direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C14×C4.4D4, (C2×C42)⋊9C14, C4.13(D4×C14), C42⋊17(C2×C14), (C4×C28)⋊58C22, (C2×C28).430D4, C28.320(C2×D4), (C22×Q8)⋊4C14, C24.16(C2×C14), (Q8×C14)⋊50C22, C22.62(D4×C14), (C2×C14).346C24, (C2×C28).659C23, (C22×D4).11C14, C14.185(C22×D4), C23.6(C22×C14), (D4×C14).317C22, (C23×C14).13C22, C22.20(C23×C14), (C22×C14).85C23, (C22×C28).508C22, (C2×C4×C28)⋊22C2, C2.9(D4×C2×C14), (Q8×C2×C14)⋊16C2, (D4×C2×C14).24C2, C2.9(C14×C4○D4), (C2×C4).86(C7×D4), (C2×Q8)⋊10(C2×C14), (C2×C22⋊C4)⋊11C14, (C14×C22⋊C4)⋊31C2, C22⋊C4⋊14(C2×C14), (C2×D4).62(C2×C14), C14.228(C2×C4○D4), (C2×C14).683(C2×D4), C22.32(C7×C4○D4), (C7×C22⋊C4)⋊68C22, (C2×C4).58(C22×C14), (C2×C14).232(C4○D4), (C22×C4).100(C2×C14), SmallGroup(448,1309)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14×C4.4D4
G = < a,b,c,d | a14=b4=c4=1, d2=b2, ab=ba, ac=ca, ad=da, bc=cb, dbd-1=b-1, dcd-1=b2c-1 >
Subgroups: 530 in 330 conjugacy classes, 178 normal (18 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, Q8, C23, C23, C23, C14, C14, C14, C42, C22⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, C24, C28, C28, C2×C14, C2×C14, C2×C14, C2×C42, C2×C22⋊C4, C4.4D4, C22×D4, C22×Q8, C2×C28, C2×C28, C7×D4, C7×Q8, C22×C14, C22×C14, C22×C14, C2×C4.4D4, C4×C28, C7×C22⋊C4, C22×C28, C22×C28, D4×C14, D4×C14, Q8×C14, Q8×C14, C23×C14, C2×C4×C28, C14×C22⋊C4, C7×C4.4D4, D4×C2×C14, Q8×C2×C14, C14×C4.4D4
Quotients: C1, C2, C22, C7, D4, C23, C14, C2×D4, C4○D4, C24, C2×C14, C4.4D4, C22×D4, C2×C4○D4, C7×D4, C22×C14, C2×C4.4D4, D4×C14, C7×C4○D4, C23×C14, C7×C4.4D4, D4×C2×C14, C14×C4○D4, C14×C4.4D4
►On 224 points
Generators in S224
(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 47 136 40)(2 48 137 41)(3 49 138 42)(4 50 139 29)(5 51 140 30)(6 52 127 31)(7 53 128 32)(8 54 129 33)(9 55 130 34)(10 56 131 35)(11 43 132 36)(12 44 133 37)(13 45 134 38)(14 46 135 39)(15 167 73 154)(16 168 74 141)(17 155 75 142)(18 156 76 143)(19 157 77 144)(20 158 78 145)(21 159 79 146)(22 160 80 147)(23 161 81 148)(24 162 82 149)(25 163 83 150)(26 164 84 151)(27 165 71 152)(28 166 72 153)(57 116 86 99)(58 117 87 100)(59 118 88 101)(60 119 89 102)(61 120 90 103)(62 121 91 104)(63 122 92 105)(64 123 93 106)(65 124 94 107)(66 125 95 108)(67 126 96 109)(68 113 97 110)(69 114 98 111)(70 115 85 112)(169 186 207 220)(170 187 208 221)(171 188 209 222)(172 189 210 223)(173 190 197 224)(174 191 198 211)(175 192 199 212)(176 193 200 213)(177 194 201 214)(178 195 202 215)(179 196 203 216)(180 183 204 217)(181 184 205 218)(182 185 206 219)
(1 92 163 201)(2 93 164 202)(3 94 165 203)(4 95 166 204)(5 96 167 205)(6 97 168 206)(7 98 155 207)(8 85 156 208)(9 86 157 209)(10 87 158 210)(11 88 159 197)(12 89 160 198)(13 90 161 199)(14 91 162 200)(15 184 30 126)(16 185 31 113)(17 186 32 114)(18 187 33 115)(19 188 34 116)(20 189 35 117)(21 190 36 118)(22 191 37 119)(23 192 38 120)(24 193 39 121)(25 194 40 122)(26 195 41 123)(27 196 42 124)(28 183 29 125)(43 101 79 224)(44 102 80 211)(45 103 81 212)(46 104 82 213)(47 105 83 214)(48 106 84 215)(49 107 71 216)(50 108 72 217)(51 109 73 218)(52 110 74 219)(53 111 75 220)(54 112 76 221)(55 99 77 222)(56 100 78 223)(57 144 171 130)(58 145 172 131)(59 146 173 132)(60 147 174 133)(61 148 175 134)(62 149 176 135)(63 150 177 136)(64 151 178 137)(65 152 179 138)(66 153 180 139)(67 154 181 140)(68 141 182 127)(69 142 169 128)(70 143 170 129)
(1 187 136 221)(2 188 137 222)(3 189 138 223)(4 190 139 224)(5 191 140 211)(6 192 127 212)(7 193 128 213)(8 194 129 214)(9 195 130 215)(10 196 131 216)(11 183 132 217)(12 184 133 218)(13 185 134 219)(14 186 135 220)(15 89 73 60)(16 90 74 61)(17 91 75 62)(18 92 76 63)(19 93 77 64)(20 94 78 65)(21 95 79 66)(22 96 80 67)(23 97 81 68)(24 98 82 69)(25 85 83 70)(26 86 84 57)(27 87 71 58)(28 88 72 59)(29 197 50 173)(30 198 51 174)(31 199 52 175)(32 200 53 176)(33 201 54 177)(34 202 55 178)(35 203 56 179)(36 204 43 180)(37 205 44 181)(38 206 45 182)(39 207 46 169)(40 208 47 170)(41 209 48 171)(42 210 49 172)(99 164 116 151)(100 165 117 152)(101 166 118 153)(102 167 119 154)(103 168 120 141)(104 155 121 142)(105 156 122 143)(106 157 123 144)(107 158 124 145)(108 159 125 146)(109 160 126 147)(110 161 113 148)(111 162 114 149)(112 163 115 150)
G:=sub<Sym(224)| (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), (1,47,136,40)(2,48,137,41)(3,49,138,42)(4,50,139,29)(5,51,140,30)(6,52,127,31)(7,53,128,32)(8,54,129,33)(9,55,130,34)(10,56,131,35)(11,43,132,36)(12,44,133,37)(13,45,134,38)(14,46,135,39)(15,167,73,154)(16,168,74,141)(17,155,75,142)(18,156,76,143)(19,157,77,144)(20,158,78,145)(21,159,79,146)(22,160,80,147)(23,161,81,148)(24,162,82,149)(25,163,83,150)(26,164,84,151)(27,165,71,152)(28,166,72,153)(57,116,86,99)(58,117,87,100)(59,118,88,101)(60,119,89,102)(61,120,90,103)(62,121,91,104)(63,122,92,105)(64,123,93,106)(65,124,94,107)(66,125,95,108)(67,126,96,109)(68,113,97,110)(69,114,98,111)(70,115,85,112)(169,186,207,220)(170,187,208,221)(171,188,209,222)(172,189,210,223)(173,190,197,224)(174,191,198,211)(175,192,199,212)(176,193,200,213)(177,194,201,214)(178,195,202,215)(179,196,203,216)(180,183,204,217)(181,184,205,218)(182,185,206,219), (1,92,163,201)(2,93,164,202)(3,94,165,203)(4,95,166,204)(5,96,167,205)(6,97,168,206)(7,98,155,207)(8,85,156,208)(9,86,157,209)(10,87,158,210)(11,88,159,197)(12,89,160,198)(13,90,161,199)(14,91,162,200)(15,184,30,126)(16,185,31,113)(17,186,32,114)(18,187,33,115)(19,188,34,116)(20,189,35,117)(21,190,36,118)(22,191,37,119)(23,192,38,120)(24,193,39,121)(25,194,40,122)(26,195,41,123)(27,196,42,124)(28,183,29,125)(43,101,79,224)(44,102,80,211)(45,103,81,212)(46,104,82,213)(47,105,83,214)(48,106,84,215)(49,107,71,216)(50,108,72,217)(51,109,73,218)(52,110,74,219)(53,111,75,220)(54,112,76,221)(55,99,77,222)(56,100,78,223)(57,144,171,130)(58,145,172,131)(59,146,173,132)(60,147,174,133)(61,148,175,134)(62,149,176,135)(63,150,177,136)(64,151,178,137)(65,152,179,138)(66,153,180,139)(67,154,181,140)(68,141,182,127)(69,142,169,128)(70,143,170,129), (1,187,136,221)(2,188,137,222)(3,189,138,223)(4,190,139,224)(5,191,140,211)(6,192,127,212)(7,193,128,213)(8,194,129,214)(9,195,130,215)(10,196,131,216)(11,183,132,217)(12,184,133,218)(13,185,134,219)(14,186,135,220)(15,89,73,60)(16,90,74,61)(17,91,75,62)(18,92,76,63)(19,93,77,64)(20,94,78,65)(21,95,79,66)(22,96,80,67)(23,97,81,68)(24,98,82,69)(25,85,83,70)(26,86,84,57)(27,87,71,58)(28,88,72,59)(29,197,50,173)(30,198,51,174)(31,199,52,175)(32,200,53,176)(33,201,54,177)(34,202,55,178)(35,203,56,179)(36,204,43,180)(37,205,44,181)(38,206,45,182)(39,207,46,169)(40,208,47,170)(41,209,48,171)(42,210,49,172)(99,164,116,151)(100,165,117,152)(101,166,118,153)(102,167,119,154)(103,168,120,141)(104,155,121,142)(105,156,122,143)(106,157,123,144)(107,158,124,145)(108,159,125,146)(109,160,126,147)(110,161,113,148)(111,162,114,149)(112,163,115,150)>;
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), (1,47,136,40)(2,48,137,41)(3,49,138,42)(4,50,139,29)(5,51,140,30)(6,52,127,31)(7,53,128,32)(8,54,129,33)(9,55,130,34)(10,56,131,35)(11,43,132,36)(12,44,133,37)(13,45,134,38)(14,46,135,39)(15,167,73,154)(16,168,74,141)(17,155,75,142)(18,156,76,143)(19,157,77,144)(20,158,78,145)(21,159,79,146)(22,160,80,147)(23,161,81,148)(24,162,82,149)(25,163,83,150)(26,164,84,151)(27,165,71,152)(28,166,72,153)(57,116,86,99)(58,117,87,100)(59,118,88,101)(60,119,89,102)(61,120,90,103)(62,121,91,104)(63,122,92,105)(64,123,93,106)(65,124,94,107)(66,125,95,108)(67,126,96,109)(68,113,97,110)(69,114,98,111)(70,115,85,112)(169,186,207,220)(170,187,208,221)(171,188,209,222)(172,189,210,223)(173,190,197,224)(174,191,198,211)(175,192,199,212)(176,193,200,213)(177,194,201,214)(178,195,202,215)(179,196,203,216)(180,183,204,217)(181,184,205,218)(182,185,206,219), (1,92,163,201)(2,93,164,202)(3,94,165,203)(4,95,166,204)(5,96,167,205)(6,97,168,206)(7,98,155,207)(8,85,156,208)(9,86,157,209)(10,87,158,210)(11,88,159,197)(12,89,160,198)(13,90,161,199)(14,91,162,200)(15,184,30,126)(16,185,31,113)(17,186,32,114)(18,187,33,115)(19,188,34,116)(20,189,35,117)(21,190,36,118)(22,191,37,119)(23,192,38,120)(24,193,39,121)(25,194,40,122)(26,195,41,123)(27,196,42,124)(28,183,29,125)(43,101,79,224)(44,102,80,211)(45,103,81,212)(46,104,82,213)(47,105,83,214)(48,106,84,215)(49,107,71,216)(50,108,72,217)(51,109,73,218)(52,110,74,219)(53,111,75,220)(54,112,76,221)(55,99,77,222)(56,100,78,223)(57,144,171,130)(58,145,172,131)(59,146,173,132)(60,147,174,133)(61,148,175,134)(62,149,176,135)(63,150,177,136)(64,151,178,137)(65,152,179,138)(66,153,180,139)(67,154,181,140)(68,141,182,127)(69,142,169,128)(70,143,170,129), (1,187,136,221)(2,188,137,222)(3,189,138,223)(4,190,139,224)(5,191,140,211)(6,192,127,212)(7,193,128,213)(8,194,129,214)(9,195,130,215)(10,196,131,216)(11,183,132,217)(12,184,133,218)(13,185,134,219)(14,186,135,220)(15,89,73,60)(16,90,74,61)(17,91,75,62)(18,92,76,63)(19,93,77,64)(20,94,78,65)(21,95,79,66)(22,96,80,67)(23,97,81,68)(24,98,82,69)(25,85,83,70)(26,86,84,57)(27,87,71,58)(28,88,72,59)(29,197,50,173)(30,198,51,174)(31,199,52,175)(32,200,53,176)(33,201,54,177)(34,202,55,178)(35,203,56,179)(36,204,43,180)(37,205,44,181)(38,206,45,182)(39,207,46,169)(40,208,47,170)(41,209,48,171)(42,210,49,172)(99,164,116,151)(100,165,117,152)(101,166,118,153)(102,167,119,154)(103,168,120,141)(104,155,121,142)(105,156,122,143)(106,157,123,144)(107,158,124,145)(108,159,125,146)(109,160,126,147)(110,161,113,148)(111,162,114,149)(112,163,115,150) );
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)], [(1,47,136,40),(2,48,137,41),(3,49,138,42),(4,50,139,29),(5,51,140,30),(6,52,127,31),(7,53,128,32),(8,54,129,33),(9,55,130,34),(10,56,131,35),(11,43,132,36),(12,44,133,37),(13,45,134,38),(14,46,135,39),(15,167,73,154),(16,168,74,141),(17,155,75,142),(18,156,76,143),(19,157,77,144),(20,158,78,145),(21,159,79,146),(22,160,80,147),(23,161,81,148),(24,162,82,149),(25,163,83,150),(26,164,84,151),(27,165,71,152),(28,166,72,153),(57,116,86,99),(58,117,87,100),(59,118,88,101),(60,119,89,102),(61,120,90,103),(62,121,91,104),(63,122,92,105),(64,123,93,106),(65,124,94,107),(66,125,95,108),(67,126,96,109),(68,113,97,110),(69,114,98,111),(70,115,85,112),(169,186,207,220),(170,187,208,221),(171,188,209,222),(172,189,210,223),(173,190,197,224),(174,191,198,211),(175,192,199,212),(176,193,200,213),(177,194,201,214),(178,195,202,215),(179,196,203,216),(180,183,204,217),(181,184,205,218),(182,185,206,219)], [(1,92,163,201),(2,93,164,202),(3,94,165,203),(4,95,166,204),(5,96,167,205),(6,97,168,206),(7,98,155,207),(8,85,156,208),(9,86,157,209),(10,87,158,210),(11,88,159,197),(12,89,160,198),(13,90,161,199),(14,91,162,200),(15,184,30,126),(16,185,31,113),(17,186,32,114),(18,187,33,115),(19,188,34,116),(20,189,35,117),(21,190,36,118),(22,191,37,119),(23,192,38,120),(24,193,39,121),(25,194,40,122),(26,195,41,123),(27,196,42,124),(28,183,29,125),(43,101,79,224),(44,102,80,211),(45,103,81,212),(46,104,82,213),(47,105,83,214),(48,106,84,215),(49,107,71,216),(50,108,72,217),(51,109,73,218),(52,110,74,219),(53,111,75,220),(54,112,76,221),(55,99,77,222),(56,100,78,223),(57,144,171,130),(58,145,172,131),(59,146,173,132),(60,147,174,133),(61,148,175,134),(62,149,176,135),(63,150,177,136),(64,151,178,137),(65,152,179,138),(66,153,180,139),(67,154,181,140),(68,141,182,127),(69,142,169,128),(70,143,170,129)], [(1,187,136,221),(2,188,137,222),(3,189,138,223),(4,190,139,224),(5,191,140,211),(6,192,127,212),(7,193,128,213),(8,194,129,214),(9,195,130,215),(10,196,131,216),(11,183,132,217),(12,184,133,218),(13,185,134,219),(14,186,135,220),(15,89,73,60),(16,90,74,61),(17,91,75,62),(18,92,76,63),(19,93,77,64),(20,94,78,65),(21,95,79,66),(22,96,80,67),(23,97,81,68),(24,98,82,69),(25,85,83,70),(26,86,84,57),(27,87,71,58),(28,88,72,59),(29,197,50,173),(30,198,51,174),(31,199,52,175),(32,200,53,176),(33,201,54,177),(34,202,55,178),(35,203,56,179),(36,204,43,180),(37,205,44,181),(38,206,45,182),(39,207,46,169),(40,208,47,170),(41,209,48,171),(42,210,49,172),(99,164,116,151),(100,165,117,152),(101,166,118,153),(102,167,119,154),(103,168,120,141),(104,155,121,142),(105,156,122,143),(106,157,123,144),(107,158,124,145),(108,159,125,146),(109,160,126,147),(110,161,113,148),(111,162,114,149),(112,163,115,150)]])
196 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | ··· | 4L | 4M | 4N | 4O | 4P | 7A | ··· | 7F | 14A | ··· | 14AP | 14AQ | ··· | 14BN | 28A | ··· | 28BT | 28BU | ··· | 28CR |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | ··· | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 1 | ··· | 1 | 1 | ··· | 1 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
196 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | |||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C7 | C14 | C14 | C14 | C14 | C14 | D4 | C4○D4 | C7×D4 | C7×C4○D4 |
| kernel | C14×C4.4D4 | C2×C4×C28 | C14×C22⋊C4 | C7×C4.4D4 | D4×C2×C14 | Q8×C2×C14 | C2×C4.4D4 | C2×C42 | C2×C22⋊C4 | C4.4D4 | C22×D4 | C22×Q8 | C2×C28 | C2×C14 | C2×C4 | C22 |
| # reps | 1 | 1 | 4 | 8 | 1 | 1 | 6 | 6 | 24 | 48 | 6 | 6 | 4 | 8 | 24 | 48 |
Matrix representation of C14×C4.4D4 ►in GL5(𝔽29)
| 28 | 0 | 0 | 0 | 0 |
| 0 | 22 | 0 | 0 | 0 |
| 0 | 0 | 22 | 0 | 0 |
| 0 | 0 | 0 | 24 | 0 |
| 0 | 0 | 0 | 0 | 24 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 |
| 0 | 0 | 0 | 17 | 0 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 17 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 28 | 0 |
G:=sub<GL(5,GF(29))| [28,0,0,0,0,0,22,0,0,0,0,0,22,0,0,0,0,0,24,0,0,0,0,0,24],[1,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,0,17,0,0,0,17,0],[1,0,0,0,0,0,0,28,0,0,0,1,0,0,0,0,0,0,17,0,0,0,0,0,17],[1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,1,0] >;
C14×C4.4D4 in GAP, Magma, Sage, TeX
C_{14}\times C_4._4D_4 % in TeX
G:=Group("C14xC4.4D4"); // GroupNames label
G:=SmallGroup(448,1309);
// by ID
G=gap.SmallGroup(448,1309);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,1597,1576,4790,604]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^4=c^4=1,d^2=b^2,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=b^2*c^-1>;
// generators/relations