metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.276D14, (C2×C4)⋊8D28, (C4×D28)⋊3C2, (C2×C28)⋊31D4, C4⋊5(C4○D28), C4.90(C2×D28), (C2×C42)⋊11D7, C28⋊11(C4○D4), C28⋊4D4⋊18C2, C28⋊7D4⋊50C2, C28⋊2Q8⋊38C2, C28.307(C2×D4), C14.5(C22×D4), C22.6(C2×D28), C2.7(C22×D28), C4.D28⋊33C2, (C2×C14).21C24, (C4×C28).315C22, (C2×C28).694C23, D14⋊C4.80C22, (C22×C4).440D14, (C2×Dic7).5C23, (C22×D7).3C23, C22.64(C23×D7), (C2×D28).203C22, C4⋊Dic7.289C22, C7⋊1(C22.26C24), C23.218(C22×D7), (C22×C14).383C23, (C22×C28).524C22, (C2×Dic14).224C22, (C2×C4×C28)⋊13C2, (C2×C4○D28)⋊2C2, C14.8(C2×C4○D4), C2.10(C2×C4○D28), (C2×C14).172(C2×D4), (C2×C4×D7).187C22, (C2×C4).730(C22×D7), (C2×C7⋊D4).85C22, SmallGroup(448,930)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.276D14
G = < a,b,c,d | a4=b4=c14=1, d2=b2, ab=ba, ac=ca, dad-1=a-1, bc=cb, bd=db, dcd-1=b2c-1 >
Subgroups: 1540 in 310 conjugacy classes, 119 normal (23 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C14, C42, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C14, C2×C42, C4×D4, C4⋊D4, C4.4D4, C4⋊1D4, C4⋊Q8, C2×C4○D4, Dic14, C4×D7, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C22×D7, C22×C14, C22.26C24, C4⋊Dic7, D14⋊C4, C4×C28, C4×C28, C2×Dic14, C2×C4×D7, C2×D28, C4○D28, C2×C7⋊D4, C22×C28, C22×C28, C28⋊2Q8, C4×D28, C28⋊4D4, C4.D28, C28⋊7D4, C2×C4×C28, C2×C4○D28, C42.276D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C22×D4, C2×C4○D4, D28, C22×D7, C22.26C24, C2×D28, C4○D28, C23×D7, C22×D28, C2×C4○D28, C42.276D14
►On 224 points
Generators in S224
(1 220 8 213)(2 221 9 214)(3 222 10 215)(4 223 11 216)(5 224 12 217)(6 211 13 218)(7 212 14 219)(15 149 184 197)(16 150 185 198)(17 151 186 199)(18 152 187 200)(19 153 188 201)(20 154 189 202)(21 141 190 203)(22 142 191 204)(23 143 192 205)(24 144 193 206)(25 145 194 207)(26 146 195 208)(27 147 196 209)(28 148 183 210)(29 176 36 169)(30 177 37 170)(31 178 38 171)(32 179 39 172)(33 180 40 173)(34 181 41 174)(35 182 42 175)(43 139 162 104)(44 140 163 105)(45 127 164 106)(46 128 165 107)(47 129 166 108)(48 130 167 109)(49 131 168 110)(50 132 155 111)(51 133 156 112)(52 134 157 99)(53 135 158 100)(54 136 159 101)(55 137 160 102)(56 138 161 103)(57 72 64 79)(58 73 65 80)(59 74 66 81)(60 75 67 82)(61 76 68 83)(62 77 69 84)(63 78 70 71)(85 118 92 125)(86 119 93 126)(87 120 94 113)(88 121 95 114)(89 122 96 115)(90 123 97 116)(91 124 98 117)
(1 33 66 113)(2 34 67 114)(3 35 68 115)(4 36 69 116)(5 37 70 117)(6 38 57 118)(7 39 58 119)(8 40 59 120)(9 41 60 121)(10 42 61 122)(11 29 62 123)(12 30 63 124)(13 31 64 125)(14 32 65 126)(15 102 191 130)(16 103 192 131)(17 104 193 132)(18 105 194 133)(19 106 195 134)(20 107 196 135)(21 108 183 136)(22 109 184 137)(23 110 185 138)(24 111 186 139)(25 112 187 140)(26 99 188 127)(27 100 189 128)(28 101 190 129)(43 206 155 151)(44 207 156 152)(45 208 157 153)(46 209 158 154)(47 210 159 141)(48 197 160 142)(49 198 161 143)(50 199 162 144)(51 200 163 145)(52 201 164 146)(53 202 165 147)(54 203 166 148)(55 204 167 149)(56 205 168 150)(71 91 224 170)(72 92 211 171)(73 93 212 172)(74 94 213 173)(75 95 214 174)(76 96 215 175)(77 97 216 176)(78 98 217 177)(79 85 218 178)(80 86 219 179)(81 87 220 180)(82 88 221 181)(83 89 222 182)(84 90 223 169)
(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)
(1 197 66 142)(2 141 67 210)(3 209 68 154)(4 153 69 208)(5 207 70 152)(6 151 57 206)(7 205 58 150)(8 149 59 204)(9 203 60 148)(10 147 61 202)(11 201 62 146)(12 145 63 200)(13 199 64 144)(14 143 65 198)(15 74 191 213)(16 212 192 73)(17 72 193 211)(18 224 194 71)(19 84 195 223)(20 222 196 83)(21 82 183 221)(22 220 184 81)(23 80 185 219)(24 218 186 79)(25 78 187 217)(26 216 188 77)(27 76 189 215)(28 214 190 75)(29 164 123 52)(30 51 124 163)(31 162 125 50)(32 49 126 161)(33 160 113 48)(34 47 114 159)(35 158 115 46)(36 45 116 157)(37 156 117 44)(38 43 118 155)(39 168 119 56)(40 55 120 167)(41 166 121 54)(42 53 122 165)(85 111 178 139)(86 138 179 110)(87 109 180 137)(88 136 181 108)(89 107 182 135)(90 134 169 106)(91 105 170 133)(92 132 171 104)(93 103 172 131)(94 130 173 102)(95 101 174 129)(96 128 175 100)(97 99 176 127)(98 140 177 112)
G:=sub<Sym(224)| (1,220,8,213)(2,221,9,214)(3,222,10,215)(4,223,11,216)(5,224,12,217)(6,211,13,218)(7,212,14,219)(15,149,184,197)(16,150,185,198)(17,151,186,199)(18,152,187,200)(19,153,188,201)(20,154,189,202)(21,141,190,203)(22,142,191,204)(23,143,192,205)(24,144,193,206)(25,145,194,207)(26,146,195,208)(27,147,196,209)(28,148,183,210)(29,176,36,169)(30,177,37,170)(31,178,38,171)(32,179,39,172)(33,180,40,173)(34,181,41,174)(35,182,42,175)(43,139,162,104)(44,140,163,105)(45,127,164,106)(46,128,165,107)(47,129,166,108)(48,130,167,109)(49,131,168,110)(50,132,155,111)(51,133,156,112)(52,134,157,99)(53,135,158,100)(54,136,159,101)(55,137,160,102)(56,138,161,103)(57,72,64,79)(58,73,65,80)(59,74,66,81)(60,75,67,82)(61,76,68,83)(62,77,69,84)(63,78,70,71)(85,118,92,125)(86,119,93,126)(87,120,94,113)(88,121,95,114)(89,122,96,115)(90,123,97,116)(91,124,98,117), (1,33,66,113)(2,34,67,114)(3,35,68,115)(4,36,69,116)(5,37,70,117)(6,38,57,118)(7,39,58,119)(8,40,59,120)(9,41,60,121)(10,42,61,122)(11,29,62,123)(12,30,63,124)(13,31,64,125)(14,32,65,126)(15,102,191,130)(16,103,192,131)(17,104,193,132)(18,105,194,133)(19,106,195,134)(20,107,196,135)(21,108,183,136)(22,109,184,137)(23,110,185,138)(24,111,186,139)(25,112,187,140)(26,99,188,127)(27,100,189,128)(28,101,190,129)(43,206,155,151)(44,207,156,152)(45,208,157,153)(46,209,158,154)(47,210,159,141)(48,197,160,142)(49,198,161,143)(50,199,162,144)(51,200,163,145)(52,201,164,146)(53,202,165,147)(54,203,166,148)(55,204,167,149)(56,205,168,150)(71,91,224,170)(72,92,211,171)(73,93,212,172)(74,94,213,173)(75,95,214,174)(76,96,215,175)(77,97,216,176)(78,98,217,177)(79,85,218,178)(80,86,219,179)(81,87,220,180)(82,88,221,181)(83,89,222,182)(84,90,223,169), (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), (1,197,66,142)(2,141,67,210)(3,209,68,154)(4,153,69,208)(5,207,70,152)(6,151,57,206)(7,205,58,150)(8,149,59,204)(9,203,60,148)(10,147,61,202)(11,201,62,146)(12,145,63,200)(13,199,64,144)(14,143,65,198)(15,74,191,213)(16,212,192,73)(17,72,193,211)(18,224,194,71)(19,84,195,223)(20,222,196,83)(21,82,183,221)(22,220,184,81)(23,80,185,219)(24,218,186,79)(25,78,187,217)(26,216,188,77)(27,76,189,215)(28,214,190,75)(29,164,123,52)(30,51,124,163)(31,162,125,50)(32,49,126,161)(33,160,113,48)(34,47,114,159)(35,158,115,46)(36,45,116,157)(37,156,117,44)(38,43,118,155)(39,168,119,56)(40,55,120,167)(41,166,121,54)(42,53,122,165)(85,111,178,139)(86,138,179,110)(87,109,180,137)(88,136,181,108)(89,107,182,135)(90,134,169,106)(91,105,170,133)(92,132,171,104)(93,103,172,131)(94,130,173,102)(95,101,174,129)(96,128,175,100)(97,99,176,127)(98,140,177,112)>;
G:=Group( (1,220,8,213)(2,221,9,214)(3,222,10,215)(4,223,11,216)(5,224,12,217)(6,211,13,218)(7,212,14,219)(15,149,184,197)(16,150,185,198)(17,151,186,199)(18,152,187,200)(19,153,188,201)(20,154,189,202)(21,141,190,203)(22,142,191,204)(23,143,192,205)(24,144,193,206)(25,145,194,207)(26,146,195,208)(27,147,196,209)(28,148,183,210)(29,176,36,169)(30,177,37,170)(31,178,38,171)(32,179,39,172)(33,180,40,173)(34,181,41,174)(35,182,42,175)(43,139,162,104)(44,140,163,105)(45,127,164,106)(46,128,165,107)(47,129,166,108)(48,130,167,109)(49,131,168,110)(50,132,155,111)(51,133,156,112)(52,134,157,99)(53,135,158,100)(54,136,159,101)(55,137,160,102)(56,138,161,103)(57,72,64,79)(58,73,65,80)(59,74,66,81)(60,75,67,82)(61,76,68,83)(62,77,69,84)(63,78,70,71)(85,118,92,125)(86,119,93,126)(87,120,94,113)(88,121,95,114)(89,122,96,115)(90,123,97,116)(91,124,98,117), (1,33,66,113)(2,34,67,114)(3,35,68,115)(4,36,69,116)(5,37,70,117)(6,38,57,118)(7,39,58,119)(8,40,59,120)(9,41,60,121)(10,42,61,122)(11,29,62,123)(12,30,63,124)(13,31,64,125)(14,32,65,126)(15,102,191,130)(16,103,192,131)(17,104,193,132)(18,105,194,133)(19,106,195,134)(20,107,196,135)(21,108,183,136)(22,109,184,137)(23,110,185,138)(24,111,186,139)(25,112,187,140)(26,99,188,127)(27,100,189,128)(28,101,190,129)(43,206,155,151)(44,207,156,152)(45,208,157,153)(46,209,158,154)(47,210,159,141)(48,197,160,142)(49,198,161,143)(50,199,162,144)(51,200,163,145)(52,201,164,146)(53,202,165,147)(54,203,166,148)(55,204,167,149)(56,205,168,150)(71,91,224,170)(72,92,211,171)(73,93,212,172)(74,94,213,173)(75,95,214,174)(76,96,215,175)(77,97,216,176)(78,98,217,177)(79,85,218,178)(80,86,219,179)(81,87,220,180)(82,88,221,181)(83,89,222,182)(84,90,223,169), (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), (1,197,66,142)(2,141,67,210)(3,209,68,154)(4,153,69,208)(5,207,70,152)(6,151,57,206)(7,205,58,150)(8,149,59,204)(9,203,60,148)(10,147,61,202)(11,201,62,146)(12,145,63,200)(13,199,64,144)(14,143,65,198)(15,74,191,213)(16,212,192,73)(17,72,193,211)(18,224,194,71)(19,84,195,223)(20,222,196,83)(21,82,183,221)(22,220,184,81)(23,80,185,219)(24,218,186,79)(25,78,187,217)(26,216,188,77)(27,76,189,215)(28,214,190,75)(29,164,123,52)(30,51,124,163)(31,162,125,50)(32,49,126,161)(33,160,113,48)(34,47,114,159)(35,158,115,46)(36,45,116,157)(37,156,117,44)(38,43,118,155)(39,168,119,56)(40,55,120,167)(41,166,121,54)(42,53,122,165)(85,111,178,139)(86,138,179,110)(87,109,180,137)(88,136,181,108)(89,107,182,135)(90,134,169,106)(91,105,170,133)(92,132,171,104)(93,103,172,131)(94,130,173,102)(95,101,174,129)(96,128,175,100)(97,99,176,127)(98,140,177,112) );
G=PermutationGroup([[(1,220,8,213),(2,221,9,214),(3,222,10,215),(4,223,11,216),(5,224,12,217),(6,211,13,218),(7,212,14,219),(15,149,184,197),(16,150,185,198),(17,151,186,199),(18,152,187,200),(19,153,188,201),(20,154,189,202),(21,141,190,203),(22,142,191,204),(23,143,192,205),(24,144,193,206),(25,145,194,207),(26,146,195,208),(27,147,196,209),(28,148,183,210),(29,176,36,169),(30,177,37,170),(31,178,38,171),(32,179,39,172),(33,180,40,173),(34,181,41,174),(35,182,42,175),(43,139,162,104),(44,140,163,105),(45,127,164,106),(46,128,165,107),(47,129,166,108),(48,130,167,109),(49,131,168,110),(50,132,155,111),(51,133,156,112),(52,134,157,99),(53,135,158,100),(54,136,159,101),(55,137,160,102),(56,138,161,103),(57,72,64,79),(58,73,65,80),(59,74,66,81),(60,75,67,82),(61,76,68,83),(62,77,69,84),(63,78,70,71),(85,118,92,125),(86,119,93,126),(87,120,94,113),(88,121,95,114),(89,122,96,115),(90,123,97,116),(91,124,98,117)], [(1,33,66,113),(2,34,67,114),(3,35,68,115),(4,36,69,116),(5,37,70,117),(6,38,57,118),(7,39,58,119),(8,40,59,120),(9,41,60,121),(10,42,61,122),(11,29,62,123),(12,30,63,124),(13,31,64,125),(14,32,65,126),(15,102,191,130),(16,103,192,131),(17,104,193,132),(18,105,194,133),(19,106,195,134),(20,107,196,135),(21,108,183,136),(22,109,184,137),(23,110,185,138),(24,111,186,139),(25,112,187,140),(26,99,188,127),(27,100,189,128),(28,101,190,129),(43,206,155,151),(44,207,156,152),(45,208,157,153),(46,209,158,154),(47,210,159,141),(48,197,160,142),(49,198,161,143),(50,199,162,144),(51,200,163,145),(52,201,164,146),(53,202,165,147),(54,203,166,148),(55,204,167,149),(56,205,168,150),(71,91,224,170),(72,92,211,171),(73,93,212,172),(74,94,213,173),(75,95,214,174),(76,96,215,175),(77,97,216,176),(78,98,217,177),(79,85,218,178),(80,86,219,179),(81,87,220,180),(82,88,221,181),(83,89,222,182),(84,90,223,169)], [(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)], [(1,197,66,142),(2,141,67,210),(3,209,68,154),(4,153,69,208),(5,207,70,152),(6,151,57,206),(7,205,58,150),(8,149,59,204),(9,203,60,148),(10,147,61,202),(11,201,62,146),(12,145,63,200),(13,199,64,144),(14,143,65,198),(15,74,191,213),(16,212,192,73),(17,72,193,211),(18,224,194,71),(19,84,195,223),(20,222,196,83),(21,82,183,221),(22,220,184,81),(23,80,185,219),(24,218,186,79),(25,78,187,217),(26,216,188,77),(27,76,189,215),(28,214,190,75),(29,164,123,52),(30,51,124,163),(31,162,125,50),(32,49,126,161),(33,160,113,48),(34,47,114,159),(35,158,115,46),(36,45,116,157),(37,156,117,44),(38,43,118,155),(39,168,119,56),(40,55,120,167),(41,166,121,54),(42,53,122,165),(85,111,178,139),(86,138,179,110),(87,109,180,137),(88,136,181,108),(89,107,182,135),(90,134,169,106),(91,105,170,133),(92,132,171,104),(93,103,172,131),(94,130,173,102),(95,101,174,129),(96,128,175,100),(97,99,176,127),(98,140,177,112)]])
124 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | ··· | 4N | 4O | 4P | 4Q | 4R | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28BT |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 28 | 28 | 28 | 28 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
124 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D28 | C4○D28 |
| kernel | C42.276D14 | C28⋊2Q8 | C4×D28 | C28⋊4D4 | C4.D28 | C28⋊7D4 | C2×C4×C28 | C2×C4○D28 | C2×C28 | C2×C42 | C28 | C42 | C22×C4 | C2×C4 | C4 |
| # reps | 1 | 1 | 4 | 1 | 2 | 4 | 1 | 2 | 4 | 3 | 8 | 12 | 9 | 24 | 48 |
Matrix representation of C42.276D14 ►in GL4(𝔽29) generated by
| 2 | 18 | 0 | 0 |
| 11 | 27 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 28 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 12 |
| 8 | 8 | 0 | 0 |
| 21 | 3 | 0 | 0 |
| 0 | 0 | 7 | 0 |
| 0 | 0 | 19 | 4 |
| 11 | 27 | 0 | 0 |
| 2 | 18 | 0 | 0 |
| 0 | 0 | 16 | 28 |
| 0 | 0 | 25 | 13 |
G:=sub<GL(4,GF(29))| [2,11,0,0,18,27,0,0,0,0,1,0,0,0,0,1],[28,0,0,0,0,28,0,0,0,0,12,0,0,0,0,12],[8,21,0,0,8,3,0,0,0,0,7,19,0,0,0,4],[11,2,0,0,27,18,0,0,0,0,16,25,0,0,28,13] >;
C42.276D14 in GAP, Magma, Sage, TeX
C_4^2._{276}D_{14} % in TeX
G:=Group("C4^2.276D14"); // GroupNames label
G:=SmallGroup(448,930);
// by ID
G=gap.SmallGroup(448,930);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,232,100,675,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=b^2,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,b*c=c*b,b*d=d*b,d*c*d^-1=b^2*c^-1>;
// generators/relations