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G = C42.144D14  order 448 = 26·7

144th non-split extension by C42 of D14 acting via D14/C7=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C42.144D14, C14.922- 1+4, C14.1282+ 1+4, C28⋊2Q8⋊31C2, (Q8×Dic7)⋊21C2, (D4×Dic7)⋊32C2, C4.4D4⋊15D7, D14⋊3Q8⋊33C2, (C2×D4).177D14, C28⋊2D4.13C2, C42⋊D7⋊21C2, (C2×C28).82C23, (C2×Q8).140D14, C22⋊C4.37D14, C28.127(C4○D4), C4.39(D4⋊2D7), (C2×C14).226C24, (C4×C28).189C22, C2.52(D4⋊8D14), C23.48(C22×D7), D14⋊C4.111C22, Dic7.D4⋊42C2, C22⋊Dic14⋊42C2, (D4×C14).159C22, C22.D28⋊27C2, C23.D14⋊42C2, Dic7⋊C4.49C22, C4⋊Dic7.236C22, (C22×C14).56C23, (Q8×C14).130C22, (C22×D7).98C23, C22.247(C23×D7), C23.D7.59C22, C7⋊9(C22.36C24), (C2×Dic7).116C23, (C4×Dic7).136C22, (C2×Dic14).38C22, C2.53(D4.10D14), (C22×Dic7).146C22, C14.94(C2×C4○D4), (C7×C4.4D4)⋊18C2, C2.58(C2×D4⋊2D7), (C2×C4×D7).122C22, (C2×C4).199(C22×D7), (C2×C7⋊D4).64C22, (C7×C22⋊C4).68C22, SmallGroup(448,1135)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C2×C14 — C42.144D14
Chief series
C1 — C7 — C14 — C2×C14 — C22×D7 — C2×C4×D7 — C42⋊D7 — C42.144D14
Lower central
C7 — C2×C14 — C42.144D14
Upper central
C1 — C22 — C4.4D4

Generators and relations for C42.144D14
 G = < a,b,c,d | a4=b4=c14=1, d2=b2, ab=ba, cac-1=dad-1=a-1, cbc-1=a2b-1, dbd-1=b-1, dcd-1=b2c-1 >

Subgroups: 940 in 216 conjugacy classes, 95 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, Dic7, C28, C28, D14, C2×C14, C2×C14, C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22.D4, C4.4D4, C4.4D4, C42⋊2C2, C4⋊Q8, Dic14, C4×D7, C2×Dic7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C7×Q8, C22×D7, C22×C14, C22.36C24, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C2×Dic14, C2×C4×D7, C22×Dic7, C2×C7⋊D4, D4×C14, Q8×C14, C28⋊2Q8, C42⋊D7, C22⋊Dic14, C23.D14, Dic7.D4, C22.D28, D4×Dic7, C28⋊2D4, Q8×Dic7, D14⋊3Q8, C7×C4.4D4, C42.144D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, 2- 1+4, C22×D7, C22.36C24, D4⋊2D7, C23×D7, C2×D4⋊2D7, D4⋊8D14, D4.10D14, C42.144D14

Smallest permutation representation of C42.144D14
►On 224 points
Generators in S224
(1 68 12 61)(2 62 13 69)(3 70 14 63)(4 64 8 57)(5 58 9 65)(6 66 10 59)(7 60 11 67)(15 80 24 73)(16 74 25 81)(17 82 26 75)(18 76 27 83)(19 84 28 77)(20 78 22 71)(21 72 23 79)(29 166 53 159)(30 160 54 167)(31 168 55 161)(32 162 56 155)(33 156 50 163)(34 164 51 157)(35 158 52 165)(36 217 47 224)(37 211 48 218)(38 219 49 212)(39 213 43 220)(40 221 44 214)(41 215 45 222)(42 223 46 216)(85 191 182 143)(86 144 169 192)(87 193 170 145)(88 146 171 194)(89 195 172 147)(90 148 173 196)(91 183 174 149)(92 150 175 184)(93 185 176 151)(94 152 177 186)(95 187 178 153)(96 154 179 188)(97 189 180 141)(98 142 181 190)(99 118 131 206)(100 207 132 119)(101 120 133 208)(102 209 134 121)(103 122 135 210)(104 197 136 123)(105 124 137 198)(106 199 138 125)(107 126 139 200)(108 201 140 113)(109 114 127 202)(110 203 128 115)(111 116 129 204)(112 205 130 117)

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

(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)

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

64 conjugacy classes

class 1 2A2B2C2D2E2F4A4B4C4D4E4F4G4H4I4J4K···4O7A7B7C14A···14I14J···14O28A···28R28S···28X
order122222244444444444···477714···1414···1428···2828···28
size111144282244441414141428···282222···28···84···48···8

64 irreducible representations

dim11111111111122222244444
type++++++++++++++++++--+-
imageC1C2C2C2C2C2C2C2C2C2C2C2D7C4○D4D14D14D14D142+ 1+42- 1+4D4⋊2D7D4⋊8D14D4.10D14
kernelC42.144D14C28⋊2Q8C42⋊D7C22⋊Dic14C23.D14Dic7.D4C22.D28D4×Dic7C28⋊2D4Q8×Dic7D14⋊3Q8C7×C4.4D4C4.4D4C28C42C22⋊C4C2×D4C2×Q8C14C14C4C2C2
# reps111222211111343123311666

Matrix representation of C42.144D14 ►in GL8(𝔽29)

280000000
028000000
00100000
00010000
000010240
000001024
0000120280
0000012028
,
2828000000
21000000
002800000
000280000
00000100
000028000
00000001
000000280
,
11000000
028000000
001100000
00320000
00001000
00000100
0000120280
0000012028
,
170000000
2412000000
002060000
00690000
000001702
000017020
000000012
000000120

G:=sub<GL(8,GF(29))| [28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,12,0,0,0,0,0,0,1,0,12,0,0,0,0,24,0,28,0,0,0,0,0,0,24,0,28],[28,2,0,0,0,0,0,0,28,1,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0,1,28,0,0,0,0,0,0,0,0,1,3,0,0,0,0,0,0,10,2,0,0,0,0,0,0,0,0,1,0,12,0,0,0,0,0,0,1,0,12,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28],[17,24,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,20,6,0,0,0,0,0,0,6,9,0,0,0,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,0,0,0,0,0,0,2,0,12,0,0,0,0,2,0,12,0] >;
 

C42.144D14 in GAP, Magma, Sage, TeX 

C_4^2._{144}D_{14}
 
% in TeX
 
G:=Group("C4^2.144D14");
 
// GroupNames label
 
G:=SmallGroup(448,1135);
 
// by ID
 
G=gap.SmallGroup(448,1135);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,100,675,570,409,18822]);
 
// Polycyclic
 
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=a^2*b^-1,d*b*d^-1=b^-1,d*c*d^-1=b^2*c^-1>;
 
// generators/relations
 

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