), (C2×C10).135(C22×S3), SmallGroup(480,509)

Series: Derived Chief Lower central Upper central

C1C2×C30 — D30.6D4
C1C5C15C30C2×C30C6×Dic5C2×D30.C2 — D30.6D4
C15C2×C30 — D30.6D4
C1C22C2×C4

Generators and relations for D30.6D4
 G = < a,b,c,d | a30=b2=c4=1, d2=a15, bab=a-1, cac-1=dad-1=a19, cbc-1=a3b, dbd-1=a18b, dcd-1=c-1 >

Subgroups: 1036 in 156 conjugacy classes, 46 normal (44 characteristic)
C1, C2 [×3], C2 [×3], C3, C4 [×5], C22, C22 [×7], C5, S3 [×3], C6 [×3], C2×C4, C2×C4 [×6], D4 [×2], C23 [×2], D5 [×3], C10 [×3], Dic3 [×2], C12 [×3], D6 [×7], C2×C6, C15, C22⋊C4 [×3], C4⋊C4 [×2], C22×C4, C2×D4, Dic5 [×2], C20 [×3], D10 [×7], C2×C10, C4×S3 [×2], D12 [×2], C2×Dic3 [×2], C2×C12, C2×C12 [×2], C22×S3 [×2], D15 [×3], C30 [×3], C22.D4, C4×D5 [×2], D20 [×2], C2×Dic5 [×2], C2×C20, C2×C20 [×2], C22×D5 [×2], Dic3⋊C4, D6⋊C4 [×3], C3×C4⋊C4, S3×C2×C4, C2×D12, C5×Dic3 [×2], C3×Dic5 [×2], C60, D30 [×2], D30 [×5], C2×C30, C10.D4, D10⋊C4 [×3], C5×C4⋊C4, C2×C4×D5, C2×D20, D6.D4, D30.C2 [×2], C6×Dic5 [×2], C10×Dic3 [×2], D60 [×2], C2×C60, C22×D15 [×2], D10.13D4, D304C4 [×3], C3×C10.D4, C5×Dic3⋊C4, C2×D30.C2, C2×D60, D30.6D4
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, C4○D4 [×2], D10 [×3], C22×S3, C22.D4, C22×D5, C4○D12, S3×D4, Q83S3, S3×D5, C4○D20, D4×D5, Q82D5, D6.D4, C2×S3×D5, D10.13D4, D60⋊C2, C12.28D10, D10⋊D6, D30.6D4

Smallest permutation representation of D30.6D4
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 54)(32 53)(33 52)(34 51)(35 50)(36 49)(37 48)(38 47)(39 46)(40 45)(41 44)(42 43)(55 60)(56 59)(57 58)(61 81)(62 80)(63 79)(64 78)(65 77)(66 76)(67 75)(68 74)(69 73)(70 72)(82 90)(83 89)(84 88)(85 87)(91 104)(92 103)(93 102)(94 101)(95 100)(96 99)(97 98)(105 120)(106 119)(107 118)(108 117)(109 116)(110 115)(111 114)(112 113)(121 149)(122 148)(123 147)(124 146)(125 145)(126 144)(127 143)(128 142)(129 141)(130 140)(131 139)(132 138)(133 137)(134 136)(151 169)(152 168)(153 167)(154 166)(155 165)(156 164)(157 163)(158 162)(159 161)(170 180)(171 179)(172 178)(173 177)(174 176)(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)(211 214)(212 213)(215 240)(216 239)(217 238)(218 237)(219 236)(220 235)(221 234)(222 233)(223 232)(224 231)(225 230)(226 229)(227 228)
(1 64 213 153)(2 83 214 172)(3 72 215 161)(4 61 216 180)(5 80 217 169)(6 69 218 158)(7 88 219 177)(8 77 220 166)(9 66 221 155)(10 85 222 174)(11 74 223 163)(12 63 224 152)(13 82 225 171)(14 71 226 160)(15 90 227 179)(16 79 228 168)(17 68 229 157)(18 87 230 176)(19 76 231 165)(20 65 232 154)(21 84 233 173)(22 73 234 162)(23 62 235 151)(24 81 236 170)(25 70 237 159)(26 89 238 178)(27 78 239 167)(28 67 240 156)(29 86 211 175)(30 75 212 164)(31 125 116 203)(32 144 117 192)(33 133 118 181)(34 122 119 200)(35 141 120 189)(36 130 91 208)(37 149 92 197)(38 138 93 186)(39 127 94 205)(40 146 95 194)(41 135 96 183)(42 124 97 202)(43 143 98 191)(44 132 99 210)(45 121 100 199)(46 140 101 188)(47 129 102 207)(48 148 103 196)(49 137 104 185)(50 126 105 204)(51 145 106 193)(52 134 107 182)(53 123 108 201)(54 142 109 190)(55 131 110 209)(56 150 111 198)(57 139 112 187)(58 128 113 206)(59 147 114 195)(60 136 115 184)
(1 113 16 98)(2 102 17 117)(3 91 18 106)(4 110 19 95)(5 99 20 114)(6 118 21 103)(7 107 22 92)(8 96 23 111)(9 115 24 100)(10 104 25 119)(11 93 26 108)(12 112 27 97)(13 101 28 116)(14 120 29 105)(15 109 30 94)(31 225 46 240)(32 214 47 229)(33 233 48 218)(34 222 49 237)(35 211 50 226)(36 230 51 215)(37 219 52 234)(38 238 53 223)(39 227 54 212)(40 216 55 231)(41 235 56 220)(42 224 57 239)(43 213 58 228)(44 232 59 217)(45 221 60 236)(61 131 76 146)(62 150 77 135)(63 139 78 124)(64 128 79 143)(65 147 80 132)(66 136 81 121)(67 125 82 140)(68 144 83 129)(69 133 84 148)(70 122 85 137)(71 141 86 126)(72 130 87 145)(73 149 88 134)(74 138 89 123)(75 127 90 142)(151 198 166 183)(152 187 167 202)(153 206 168 191)(154 195 169 210)(155 184 170 199)(156 203 171 188)(157 192 172 207)(158 181 173 196)(159 200 174 185)(160 189 175 204)(161 208 176 193)(162 197 177 182)(163 186 178 201)(164 205 179 190)(165 194 180 209)

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

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

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

60 conjugacy classes

class 1 2A2B2C2D2E2F 3 4A4B4C4D4E4F4G5A5B6A6B6C10A···10F12A12B12C12D12E12F15A15B20A20B20C20D20E···20L30A···30F60A···60H
order1222222344444445566610···1012121212121215152020202020···2030···3060···60
size1111303060246610101220222222···2442020202044444412···124···44···4

60 irreducible representations

dim1111112222222222444444444
type++++++++++++++++++++++
imageC1C2C2C2C2C2S3D4D5D6D6C4○D4D10D10C4○D12C4○D20S3×D4Q83S3S3×D5D4×D5Q82D5C2×S3×D5D60⋊C2C12.28D10D10⋊D6
kernelD30.6D4D304C4C3×C10.D4C5×Dic3⋊C4C2×D30.C2C2×D60C10.D4D30Dic3⋊C4C2×Dic5C2×C20C30C2×Dic3C2×C12C10C6C10C10C2×C4C6C6C22C2C2C2
# reps1311111222144248112222444

Matrix representation of D30.6D4 in GL4(𝔽61) generated by

14500
601700
00060
0011
,
01700
18000
00060
00600
,
22600
313900
005243
00189
,
575700
50400
00110
00011
G:=sub<GL(4,GF(61))| [1,60,0,0,45,17,0,0,0,0,0,1,0,0,60,1],[0,18,0,0,17,0,0,0,0,0,0,60,0,0,60,0],[22,31,0,0,6,39,0,0,0,0,52,18,0,0,43,9],[57,50,0,0,57,4,0,0,0,0,11,0,0,0,0,11] >;

D30.6D4 in GAP, Magma, Sage, TeX

D_{30}._6D_4
% in TeX

G:=Group("D30.6D4");
// GroupNames label

G:=SmallGroup(480,509);
// by ID

G=gap.SmallGroup(480,509);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,64,590,219,58,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^30=b^2=c^4=1,d^2=a^15,b*a*b=a^-1,c*a*c^-1=d*a*d^-1=a^19,c*b*c^-1=a^3*b,d*b*d^-1=a^18*b,d*c*d^-1=c^-1>;
// generators/relations

׿
×
𝔽