direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: M4(2)×C2×C14, C56⋊15C23, C24.6C28, C28.92C24, C8⋊4(C22×C14), (C22×C8)⋊12C14, (C2×C56)⋊53C22, (C22×C56)⋊26C2, (C23×C14).7C4, (C22×C4).18C28, C23.40(C2×C28), (C23×C4).13C14, C4.16(C23×C14), (C22×C28).39C4, C4.31(C22×C28), (C23×C28).26C2, C2.10(C23×C28), C14.62(C23×C4), (C2×C28).968C23, C28.189(C22×C4), C22.27(C22×C28), (C22×C28).599C22, (C2×C8)⋊15(C2×C14), (C2×C4).79(C2×C28), (C2×C28).341(C2×C4), (C2×C14).166(C22×C4), (C22×C4).126(C2×C14), (C2×C4).138(C22×C14), (C22×C14).121(C2×C4), SmallGroup(448,1349)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 338 in 298 conjugacy classes, 258 normal (18 characteristic)
C1, C2, C2 [×6], C2 [×4], C4, C4 [×7], C22 [×11], C22 [×12], C7, C8 [×8], C2×C4 [×28], C23, C23 [×6], C23 [×4], C14, C14 [×6], C14 [×4], C2×C8 [×12], M4(2) [×16], C22×C4 [×2], C22×C4 [×12], C24, C28, C28 [×7], C2×C14 [×11], C2×C14 [×12], C22×C8 [×2], C2×M4(2) [×12], C23×C4, C56 [×8], C2×C28 [×28], C22×C14, C22×C14 [×6], C22×C14 [×4], C22×M4(2), C2×C56 [×12], C7×M4(2) [×16], C22×C28 [×2], C22×C28 [×12], C23×C14, C22×C56 [×2], C14×M4(2) [×12], C23×C28, M4(2)×C2×C14
Quotients:
C1, C2 [×15], C4 [×8], C22 [×35], C7, C2×C4 [×28], C23 [×15], C14 [×15], M4(2) [×4], C22×C4 [×14], C24, C28 [×8], C2×C14 [×35], C2×M4(2) [×6], C23×C4, C2×C28 [×28], C22×C14 [×15], C22×M4(2), C7×M4(2) [×4], C22×C28 [×14], C23×C14, C14×M4(2) [×6], C23×C28, M4(2)×C2×C14
Generators and relations
G = < a,b,c,d | a2=b14=c8=d2=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd=c5 >
►On 224 points
Generators in S224
(1 212)(2 213)(3 214)(4 215)(5 216)(6 217)(7 218)(8 219)(9 220)(10 221)(11 222)(12 223)(13 224)(14 211)(15 127)(16 128)(17 129)(18 130)(19 131)(20 132)(21 133)(22 134)(23 135)(24 136)(25 137)(26 138)(27 139)(28 140)(29 65)(30 66)(31 67)(32 68)(33 69)(34 70)(35 57)(36 58)(37 59)(38 60)(39 61)(40 62)(41 63)(42 64)(43 90)(44 91)(45 92)(46 93)(47 94)(48 95)(49 96)(50 97)(51 98)(52 85)(53 86)(54 87)(55 88)(56 89)(71 107)(72 108)(73 109)(74 110)(75 111)(76 112)(77 99)(78 100)(79 101)(80 102)(81 103)(82 104)(83 105)(84 106)(113 173)(114 174)(115 175)(116 176)(117 177)(118 178)(119 179)(120 180)(121 181)(122 182)(123 169)(124 170)(125 171)(126 172)(141 164)(142 165)(143 166)(144 167)(145 168)(146 155)(147 156)(148 157)(149 158)(150 159)(151 160)(152 161)(153 162)(154 163)(183 209)(184 210)(185 197)(186 198)(187 199)(188 200)(189 201)(190 202)(191 203)(192 204)(193 205)(194 206)(195 207)(196 208)
(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 87 153 120 32 22 206 100)(2 88 154 121 33 23 207 101)(3 89 141 122 34 24 208 102)(4 90 142 123 35 25 209 103)(5 91 143 124 36 26 210 104)(6 92 144 125 37 27 197 105)(7 93 145 126 38 28 198 106)(8 94 146 113 39 15 199 107)(9 95 147 114 40 16 200 108)(10 96 148 115 41 17 201 109)(11 97 149 116 42 18 202 110)(12 98 150 117 29 19 203 111)(13 85 151 118 30 20 204 112)(14 86 152 119 31 21 205 99)(43 165 169 57 137 183 81 215)(44 166 170 58 138 184 82 216)(45 167 171 59 139 185 83 217)(46 168 172 60 140 186 84 218)(47 155 173 61 127 187 71 219)(48 156 174 62 128 188 72 220)(49 157 175 63 129 189 73 221)(50 158 176 64 130 190 74 222)(51 159 177 65 131 191 75 223)(52 160 178 66 132 192 76 224)(53 161 179 67 133 193 77 211)(54 162 180 68 134 194 78 212)(55 163 181 69 135 195 79 213)(56 164 182 70 136 196 80 214)
(1 61)(2 62)(3 63)(4 64)(5 65)(6 66)(7 67)(8 68)(9 69)(10 70)(11 57)(12 58)(13 59)(14 60)(15 134)(16 135)(17 136)(18 137)(19 138)(20 139)(21 140)(22 127)(23 128)(24 129)(25 130)(26 131)(27 132)(28 133)(29 216)(30 217)(31 218)(32 219)(33 220)(34 221)(35 222)(36 223)(37 224)(38 211)(39 212)(40 213)(41 214)(42 215)(43 97)(44 98)(45 85)(46 86)(47 87)(48 88)(49 89)(50 90)(51 91)(52 92)(53 93)(54 94)(55 95)(56 96)(71 100)(72 101)(73 102)(74 103)(75 104)(76 105)(77 106)(78 107)(79 108)(80 109)(81 110)(82 111)(83 112)(84 99)(113 180)(114 181)(115 182)(116 169)(117 170)(118 171)(119 172)(120 173)(121 174)(122 175)(123 176)(124 177)(125 178)(126 179)(141 189)(142 190)(143 191)(144 192)(145 193)(146 194)(147 195)(148 196)(149 183)(150 184)(151 185)(152 186)(153 187)(154 188)(155 206)(156 207)(157 208)(158 209)(159 210)(160 197)(161 198)(162 199)(163 200)(164 201)(165 202)(166 203)(167 204)(168 205)
G:=sub<Sym(224)| (1,212)(2,213)(3,214)(4,215)(5,216)(6,217)(7,218)(8,219)(9,220)(10,221)(11,222)(12,223)(13,224)(14,211)(15,127)(16,128)(17,129)(18,130)(19,131)(20,132)(21,133)(22,134)(23,135)(24,136)(25,137)(26,138)(27,139)(28,140)(29,65)(30,66)(31,67)(32,68)(33,69)(34,70)(35,57)(36,58)(37,59)(38,60)(39,61)(40,62)(41,63)(42,64)(43,90)(44,91)(45,92)(46,93)(47,94)(48,95)(49,96)(50,97)(51,98)(52,85)(53,86)(54,87)(55,88)(56,89)(71,107)(72,108)(73,109)(74,110)(75,111)(76,112)(77,99)(78,100)(79,101)(80,102)(81,103)(82,104)(83,105)(84,106)(113,173)(114,174)(115,175)(116,176)(117,177)(118,178)(119,179)(120,180)(121,181)(122,182)(123,169)(124,170)(125,171)(126,172)(141,164)(142,165)(143,166)(144,167)(145,168)(146,155)(147,156)(148,157)(149,158)(150,159)(151,160)(152,161)(153,162)(154,163)(183,209)(184,210)(185,197)(186,198)(187,199)(188,200)(189,201)(190,202)(191,203)(192,204)(193,205)(194,206)(195,207)(196,208), (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), (1,87,153,120,32,22,206,100)(2,88,154,121,33,23,207,101)(3,89,141,122,34,24,208,102)(4,90,142,123,35,25,209,103)(5,91,143,124,36,26,210,104)(6,92,144,125,37,27,197,105)(7,93,145,126,38,28,198,106)(8,94,146,113,39,15,199,107)(9,95,147,114,40,16,200,108)(10,96,148,115,41,17,201,109)(11,97,149,116,42,18,202,110)(12,98,150,117,29,19,203,111)(13,85,151,118,30,20,204,112)(14,86,152,119,31,21,205,99)(43,165,169,57,137,183,81,215)(44,166,170,58,138,184,82,216)(45,167,171,59,139,185,83,217)(46,168,172,60,140,186,84,218)(47,155,173,61,127,187,71,219)(48,156,174,62,128,188,72,220)(49,157,175,63,129,189,73,221)(50,158,176,64,130,190,74,222)(51,159,177,65,131,191,75,223)(52,160,178,66,132,192,76,224)(53,161,179,67,133,193,77,211)(54,162,180,68,134,194,78,212)(55,163,181,69,135,195,79,213)(56,164,182,70,136,196,80,214), (1,61)(2,62)(3,63)(4,64)(5,65)(6,66)(7,67)(8,68)(9,69)(10,70)(11,57)(12,58)(13,59)(14,60)(15,134)(16,135)(17,136)(18,137)(19,138)(20,139)(21,140)(22,127)(23,128)(24,129)(25,130)(26,131)(27,132)(28,133)(29,216)(30,217)(31,218)(32,219)(33,220)(34,221)(35,222)(36,223)(37,224)(38,211)(39,212)(40,213)(41,214)(42,215)(43,97)(44,98)(45,85)(46,86)(47,87)(48,88)(49,89)(50,90)(51,91)(52,92)(53,93)(54,94)(55,95)(56,96)(71,100)(72,101)(73,102)(74,103)(75,104)(76,105)(77,106)(78,107)(79,108)(80,109)(81,110)(82,111)(83,112)(84,99)(113,180)(114,181)(115,182)(116,169)(117,170)(118,171)(119,172)(120,173)(121,174)(122,175)(123,176)(124,177)(125,178)(126,179)(141,189)(142,190)(143,191)(144,192)(145,193)(146,194)(147,195)(148,196)(149,183)(150,184)(151,185)(152,186)(153,187)(154,188)(155,206)(156,207)(157,208)(158,209)(159,210)(160,197)(161,198)(162,199)(163,200)(164,201)(165,202)(166,203)(167,204)(168,205)>;
G:=Group( (1,212)(2,213)(3,214)(4,215)(5,216)(6,217)(7,218)(8,219)(9,220)(10,221)(11,222)(12,223)(13,224)(14,211)(15,127)(16,128)(17,129)(18,130)(19,131)(20,132)(21,133)(22,134)(23,135)(24,136)(25,137)(26,138)(27,139)(28,140)(29,65)(30,66)(31,67)(32,68)(33,69)(34,70)(35,57)(36,58)(37,59)(38,60)(39,61)(40,62)(41,63)(42,64)(43,90)(44,91)(45,92)(46,93)(47,94)(48,95)(49,96)(50,97)(51,98)(52,85)(53,86)(54,87)(55,88)(56,89)(71,107)(72,108)(73,109)(74,110)(75,111)(76,112)(77,99)(78,100)(79,101)(80,102)(81,103)(82,104)(83,105)(84,106)(113,173)(114,174)(115,175)(116,176)(117,177)(118,178)(119,179)(120,180)(121,181)(122,182)(123,169)(124,170)(125,171)(126,172)(141,164)(142,165)(143,166)(144,167)(145,168)(146,155)(147,156)(148,157)(149,158)(150,159)(151,160)(152,161)(153,162)(154,163)(183,209)(184,210)(185,197)(186,198)(187,199)(188,200)(189,201)(190,202)(191,203)(192,204)(193,205)(194,206)(195,207)(196,208), (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), (1,87,153,120,32,22,206,100)(2,88,154,121,33,23,207,101)(3,89,141,122,34,24,208,102)(4,90,142,123,35,25,209,103)(5,91,143,124,36,26,210,104)(6,92,144,125,37,27,197,105)(7,93,145,126,38,28,198,106)(8,94,146,113,39,15,199,107)(9,95,147,114,40,16,200,108)(10,96,148,115,41,17,201,109)(11,97,149,116,42,18,202,110)(12,98,150,117,29,19,203,111)(13,85,151,118,30,20,204,112)(14,86,152,119,31,21,205,99)(43,165,169,57,137,183,81,215)(44,166,170,58,138,184,82,216)(45,167,171,59,139,185,83,217)(46,168,172,60,140,186,84,218)(47,155,173,61,127,187,71,219)(48,156,174,62,128,188,72,220)(49,157,175,63,129,189,73,221)(50,158,176,64,130,190,74,222)(51,159,177,65,131,191,75,223)(52,160,178,66,132,192,76,224)(53,161,179,67,133,193,77,211)(54,162,180,68,134,194,78,212)(55,163,181,69,135,195,79,213)(56,164,182,70,136,196,80,214), (1,61)(2,62)(3,63)(4,64)(5,65)(6,66)(7,67)(8,68)(9,69)(10,70)(11,57)(12,58)(13,59)(14,60)(15,134)(16,135)(17,136)(18,137)(19,138)(20,139)(21,140)(22,127)(23,128)(24,129)(25,130)(26,131)(27,132)(28,133)(29,216)(30,217)(31,218)(32,219)(33,220)(34,221)(35,222)(36,223)(37,224)(38,211)(39,212)(40,213)(41,214)(42,215)(43,97)(44,98)(45,85)(46,86)(47,87)(48,88)(49,89)(50,90)(51,91)(52,92)(53,93)(54,94)(55,95)(56,96)(71,100)(72,101)(73,102)(74,103)(75,104)(76,105)(77,106)(78,107)(79,108)(80,109)(81,110)(82,111)(83,112)(84,99)(113,180)(114,181)(115,182)(116,169)(117,170)(118,171)(119,172)(120,173)(121,174)(122,175)(123,176)(124,177)(125,178)(126,179)(141,189)(142,190)(143,191)(144,192)(145,193)(146,194)(147,195)(148,196)(149,183)(150,184)(151,185)(152,186)(153,187)(154,188)(155,206)(156,207)(157,208)(158,209)(159,210)(160,197)(161,198)(162,199)(163,200)(164,201)(165,202)(166,203)(167,204)(168,205) );
G=PermutationGroup([(1,212),(2,213),(3,214),(4,215),(5,216),(6,217),(7,218),(8,219),(9,220),(10,221),(11,222),(12,223),(13,224),(14,211),(15,127),(16,128),(17,129),(18,130),(19,131),(20,132),(21,133),(22,134),(23,135),(24,136),(25,137),(26,138),(27,139),(28,140),(29,65),(30,66),(31,67),(32,68),(33,69),(34,70),(35,57),(36,58),(37,59),(38,60),(39,61),(40,62),(41,63),(42,64),(43,90),(44,91),(45,92),(46,93),(47,94),(48,95),(49,96),(50,97),(51,98),(52,85),(53,86),(54,87),(55,88),(56,89),(71,107),(72,108),(73,109),(74,110),(75,111),(76,112),(77,99),(78,100),(79,101),(80,102),(81,103),(82,104),(83,105),(84,106),(113,173),(114,174),(115,175),(116,176),(117,177),(118,178),(119,179),(120,180),(121,181),(122,182),(123,169),(124,170),(125,171),(126,172),(141,164),(142,165),(143,166),(144,167),(145,168),(146,155),(147,156),(148,157),(149,158),(150,159),(151,160),(152,161),(153,162),(154,163),(183,209),(184,210),(185,197),(186,198),(187,199),(188,200),(189,201),(190,202),(191,203),(192,204),(193,205),(194,206),(195,207),(196,208)], [(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)], [(1,87,153,120,32,22,206,100),(2,88,154,121,33,23,207,101),(3,89,141,122,34,24,208,102),(4,90,142,123,35,25,209,103),(5,91,143,124,36,26,210,104),(6,92,144,125,37,27,197,105),(7,93,145,126,38,28,198,106),(8,94,146,113,39,15,199,107),(9,95,147,114,40,16,200,108),(10,96,148,115,41,17,201,109),(11,97,149,116,42,18,202,110),(12,98,150,117,29,19,203,111),(13,85,151,118,30,20,204,112),(14,86,152,119,31,21,205,99),(43,165,169,57,137,183,81,215),(44,166,170,58,138,184,82,216),(45,167,171,59,139,185,83,217),(46,168,172,60,140,186,84,218),(47,155,173,61,127,187,71,219),(48,156,174,62,128,188,72,220),(49,157,175,63,129,189,73,221),(50,158,176,64,130,190,74,222),(51,159,177,65,131,191,75,223),(52,160,178,66,132,192,76,224),(53,161,179,67,133,193,77,211),(54,162,180,68,134,194,78,212),(55,163,181,69,135,195,79,213),(56,164,182,70,136,196,80,214)], [(1,61),(2,62),(3,63),(4,64),(5,65),(6,66),(7,67),(8,68),(9,69),(10,70),(11,57),(12,58),(13,59),(14,60),(15,134),(16,135),(17,136),(18,137),(19,138),(20,139),(21,140),(22,127),(23,128),(24,129),(25,130),(26,131),(27,132),(28,133),(29,216),(30,217),(31,218),(32,219),(33,220),(34,221),(35,222),(36,223),(37,224),(38,211),(39,212),(40,213),(41,214),(42,215),(43,97),(44,98),(45,85),(46,86),(47,87),(48,88),(49,89),(50,90),(51,91),(52,92),(53,93),(54,94),(55,95),(56,96),(71,100),(72,101),(73,102),(74,103),(75,104),(76,105),(77,106),(78,107),(79,108),(80,109),(81,110),(82,111),(83,112),(84,99),(113,180),(114,181),(115,182),(116,169),(117,170),(118,171),(119,172),(120,173),(121,174),(122,175),(123,176),(124,177),(125,178),(126,179),(141,189),(142,190),(143,191),(144,192),(145,193),(146,194),(147,195),(148,196),(149,183),(150,184),(151,185),(152,186),(153,187),(154,188),(155,206),(156,207),(157,208),(158,209),(159,210),(160,197),(161,198),(162,199),(163,200),(164,201),(165,202),(166,203),(167,204),(168,205)])
Matrix representation ►G ⊆ GL4(𝔽113) generated by
| 112 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 7 | 0 |
| 0 | 0 | 0 | 7 |
| 1 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 72 | 111 |
| 0 | 0 | 57 | 41 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 72 | 112 |
G:=sub<GL(4,GF(113))| [112,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,112,0,0,0,0,7,0,0,0,0,7],[1,0,0,0,0,112,0,0,0,0,72,57,0,0,111,41],[1,0,0,0,0,1,0,0,0,0,1,72,0,0,0,112] >;
280 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 7A | ··· | 7F | 8A | ··· | 8P | 14A | ··· | 14AP | 14AQ | ··· | 14BN | 28A | ··· | 28AV | 28AW | ··· | 28BT | 56A | ··· | 56CR |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | ··· | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | ··· | 2 |
280 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 |
| type | + | + | + | + | ||||||||||
| image | C1 | C2 | C2 | C2 | C4 | C4 | C7 | C14 | C14 | C14 | C28 | C28 | M4(2) | C7×M4(2) |
| kernel | M4(2)×C2×C14 | C22×C56 | C14×M4(2) | C23×C28 | C22×C28 | C23×C14 | C22×M4(2) | C22×C8 | C2×M4(2) | C23×C4 | C22×C4 | C24 | C2×C14 | C22 |
| # reps | 1 | 2 | 12 | 1 | 14 | 2 | 6 | 12 | 72 | 6 | 84 | 12 | 8 | 48 |
In GAP, Magma, Sage, TeX
M_{4(2)}\times C_2\times C_{14} % in TeX
G:=Group("M4(2)xC2xC14"); // GroupNames label
G:=SmallGroup(448,1349);
// by ID
G=gap.SmallGroup(448,1349);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,784,3165,124]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^14=c^8=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d=c^5>;
// generators/relations
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