metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D30.44D4, D12.17D10, C60.48C23, Dic15.18D4, Dic10.17D6, Dic30.18C22, C3⋊C8.12D10, (Q8×D15)⋊3C2, C5⋊Q16⋊6S3, C6.82(D4×D5), Q8⋊2S3⋊6D5, C3⋊Dic20⋊8C2, C10.83(S3×D4), C5⋊2C8.12D6, C5⋊3(Q16⋊S3), (C5×Q8).29D6, Q8.25(S3×D5), C30.210(C2×D4), D12.D5⋊8C2, C3⋊4(SD16⋊D5), (C3×Q8).12D10, D12⋊D5.1C2, D30.5C4⋊8C2, C15⋊24(C8.C22), C20.48(C22×S3), C12.48(C22×D5), (C4×D15).16C22, (C5×D12).18C22, (Q8×C15).18C22, C2.35(D10⋊D6), (C3×Dic10).18C22, C4.48(C2×S3×D5), (C3×C5⋊Q16)⋊8C2, (C5×Q8⋊2S3)⋊8C2, (C5×C3⋊C8).18C22, (C3×C5⋊2C8).18C22, SmallGroup(480,600)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D30.44D4
G = < a,b,c,d | a30=b2=1, c4=d2=a15, bab=a-1, cac-1=dad-1=a19, cbc-1=dbd-1=a3b, dcd-1=a15c3 >
Subgroups: 684 in 120 conjugacy classes, 38 normal (all characteristic)
C1, C2, C2, C3, C4, C4, C22, C5, S3, C6, C8, C2×C4, D4, Q8, Q8, D5, C10, C10, Dic3, C12, C12, D6, C15, M4(2), SD16, Q16, C2×Q8, C4○D4, Dic5, C20, C20, D10, C2×C10, C3⋊C8, C24, Dic6, C4×S3, D12, D12, C3×Q8, C3×Q8, C5×S3, D15, C30, C8.C22, C5⋊2C8, C40, Dic10, Dic10, C4×D5, C2×Dic5, C5⋊D4, C5×D4, C5×Q8, C8⋊S3, C24⋊C2, Q8⋊2S3, C3⋊Q16, C3×Q16, S3×Q8, Q8⋊3S3, C3×Dic5, Dic15, Dic15, C60, C60, S3×C10, D30, C8⋊D5, Dic20, D4.D5, C5⋊Q16, C5×SD16, D4⋊2D5, Q8×D5, Q16⋊S3, C5×C3⋊C8, C3×C5⋊2C8, S3×Dic5, C5⋊D12, C3×Dic10, C5×D12, Dic30, Dic30, C4×D15, C4×D15, Q8×C15, SD16⋊D5, D30.5C4, D12.D5, C3⋊Dic20, C3×C5⋊Q16, C5×Q8⋊2S3, D12⋊D5, Q8×D15, D30.44D4
Quotients: C1, C2, C22, S3, D4, C23, D5, D6, C2×D4, D10, C22×S3, C8.C22, C22×D5, S3×D4, S3×D5, D4×D5, Q16⋊S3, C2×S3×D5, SD16⋊D5, D10⋊D6, D30.44D4
►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 50)(32 49)(33 48)(34 47)(35 46)(36 45)(37 44)(38 43)(39 42)(40 41)(51 60)(52 59)(53 58)(54 57)(55 56)(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)(121 135)(122 134)(123 133)(124 132)(125 131)(126 130)(127 129)(136 150)(137 149)(138 148)(139 147)(140 146)(141 145)(142 144)(151 155)(152 154)(156 180)(157 179)(158 178)(159 177)(160 176)(161 175)(162 174)(163 173)(164 172)(165 171)(166 170)(167 169)(181 195)(182 194)(183 193)(184 192)(185 191)(186 190)(187 189)(196 210)(197 209)(198 208)(199 207)(200 206)(201 205)(202 204)(211 225)(212 224)(213 223)(214 222)(215 221)(216 220)(217 219)(226 240)(227 239)(228 238)(229 237)(230 236)(231 235)(232 234)
(1 226 56 196 16 211 41 181)(2 215 57 185 17 230 42 200)(3 234 58 204 18 219 43 189)(4 223 59 193 19 238 44 208)(5 212 60 182 20 227 45 197)(6 231 31 201 21 216 46 186)(7 220 32 190 22 235 47 205)(8 239 33 209 23 224 48 194)(9 228 34 198 24 213 49 183)(10 217 35 187 25 232 50 202)(11 236 36 206 26 221 51 191)(12 225 37 195 27 240 52 210)(13 214 38 184 28 229 53 199)(14 233 39 203 29 218 54 188)(15 222 40 192 30 237 55 207)(61 171 96 131 76 156 111 146)(62 160 97 150 77 175 112 135)(63 179 98 139 78 164 113 124)(64 168 99 128 79 153 114 143)(65 157 100 147 80 172 115 132)(66 176 101 136 81 161 116 121)(67 165 102 125 82 180 117 140)(68 154 103 144 83 169 118 129)(69 173 104 133 84 158 119 148)(70 162 105 122 85 177 120 137)(71 151 106 141 86 166 91 126)(72 170 107 130 87 155 92 145)(73 159 108 149 88 174 93 134)(74 178 109 138 89 163 94 123)(75 167 110 127 90 152 95 142)
(1 121 16 136)(2 140 17 125)(3 129 18 144)(4 148 19 133)(5 137 20 122)(6 126 21 141)(7 145 22 130)(8 134 23 149)(9 123 24 138)(10 142 25 127)(11 131 26 146)(12 150 27 135)(13 139 28 124)(14 128 29 143)(15 147 30 132)(31 166 46 151)(32 155 47 170)(33 174 48 159)(34 163 49 178)(35 152 50 167)(36 171 51 156)(37 160 52 175)(38 179 53 164)(39 168 54 153)(40 157 55 172)(41 176 56 161)(42 165 57 180)(43 154 58 169)(44 173 59 158)(45 162 60 177)(61 191 76 206)(62 210 77 195)(63 199 78 184)(64 188 79 203)(65 207 80 192)(66 196 81 181)(67 185 82 200)(68 204 83 189)(69 193 84 208)(70 182 85 197)(71 201 86 186)(72 190 87 205)(73 209 88 194)(74 198 89 183)(75 187 90 202)(91 216 106 231)(92 235 107 220)(93 224 108 239)(94 213 109 228)(95 232 110 217)(96 221 111 236)(97 240 112 225)(98 229 113 214)(99 218 114 233)(100 237 115 222)(101 226 116 211)(102 215 117 230)(103 234 118 219)(104 223 119 238)(105 212 120 227)
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)(31,50)(32,49)(33,48)(34,47)(35,46)(36,45)(37,44)(38,43)(39,42)(40,41)(51,60)(52,59)(53,58)(54,57)(55,56)(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)(121,135)(122,134)(123,133)(124,132)(125,131)(126,130)(127,129)(136,150)(137,149)(138,148)(139,147)(140,146)(141,145)(142,144)(151,155)(152,154)(156,180)(157,179)(158,178)(159,177)(160,176)(161,175)(162,174)(163,173)(164,172)(165,171)(166,170)(167,169)(181,195)(182,194)(183,193)(184,192)(185,191)(186,190)(187,189)(196,210)(197,209)(198,208)(199,207)(200,206)(201,205)(202,204)(211,225)(212,224)(213,223)(214,222)(215,221)(216,220)(217,219)(226,240)(227,239)(228,238)(229,237)(230,236)(231,235)(232,234), (1,226,56,196,16,211,41,181)(2,215,57,185,17,230,42,200)(3,234,58,204,18,219,43,189)(4,223,59,193,19,238,44,208)(5,212,60,182,20,227,45,197)(6,231,31,201,21,216,46,186)(7,220,32,190,22,235,47,205)(8,239,33,209,23,224,48,194)(9,228,34,198,24,213,49,183)(10,217,35,187,25,232,50,202)(11,236,36,206,26,221,51,191)(12,225,37,195,27,240,52,210)(13,214,38,184,28,229,53,199)(14,233,39,203,29,218,54,188)(15,222,40,192,30,237,55,207)(61,171,96,131,76,156,111,146)(62,160,97,150,77,175,112,135)(63,179,98,139,78,164,113,124)(64,168,99,128,79,153,114,143)(65,157,100,147,80,172,115,132)(66,176,101,136,81,161,116,121)(67,165,102,125,82,180,117,140)(68,154,103,144,83,169,118,129)(69,173,104,133,84,158,119,148)(70,162,105,122,85,177,120,137)(71,151,106,141,86,166,91,126)(72,170,107,130,87,155,92,145)(73,159,108,149,88,174,93,134)(74,178,109,138,89,163,94,123)(75,167,110,127,90,152,95,142), (1,121,16,136)(2,140,17,125)(3,129,18,144)(4,148,19,133)(5,137,20,122)(6,126,21,141)(7,145,22,130)(8,134,23,149)(9,123,24,138)(10,142,25,127)(11,131,26,146)(12,150,27,135)(13,139,28,124)(14,128,29,143)(15,147,30,132)(31,166,46,151)(32,155,47,170)(33,174,48,159)(34,163,49,178)(35,152,50,167)(36,171,51,156)(37,160,52,175)(38,179,53,164)(39,168,54,153)(40,157,55,172)(41,176,56,161)(42,165,57,180)(43,154,58,169)(44,173,59,158)(45,162,60,177)(61,191,76,206)(62,210,77,195)(63,199,78,184)(64,188,79,203)(65,207,80,192)(66,196,81,181)(67,185,82,200)(68,204,83,189)(69,193,84,208)(70,182,85,197)(71,201,86,186)(72,190,87,205)(73,209,88,194)(74,198,89,183)(75,187,90,202)(91,216,106,231)(92,235,107,220)(93,224,108,239)(94,213,109,228)(95,232,110,217)(96,221,111,236)(97,240,112,225)(98,229,113,214)(99,218,114,233)(100,237,115,222)(101,226,116,211)(102,215,117,230)(103,234,118,219)(104,223,119,238)(105,212,120,227)>;
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)(31,50)(32,49)(33,48)(34,47)(35,46)(36,45)(37,44)(38,43)(39,42)(40,41)(51,60)(52,59)(53,58)(54,57)(55,56)(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)(121,135)(122,134)(123,133)(124,132)(125,131)(126,130)(127,129)(136,150)(137,149)(138,148)(139,147)(140,146)(141,145)(142,144)(151,155)(152,154)(156,180)(157,179)(158,178)(159,177)(160,176)(161,175)(162,174)(163,173)(164,172)(165,171)(166,170)(167,169)(181,195)(182,194)(183,193)(184,192)(185,191)(186,190)(187,189)(196,210)(197,209)(198,208)(199,207)(200,206)(201,205)(202,204)(211,225)(212,224)(213,223)(214,222)(215,221)(216,220)(217,219)(226,240)(227,239)(228,238)(229,237)(230,236)(231,235)(232,234), (1,226,56,196,16,211,41,181)(2,215,57,185,17,230,42,200)(3,234,58,204,18,219,43,189)(4,223,59,193,19,238,44,208)(5,212,60,182,20,227,45,197)(6,231,31,201,21,216,46,186)(7,220,32,190,22,235,47,205)(8,239,33,209,23,224,48,194)(9,228,34,198,24,213,49,183)(10,217,35,187,25,232,50,202)(11,236,36,206,26,221,51,191)(12,225,37,195,27,240,52,210)(13,214,38,184,28,229,53,199)(14,233,39,203,29,218,54,188)(15,222,40,192,30,237,55,207)(61,171,96,131,76,156,111,146)(62,160,97,150,77,175,112,135)(63,179,98,139,78,164,113,124)(64,168,99,128,79,153,114,143)(65,157,100,147,80,172,115,132)(66,176,101,136,81,161,116,121)(67,165,102,125,82,180,117,140)(68,154,103,144,83,169,118,129)(69,173,104,133,84,158,119,148)(70,162,105,122,85,177,120,137)(71,151,106,141,86,166,91,126)(72,170,107,130,87,155,92,145)(73,159,108,149,88,174,93,134)(74,178,109,138,89,163,94,123)(75,167,110,127,90,152,95,142), (1,121,16,136)(2,140,17,125)(3,129,18,144)(4,148,19,133)(5,137,20,122)(6,126,21,141)(7,145,22,130)(8,134,23,149)(9,123,24,138)(10,142,25,127)(11,131,26,146)(12,150,27,135)(13,139,28,124)(14,128,29,143)(15,147,30,132)(31,166,46,151)(32,155,47,170)(33,174,48,159)(34,163,49,178)(35,152,50,167)(36,171,51,156)(37,160,52,175)(38,179,53,164)(39,168,54,153)(40,157,55,172)(41,176,56,161)(42,165,57,180)(43,154,58,169)(44,173,59,158)(45,162,60,177)(61,191,76,206)(62,210,77,195)(63,199,78,184)(64,188,79,203)(65,207,80,192)(66,196,81,181)(67,185,82,200)(68,204,83,189)(69,193,84,208)(70,182,85,197)(71,201,86,186)(72,190,87,205)(73,209,88,194)(74,198,89,183)(75,187,90,202)(91,216,106,231)(92,235,107,220)(93,224,108,239)(94,213,109,228)(95,232,110,217)(96,221,111,236)(97,240,112,225)(98,229,113,214)(99,218,114,233)(100,237,115,222)(101,226,116,211)(102,215,117,230)(103,234,118,219)(104,223,119,238)(105,212,120,227) );
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),(31,50),(32,49),(33,48),(34,47),(35,46),(36,45),(37,44),(38,43),(39,42),(40,41),(51,60),(52,59),(53,58),(54,57),(55,56),(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),(121,135),(122,134),(123,133),(124,132),(125,131),(126,130),(127,129),(136,150),(137,149),(138,148),(139,147),(140,146),(141,145),(142,144),(151,155),(152,154),(156,180),(157,179),(158,178),(159,177),(160,176),(161,175),(162,174),(163,173),(164,172),(165,171),(166,170),(167,169),(181,195),(182,194),(183,193),(184,192),(185,191),(186,190),(187,189),(196,210),(197,209),(198,208),(199,207),(200,206),(201,205),(202,204),(211,225),(212,224),(213,223),(214,222),(215,221),(216,220),(217,219),(226,240),(227,239),(228,238),(229,237),(230,236),(231,235),(232,234)], [(1,226,56,196,16,211,41,181),(2,215,57,185,17,230,42,200),(3,234,58,204,18,219,43,189),(4,223,59,193,19,238,44,208),(5,212,60,182,20,227,45,197),(6,231,31,201,21,216,46,186),(7,220,32,190,22,235,47,205),(8,239,33,209,23,224,48,194),(9,228,34,198,24,213,49,183),(10,217,35,187,25,232,50,202),(11,236,36,206,26,221,51,191),(12,225,37,195,27,240,52,210),(13,214,38,184,28,229,53,199),(14,233,39,203,29,218,54,188),(15,222,40,192,30,237,55,207),(61,171,96,131,76,156,111,146),(62,160,97,150,77,175,112,135),(63,179,98,139,78,164,113,124),(64,168,99,128,79,153,114,143),(65,157,100,147,80,172,115,132),(66,176,101,136,81,161,116,121),(67,165,102,125,82,180,117,140),(68,154,103,144,83,169,118,129),(69,173,104,133,84,158,119,148),(70,162,105,122,85,177,120,137),(71,151,106,141,86,166,91,126),(72,170,107,130,87,155,92,145),(73,159,108,149,88,174,93,134),(74,178,109,138,89,163,94,123),(75,167,110,127,90,152,95,142)], [(1,121,16,136),(2,140,17,125),(3,129,18,144),(4,148,19,133),(5,137,20,122),(6,126,21,141),(7,145,22,130),(8,134,23,149),(9,123,24,138),(10,142,25,127),(11,131,26,146),(12,150,27,135),(13,139,28,124),(14,128,29,143),(15,147,30,132),(31,166,46,151),(32,155,47,170),(33,174,48,159),(34,163,49,178),(35,152,50,167),(36,171,51,156),(37,160,52,175),(38,179,53,164),(39,168,54,153),(40,157,55,172),(41,176,56,161),(42,165,57,180),(43,154,58,169),(44,173,59,158),(45,162,60,177),(61,191,76,206),(62,210,77,195),(63,199,78,184),(64,188,79,203),(65,207,80,192),(66,196,81,181),(67,185,82,200),(68,204,83,189),(69,193,84,208),(70,182,85,197),(71,201,86,186),(72,190,87,205),(73,209,88,194),(74,198,89,183),(75,187,90,202),(91,216,106,231),(92,235,107,220),(93,224,108,239),(94,213,109,228),(95,232,110,217),(96,221,111,236),(97,240,112,225),(98,229,113,214),(99,218,114,233),(100,237,115,222),(101,226,116,211),(102,215,117,230),(103,234,118,219),(104,223,119,238),(105,212,120,227)]])
42 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3 | 4A | 4B | 4C | 4D | 4E | 5A | 5B | 6 | 8A | 8B | 10A | 10B | 10C | 10D | 12A | 12B | 12C | 15A | 15B | 20A | 20B | 20C | 20D | 24A | 24B | 30A | 30B | 40A | 40B | 40C | 40D | 60A | ··· | 60F |
| order | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 8 | 8 | 10 | 10 | 10 | 10 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 20 | 24 | 24 | 30 | 30 | 40 | 40 | 40 | 40 | 60 | ··· | 60 |
| size | 1 | 1 | 12 | 30 | 2 | 2 | 4 | 20 | 30 | 60 | 2 | 2 | 2 | 12 | 20 | 2 | 2 | 24 | 24 | 4 | 8 | 40 | 4 | 4 | 4 | 4 | 8 | 8 | 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 | Q16⋊S3 | C2×S3×D5 | SD16⋊D5 | D10⋊D6 | D30.44D4 |
| kernel | D30.44D4 | D30.5C4 | D12.D5 | C3⋊Dic20 | C3×C5⋊Q16 | C5×Q8⋊2S3 | D12⋊D5 | Q8×D15 | C5⋊Q16 | Dic15 | D30 | Q8⋊2S3 | C5⋊2C8 | Dic10 | C5×Q8 | C3⋊C8 | D12 | 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 D30.44D4 ►in GL6(𝔽241)
| 189 | 240 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 240 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 240 |
| 0 | 0 | 0 | 0 | 1 | 1 |
| 189 | 240 | 0 | 0 | 0 | 0 |
| 52 | 52 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 240 | 0 | 0 |
| 0 | 0 | 240 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 240 |
| 0 | 0 | 0 | 0 | 240 | 0 |
| 240 | 0 | 0 | 0 | 0 | 0 |
| 52 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 47 | 94 | 47 | 94 |
| 0 | 0 | 147 | 194 | 147 | 194 |
| 0 | 0 | 194 | 147 | 47 | 94 |
| 0 | 0 | 94 | 47 | 147 | 194 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 189 | 240 | 0 | 0 | 0 | 0 |
| 0 | 0 | 64 | 128 | 198 | 155 |
| 0 | 0 | 113 | 177 | 86 | 43 |
| 0 | 0 | 198 | 155 | 177 | 113 |
| 0 | 0 | 86 | 43 | 128 | 64 |
G:=sub<GL(6,GF(241))| [189,1,0,0,0,0,240,0,0,0,0,0,0,0,0,1,0,0,0,0,240,1,0,0,0,0,0,0,0,1,0,0,0,0,240,1],[189,52,0,0,0,0,240,52,0,0,0,0,0,0,0,240,0,0,0,0,240,0,0,0,0,0,0,0,0,240,0,0,0,0,240,0],[240,52,0,0,0,0,0,1,0,0,0,0,0,0,47,147,194,94,0,0,94,194,147,47,0,0,47,147,47,147,0,0,94,194,94,194],[1,189,0,0,0,0,0,240,0,0,0,0,0,0,64,113,198,86,0,0,128,177,155,43,0,0,198,86,177,128,0,0,155,43,113,64] >;
D30.44D4 in GAP, Magma, Sage, TeX
D_{30}._{44}D_4 % in TeX
G:=Group("D30.44D4"); // GroupNames label
G:=SmallGroup(480,600);
// by ID
G=gap.SmallGroup(480,600);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,254,303,100,675,346,185,80,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^30=b^2=1,c^4=d^2=a^15,b*a*b=a^-1,c*a*c^-1=d*a*d^-1=a^19,c*b*c^-1=d*b*d^-1=a^3*b,d*c*d^-1=a^15*c^3>;
// generators/relations