metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14⋊3M4(2), C42.29D14, C7⋊C8⋊27D4, C4⋊C8⋊12D7, C7⋊4(C8⋊9D4), D14⋊C8⋊23C2, (C4×D28).8C2, (C2×D28).9C4, C14.47(C4×D4), C4.206(D4×D7), D14⋊C4.13C4, C28.365(C2×D4), (C2×C8).217D14, C4⋊Dic7.12C4, C14.12(C8○D4), (C4×C28).62C22, C42.D7⋊3C2, C2.17(D7×M4(2)), C28.335(C4○D4), C2.7(D28⋊C4), (C2×C56).212C22, (C2×C28).833C23, C4.55(Q8⋊2D7), C14.28(C2×M4(2)), C2.14(D28.2C4), (D7×C2×C8)⋊23C2, (C7×C4⋊C8)⋊17C2, (C2×C4).35(C4×D7), (C2×C8⋊D7)⋊21C2, (C2×C28).43(C2×C4), C22.111(C2×C4×D7), (C2×C7⋊C8).195C22, (C2×C4×D7).279C22, (C2×C14).88(C22×C4), (C2×Dic7).22(C2×C4), (C22×D7).38(C2×C4), (C2×C4).775(C22×D7), SmallGroup(448,370)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14⋊3M4(2)
G = < a,b,c,d | a14=b2=c8=d2=1, bab=dad=a-1, ac=ca, cbc-1=a7b, dbd=a5b, dcd=c5 >
Subgroups: 580 in 124 conjugacy classes, 51 normal (47 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, C23, D7, C14, C42, C22⋊C4, C4⋊C4, C2×C8, C2×C8, M4(2), C22×C4, C2×D4, Dic7, C28, C28, D14, D14, C2×C14, C8⋊C4, C22⋊C8, C4⋊C8, C4×D4, C22×C8, C2×M4(2), C7⋊C8, C7⋊C8, C56, C4×D7, D28, C2×Dic7, C2×C28, C22×D7, C8⋊9D4, C8×D7, C8⋊D7, C2×C7⋊C8, C4⋊Dic7, D14⋊C4, C4×C28, C2×C56, C2×C4×D7, C2×D28, C42.D7, D14⋊C8, C7×C4⋊C8, C4×D28, D7×C2×C8, C2×C8⋊D7, D14⋊3M4(2)
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, M4(2), C22×C4, C2×D4, C4○D4, D14, C4×D4, C2×M4(2), C8○D4, C4×D7, C22×D7, C8⋊9D4, C2×C4×D7, D4×D7, Q8⋊2D7, D28⋊C4, D28.2C4, D7×M4(2), D14⋊3M4(2)
►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)
(1 108)(2 107)(3 106)(4 105)(5 104)(6 103)(7 102)(8 101)(9 100)(10 99)(11 112)(12 111)(13 110)(14 109)(15 44)(16 43)(17 56)(18 55)(19 54)(20 53)(21 52)(22 51)(23 50)(24 49)(25 48)(26 47)(27 46)(28 45)(29 120)(30 119)(31 118)(32 117)(33 116)(34 115)(35 114)(36 113)(37 126)(38 125)(39 124)(40 123)(41 122)(42 121)(57 204)(58 203)(59 202)(60 201)(61 200)(62 199)(63 198)(64 197)(65 210)(66 209)(67 208)(68 207)(69 206)(70 205)(71 91)(72 90)(73 89)(74 88)(75 87)(76 86)(77 85)(78 98)(79 97)(80 96)(81 95)(82 94)(83 93)(84 92)(127 171)(128 170)(129 169)(130 182)(131 181)(132 180)(133 179)(134 178)(135 177)(136 176)(137 175)(138 174)(139 173)(140 172)(141 221)(142 220)(143 219)(144 218)(145 217)(146 216)(147 215)(148 214)(149 213)(150 212)(151 211)(152 224)(153 223)(154 222)(155 189)(156 188)(157 187)(158 186)(159 185)(160 184)(161 183)(162 196)(163 195)(164 194)(165 193)(166 192)(167 191)(168 190)
(1 88 27 176 109 82 47 130)(2 89 28 177 110 83 48 131)(3 90 15 178 111 84 49 132)(4 91 16 179 112 71 50 133)(5 92 17 180 99 72 51 134)(6 93 18 181 100 73 52 135)(7 94 19 182 101 74 53 136)(8 95 20 169 102 75 54 137)(9 96 21 170 103 76 55 138)(10 97 22 171 104 77 56 139)(11 98 23 172 105 78 43 140)(12 85 24 173 106 79 44 127)(13 86 25 174 107 80 45 128)(14 87 26 175 108 81 46 129)(29 155 200 142 124 186 65 217)(30 156 201 143 125 187 66 218)(31 157 202 144 126 188 67 219)(32 158 203 145 113 189 68 220)(33 159 204 146 114 190 69 221)(34 160 205 147 115 191 70 222)(35 161 206 148 116 192 57 223)(36 162 207 149 117 193 58 224)(37 163 208 150 118 194 59 211)(38 164 209 151 119 195 60 212)(39 165 210 152 120 196 61 213)(40 166 197 153 121 183 62 214)(41 167 198 154 122 184 63 215)(42 168 199 141 123 185 64 216)
(1 31)(2 30)(3 29)(4 42)(5 41)(6 40)(7 39)(8 38)(9 37)(10 36)(11 35)(12 34)(13 33)(14 32)(15 200)(16 199)(17 198)(18 197)(19 210)(20 209)(21 208)(22 207)(23 206)(24 205)(25 204)(26 203)(27 202)(28 201)(43 57)(44 70)(45 69)(46 68)(47 67)(48 66)(49 65)(50 64)(51 63)(52 62)(53 61)(54 60)(55 59)(56 58)(71 168)(72 167)(73 166)(74 165)(75 164)(76 163)(77 162)(78 161)(79 160)(80 159)(81 158)(82 157)(83 156)(84 155)(85 191)(86 190)(87 189)(88 188)(89 187)(90 186)(91 185)(92 184)(93 183)(94 196)(95 195)(96 194)(97 193)(98 192)(99 122)(100 121)(101 120)(102 119)(103 118)(104 117)(105 116)(106 115)(107 114)(108 113)(109 126)(110 125)(111 124)(112 123)(127 147)(128 146)(129 145)(130 144)(131 143)(132 142)(133 141)(134 154)(135 153)(136 152)(137 151)(138 150)(139 149)(140 148)(169 212)(170 211)(171 224)(172 223)(173 222)(174 221)(175 220)(176 219)(177 218)(178 217)(179 216)(180 215)(181 214)(182 213)
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), (1,108)(2,107)(3,106)(4,105)(5,104)(6,103)(7,102)(8,101)(9,100)(10,99)(11,112)(12,111)(13,110)(14,109)(15,44)(16,43)(17,56)(18,55)(19,54)(20,53)(21,52)(22,51)(23,50)(24,49)(25,48)(26,47)(27,46)(28,45)(29,120)(30,119)(31,118)(32,117)(33,116)(34,115)(35,114)(36,113)(37,126)(38,125)(39,124)(40,123)(41,122)(42,121)(57,204)(58,203)(59,202)(60,201)(61,200)(62,199)(63,198)(64,197)(65,210)(66,209)(67,208)(68,207)(69,206)(70,205)(71,91)(72,90)(73,89)(74,88)(75,87)(76,86)(77,85)(78,98)(79,97)(80,96)(81,95)(82,94)(83,93)(84,92)(127,171)(128,170)(129,169)(130,182)(131,181)(132,180)(133,179)(134,178)(135,177)(136,176)(137,175)(138,174)(139,173)(140,172)(141,221)(142,220)(143,219)(144,218)(145,217)(146,216)(147,215)(148,214)(149,213)(150,212)(151,211)(152,224)(153,223)(154,222)(155,189)(156,188)(157,187)(158,186)(159,185)(160,184)(161,183)(162,196)(163,195)(164,194)(165,193)(166,192)(167,191)(168,190), (1,88,27,176,109,82,47,130)(2,89,28,177,110,83,48,131)(3,90,15,178,111,84,49,132)(4,91,16,179,112,71,50,133)(5,92,17,180,99,72,51,134)(6,93,18,181,100,73,52,135)(7,94,19,182,101,74,53,136)(8,95,20,169,102,75,54,137)(9,96,21,170,103,76,55,138)(10,97,22,171,104,77,56,139)(11,98,23,172,105,78,43,140)(12,85,24,173,106,79,44,127)(13,86,25,174,107,80,45,128)(14,87,26,175,108,81,46,129)(29,155,200,142,124,186,65,217)(30,156,201,143,125,187,66,218)(31,157,202,144,126,188,67,219)(32,158,203,145,113,189,68,220)(33,159,204,146,114,190,69,221)(34,160,205,147,115,191,70,222)(35,161,206,148,116,192,57,223)(36,162,207,149,117,193,58,224)(37,163,208,150,118,194,59,211)(38,164,209,151,119,195,60,212)(39,165,210,152,120,196,61,213)(40,166,197,153,121,183,62,214)(41,167,198,154,122,184,63,215)(42,168,199,141,123,185,64,216), (1,31)(2,30)(3,29)(4,42)(5,41)(6,40)(7,39)(8,38)(9,37)(10,36)(11,35)(12,34)(13,33)(14,32)(15,200)(16,199)(17,198)(18,197)(19,210)(20,209)(21,208)(22,207)(23,206)(24,205)(25,204)(26,203)(27,202)(28,201)(43,57)(44,70)(45,69)(46,68)(47,67)(48,66)(49,65)(50,64)(51,63)(52,62)(53,61)(54,60)(55,59)(56,58)(71,168)(72,167)(73,166)(74,165)(75,164)(76,163)(77,162)(78,161)(79,160)(80,159)(81,158)(82,157)(83,156)(84,155)(85,191)(86,190)(87,189)(88,188)(89,187)(90,186)(91,185)(92,184)(93,183)(94,196)(95,195)(96,194)(97,193)(98,192)(99,122)(100,121)(101,120)(102,119)(103,118)(104,117)(105,116)(106,115)(107,114)(108,113)(109,126)(110,125)(111,124)(112,123)(127,147)(128,146)(129,145)(130,144)(131,143)(132,142)(133,141)(134,154)(135,153)(136,152)(137,151)(138,150)(139,149)(140,148)(169,212)(170,211)(171,224)(172,223)(173,222)(174,221)(175,220)(176,219)(177,218)(178,217)(179,216)(180,215)(181,214)(182,213)>;
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), (1,108)(2,107)(3,106)(4,105)(5,104)(6,103)(7,102)(8,101)(9,100)(10,99)(11,112)(12,111)(13,110)(14,109)(15,44)(16,43)(17,56)(18,55)(19,54)(20,53)(21,52)(22,51)(23,50)(24,49)(25,48)(26,47)(27,46)(28,45)(29,120)(30,119)(31,118)(32,117)(33,116)(34,115)(35,114)(36,113)(37,126)(38,125)(39,124)(40,123)(41,122)(42,121)(57,204)(58,203)(59,202)(60,201)(61,200)(62,199)(63,198)(64,197)(65,210)(66,209)(67,208)(68,207)(69,206)(70,205)(71,91)(72,90)(73,89)(74,88)(75,87)(76,86)(77,85)(78,98)(79,97)(80,96)(81,95)(82,94)(83,93)(84,92)(127,171)(128,170)(129,169)(130,182)(131,181)(132,180)(133,179)(134,178)(135,177)(136,176)(137,175)(138,174)(139,173)(140,172)(141,221)(142,220)(143,219)(144,218)(145,217)(146,216)(147,215)(148,214)(149,213)(150,212)(151,211)(152,224)(153,223)(154,222)(155,189)(156,188)(157,187)(158,186)(159,185)(160,184)(161,183)(162,196)(163,195)(164,194)(165,193)(166,192)(167,191)(168,190), (1,88,27,176,109,82,47,130)(2,89,28,177,110,83,48,131)(3,90,15,178,111,84,49,132)(4,91,16,179,112,71,50,133)(5,92,17,180,99,72,51,134)(6,93,18,181,100,73,52,135)(7,94,19,182,101,74,53,136)(8,95,20,169,102,75,54,137)(9,96,21,170,103,76,55,138)(10,97,22,171,104,77,56,139)(11,98,23,172,105,78,43,140)(12,85,24,173,106,79,44,127)(13,86,25,174,107,80,45,128)(14,87,26,175,108,81,46,129)(29,155,200,142,124,186,65,217)(30,156,201,143,125,187,66,218)(31,157,202,144,126,188,67,219)(32,158,203,145,113,189,68,220)(33,159,204,146,114,190,69,221)(34,160,205,147,115,191,70,222)(35,161,206,148,116,192,57,223)(36,162,207,149,117,193,58,224)(37,163,208,150,118,194,59,211)(38,164,209,151,119,195,60,212)(39,165,210,152,120,196,61,213)(40,166,197,153,121,183,62,214)(41,167,198,154,122,184,63,215)(42,168,199,141,123,185,64,216), (1,31)(2,30)(3,29)(4,42)(5,41)(6,40)(7,39)(8,38)(9,37)(10,36)(11,35)(12,34)(13,33)(14,32)(15,200)(16,199)(17,198)(18,197)(19,210)(20,209)(21,208)(22,207)(23,206)(24,205)(25,204)(26,203)(27,202)(28,201)(43,57)(44,70)(45,69)(46,68)(47,67)(48,66)(49,65)(50,64)(51,63)(52,62)(53,61)(54,60)(55,59)(56,58)(71,168)(72,167)(73,166)(74,165)(75,164)(76,163)(77,162)(78,161)(79,160)(80,159)(81,158)(82,157)(83,156)(84,155)(85,191)(86,190)(87,189)(88,188)(89,187)(90,186)(91,185)(92,184)(93,183)(94,196)(95,195)(96,194)(97,193)(98,192)(99,122)(100,121)(101,120)(102,119)(103,118)(104,117)(105,116)(106,115)(107,114)(108,113)(109,126)(110,125)(111,124)(112,123)(127,147)(128,146)(129,145)(130,144)(131,143)(132,142)(133,141)(134,154)(135,153)(136,152)(137,151)(138,150)(139,149)(140,148)(169,212)(170,211)(171,224)(172,223)(173,222)(174,221)(175,220)(176,219)(177,218)(178,217)(179,216)(180,215)(181,214)(182,213) );
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)], [(1,108),(2,107),(3,106),(4,105),(5,104),(6,103),(7,102),(8,101),(9,100),(10,99),(11,112),(12,111),(13,110),(14,109),(15,44),(16,43),(17,56),(18,55),(19,54),(20,53),(21,52),(22,51),(23,50),(24,49),(25,48),(26,47),(27,46),(28,45),(29,120),(30,119),(31,118),(32,117),(33,116),(34,115),(35,114),(36,113),(37,126),(38,125),(39,124),(40,123),(41,122),(42,121),(57,204),(58,203),(59,202),(60,201),(61,200),(62,199),(63,198),(64,197),(65,210),(66,209),(67,208),(68,207),(69,206),(70,205),(71,91),(72,90),(73,89),(74,88),(75,87),(76,86),(77,85),(78,98),(79,97),(80,96),(81,95),(82,94),(83,93),(84,92),(127,171),(128,170),(129,169),(130,182),(131,181),(132,180),(133,179),(134,178),(135,177),(136,176),(137,175),(138,174),(139,173),(140,172),(141,221),(142,220),(143,219),(144,218),(145,217),(146,216),(147,215),(148,214),(149,213),(150,212),(151,211),(152,224),(153,223),(154,222),(155,189),(156,188),(157,187),(158,186),(159,185),(160,184),(161,183),(162,196),(163,195),(164,194),(165,193),(166,192),(167,191),(168,190)], [(1,88,27,176,109,82,47,130),(2,89,28,177,110,83,48,131),(3,90,15,178,111,84,49,132),(4,91,16,179,112,71,50,133),(5,92,17,180,99,72,51,134),(6,93,18,181,100,73,52,135),(7,94,19,182,101,74,53,136),(8,95,20,169,102,75,54,137),(9,96,21,170,103,76,55,138),(10,97,22,171,104,77,56,139),(11,98,23,172,105,78,43,140),(12,85,24,173,106,79,44,127),(13,86,25,174,107,80,45,128),(14,87,26,175,108,81,46,129),(29,155,200,142,124,186,65,217),(30,156,201,143,125,187,66,218),(31,157,202,144,126,188,67,219),(32,158,203,145,113,189,68,220),(33,159,204,146,114,190,69,221),(34,160,205,147,115,191,70,222),(35,161,206,148,116,192,57,223),(36,162,207,149,117,193,58,224),(37,163,208,150,118,194,59,211),(38,164,209,151,119,195,60,212),(39,165,210,152,120,196,61,213),(40,166,197,153,121,183,62,214),(41,167,198,154,122,184,63,215),(42,168,199,141,123,185,64,216)], [(1,31),(2,30),(3,29),(4,42),(5,41),(6,40),(7,39),(8,38),(9,37),(10,36),(11,35),(12,34),(13,33),(14,32),(15,200),(16,199),(17,198),(18,197),(19,210),(20,209),(21,208),(22,207),(23,206),(24,205),(25,204),(26,203),(27,202),(28,201),(43,57),(44,70),(45,69),(46,68),(47,67),(48,66),(49,65),(50,64),(51,63),(52,62),(53,61),(54,60),(55,59),(56,58),(71,168),(72,167),(73,166),(74,165),(75,164),(76,163),(77,162),(78,161),(79,160),(80,159),(81,158),(82,157),(83,156),(84,155),(85,191),(86,190),(87,189),(88,188),(89,187),(90,186),(91,185),(92,184),(93,183),(94,196),(95,195),(96,194),(97,193),(98,192),(99,122),(100,121),(101,120),(102,119),(103,118),(104,117),(105,116),(106,115),(107,114),(108,113),(109,126),(110,125),(111,124),(112,123),(127,147),(128,146),(129,145),(130,144),(131,143),(132,142),(133,141),(134,154),(135,153),(136,152),(137,151),(138,150),(139,149),(140,148),(169,212),(170,211),(171,224),(172,223),(173,222),(174,221),(175,220),(176,219),(177,218),(178,217),(179,216),(180,215),(181,214),(182,213)]])
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 8I | 8J | 8K | 8L | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28X | 56A | ··· | 56X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 28 | 1 | 1 | 1 | 1 | 4 | 4 | 14 | 14 | 28 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | |||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | C4 | C4 | D4 | D7 | C4○D4 | M4(2) | D14 | D14 | C8○D4 | C4×D7 | D28.2C4 | D4×D7 | Q8⋊2D7 | D7×M4(2) |
| kernel | D14⋊3M4(2) | C42.D7 | D14⋊C8 | C7×C4⋊C8 | C4×D28 | D7×C2×C8 | C2×C8⋊D7 | C4⋊Dic7 | D14⋊C4 | C2×D28 | C7⋊C8 | C4⋊C8 | C28 | D14 | C42 | C2×C8 | C14 | C2×C4 | C2 | C4 | C4 | C2 |
| # reps | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 2 | 4 | 2 | 2 | 3 | 2 | 4 | 3 | 6 | 4 | 12 | 24 | 3 | 3 | 6 |
Matrix representation of D14⋊3M4(2) ►in GL4(𝔽113) generated by
| 80 | 80 | 0 | 0 |
| 33 | 9 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 33 | 33 | 0 | 0 |
| 104 | 80 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 5 | 1 |
| 86 | 6 | 0 | 0 |
| 107 | 27 | 0 | 0 |
| 0 | 0 | 20 | 8 |
| 0 | 0 | 77 | 93 |
| 55 | 38 | 0 | 0 |
| 81 | 58 | 0 | 0 |
| 0 | 0 | 39 | 106 |
| 0 | 0 | 88 | 74 |
G:=sub<GL(4,GF(113))| [80,33,0,0,80,9,0,0,0,0,112,0,0,0,0,112],[33,104,0,0,33,80,0,0,0,0,112,5,0,0,0,1],[86,107,0,0,6,27,0,0,0,0,20,77,0,0,8,93],[55,81,0,0,38,58,0,0,0,0,39,88,0,0,106,74] >;
D14⋊3M4(2) in GAP, Magma, Sage, TeX
D_{14}\rtimes_3M_4(2) % in TeX
G:=Group("D14:3M4(2)"); // GroupNames label
G:=SmallGroup(448,370);
// by ID
G=gap.SmallGroup(448,370);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,701,120,219,58,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^2=c^8=d^2=1,b*a*b=d*a*d=a^-1,a*c=c*a,c*b*c^-1=a^7*b,d*b*d=a^5*b,d*c*d=c^5>;
// generators/relations