direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C14×C42⋊2C2, (C2×C42)⋊4C14, (C4×C28)⋊49C22, C42⋊14(C2×C14), C24.17(C2×C14), (C2×C14).348C24, (C2×C28).712C23, (C22×C14).86C23, C22.22(C23×C14), (C23×C14).14C22, C23.72(C22×C14), (C22×C28).510C22, (C2×C4×C28)⋊6C2, (C14×C4⋊C4)⋊44C2, (C2×C4⋊C4)⋊17C14, C4⋊C4⋊13(C2×C14), (C7×C4⋊C4)⋊69C22, C2.11(C14×C4○D4), C14.230(C2×C4○D4), C22.34(C7×C4○D4), (C14×C22⋊C4).32C2, C22⋊C4.11(C2×C14), (C2×C22⋊C4).12C14, (C2×C4).16(C22×C14), (C2×C14).234(C4○D4), (C22×C4).102(C2×C14), (C7×C22⋊C4).145C22, SmallGroup(448,1311)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 354 in 246 conjugacy classes, 162 normal (12 characteristic)
C1, C2 [×7], C2 [×2], C4 [×12], C22, C22 [×6], C22 [×10], C7, C2×C4 [×12], C2×C4 [×12], C23, C23 [×2], C23 [×6], C14 [×7], C14 [×2], C42 [×4], C22⋊C4 [×12], C4⋊C4 [×12], C22×C4 [×6], C24, C28 [×12], C2×C14, C2×C14 [×6], C2×C14 [×10], C2×C42, C2×C22⋊C4 [×3], C2×C4⋊C4 [×3], C42⋊2C2 [×8], C2×C28 [×12], C2×C28 [×12], C22×C14, C22×C14 [×2], C22×C14 [×6], C2×C42⋊2C2, C4×C28 [×4], C7×C22⋊C4 [×12], C7×C4⋊C4 [×12], C22×C28 [×6], C23×C14, C2×C4×C28, C14×C22⋊C4 [×3], C14×C4⋊C4 [×3], C7×C42⋊2C2 [×8], C14×C42⋊2C2
Quotients:
C1, C2 [×15], C22 [×35], C7, C23 [×15], C14 [×15], C4○D4 [×6], C24, C2×C14 [×35], C42⋊2C2 [×4], C2×C4○D4 [×3], C22×C14 [×15], C2×C42⋊2C2, C7×C4○D4 [×6], C23×C14, C7×C42⋊2C2 [×4], C14×C4○D4 [×3], C14×C42⋊2C2
Generators and relations
G = < a,b,c,d | a14=b4=c4=d2=1, ab=ba, ac=ca, ad=da, bc=cb, dbd=bc2, dcd=b2c-1 >
►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)
(1 152 217 30)(2 153 218 31)(3 154 219 32)(4 141 220 33)(5 142 221 34)(6 143 222 35)(7 144 223 36)(8 145 224 37)(9 146 211 38)(10 147 212 39)(11 148 213 40)(12 149 214 41)(13 150 215 42)(14 151 216 29)(15 75 137 108)(16 76 138 109)(17 77 139 110)(18 78 140 111)(19 79 127 112)(20 80 128 99)(21 81 129 100)(22 82 130 101)(23 83 131 102)(24 84 132 103)(25 71 133 104)(26 72 134 105)(27 73 135 106)(28 74 136 107)(43 121 191 70)(44 122 192 57)(45 123 193 58)(46 124 194 59)(47 125 195 60)(48 126 196 61)(49 113 183 62)(50 114 184 63)(51 115 185 64)(52 116 186 65)(53 117 187 66)(54 118 188 67)(55 119 189 68)(56 120 190 69)(85 197 182 160)(86 198 169 161)(87 199 170 162)(88 200 171 163)(89 201 172 164)(90 202 173 165)(91 203 174 166)(92 204 175 167)(93 205 176 168)(94 206 177 155)(95 207 178 156)(96 208 179 157)(97 209 180 158)(98 210 181 159)
(1 128 70 182)(2 129 57 169)(3 130 58 170)(4 131 59 171)(5 132 60 172)(6 133 61 173)(7 134 62 174)(8 135 63 175)(9 136 64 176)(10 137 65 177)(11 138 66 178)(12 139 67 179)(13 140 68 180)(14 127 69 181)(15 116 94 212)(16 117 95 213)(17 118 96 214)(18 119 97 215)(19 120 98 216)(20 121 85 217)(21 122 86 218)(22 123 87 219)(23 124 88 220)(24 125 89 221)(25 126 90 222)(26 113 91 223)(27 114 92 224)(28 115 93 211)(29 79 190 210)(30 80 191 197)(31 81 192 198)(32 82 193 199)(33 83 194 200)(34 84 195 201)(35 71 196 202)(36 72 183 203)(37 73 184 204)(38 74 185 205)(39 75 186 206)(40 76 187 207)(41 77 188 208)(42 78 189 209)(43 160 152 99)(44 161 153 100)(45 162 154 101)(46 163 141 102)(47 164 142 103)(48 165 143 104)(49 166 144 105)(50 167 145 106)(51 168 146 107)(52 155 147 108)(53 156 148 109)(54 157 149 110)(55 158 150 111)(56 159 151 112)
(1 224)(2 211)(3 212)(4 213)(5 214)(6 215)(7 216)(8 217)(9 218)(10 219)(11 220)(12 221)(13 222)(14 223)(15 87)(16 88)(17 89)(18 90)(19 91)(20 92)(21 93)(22 94)(23 95)(24 96)(25 97)(26 98)(27 85)(28 86)(29 49)(30 50)(31 51)(32 52)(33 53)(34 54)(35 55)(36 56)(37 43)(38 44)(39 45)(40 46)(41 47)(42 48)(57 115)(58 116)(59 117)(60 118)(61 119)(62 120)(63 121)(64 122)(65 123)(66 124)(67 125)(68 126)(69 113)(70 114)(71 78)(72 79)(73 80)(74 81)(75 82)(76 83)(77 84)(99 106)(100 107)(101 108)(102 109)(103 110)(104 111)(105 112)(127 174)(128 175)(129 176)(130 177)(131 178)(132 179)(133 180)(134 181)(135 182)(136 169)(137 170)(138 171)(139 172)(140 173)(141 187)(142 188)(143 189)(144 190)(145 191)(146 192)(147 193)(148 194)(149 195)(150 196)(151 183)(152 184)(153 185)(154 186)(155 162)(156 163)(157 164)(158 165)(159 166)(160 167)(161 168)(197 204)(198 205)(199 206)(200 207)(201 208)(202 209)(203 210)
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), (1,152,217,30)(2,153,218,31)(3,154,219,32)(4,141,220,33)(5,142,221,34)(6,143,222,35)(7,144,223,36)(8,145,224,37)(9,146,211,38)(10,147,212,39)(11,148,213,40)(12,149,214,41)(13,150,215,42)(14,151,216,29)(15,75,137,108)(16,76,138,109)(17,77,139,110)(18,78,140,111)(19,79,127,112)(20,80,128,99)(21,81,129,100)(22,82,130,101)(23,83,131,102)(24,84,132,103)(25,71,133,104)(26,72,134,105)(27,73,135,106)(28,74,136,107)(43,121,191,70)(44,122,192,57)(45,123,193,58)(46,124,194,59)(47,125,195,60)(48,126,196,61)(49,113,183,62)(50,114,184,63)(51,115,185,64)(52,116,186,65)(53,117,187,66)(54,118,188,67)(55,119,189,68)(56,120,190,69)(85,197,182,160)(86,198,169,161)(87,199,170,162)(88,200,171,163)(89,201,172,164)(90,202,173,165)(91,203,174,166)(92,204,175,167)(93,205,176,168)(94,206,177,155)(95,207,178,156)(96,208,179,157)(97,209,180,158)(98,210,181,159), (1,128,70,182)(2,129,57,169)(3,130,58,170)(4,131,59,171)(5,132,60,172)(6,133,61,173)(7,134,62,174)(8,135,63,175)(9,136,64,176)(10,137,65,177)(11,138,66,178)(12,139,67,179)(13,140,68,180)(14,127,69,181)(15,116,94,212)(16,117,95,213)(17,118,96,214)(18,119,97,215)(19,120,98,216)(20,121,85,217)(21,122,86,218)(22,123,87,219)(23,124,88,220)(24,125,89,221)(25,126,90,222)(26,113,91,223)(27,114,92,224)(28,115,93,211)(29,79,190,210)(30,80,191,197)(31,81,192,198)(32,82,193,199)(33,83,194,200)(34,84,195,201)(35,71,196,202)(36,72,183,203)(37,73,184,204)(38,74,185,205)(39,75,186,206)(40,76,187,207)(41,77,188,208)(42,78,189,209)(43,160,152,99)(44,161,153,100)(45,162,154,101)(46,163,141,102)(47,164,142,103)(48,165,143,104)(49,166,144,105)(50,167,145,106)(51,168,146,107)(52,155,147,108)(53,156,148,109)(54,157,149,110)(55,158,150,111)(56,159,151,112), (1,224)(2,211)(3,212)(4,213)(5,214)(6,215)(7,216)(8,217)(9,218)(10,219)(11,220)(12,221)(13,222)(14,223)(15,87)(16,88)(17,89)(18,90)(19,91)(20,92)(21,93)(22,94)(23,95)(24,96)(25,97)(26,98)(27,85)(28,86)(29,49)(30,50)(31,51)(32,52)(33,53)(34,54)(35,55)(36,56)(37,43)(38,44)(39,45)(40,46)(41,47)(42,48)(57,115)(58,116)(59,117)(60,118)(61,119)(62,120)(63,121)(64,122)(65,123)(66,124)(67,125)(68,126)(69,113)(70,114)(71,78)(72,79)(73,80)(74,81)(75,82)(76,83)(77,84)(99,106)(100,107)(101,108)(102,109)(103,110)(104,111)(105,112)(127,174)(128,175)(129,176)(130,177)(131,178)(132,179)(133,180)(134,181)(135,182)(136,169)(137,170)(138,171)(139,172)(140,173)(141,187)(142,188)(143,189)(144,190)(145,191)(146,192)(147,193)(148,194)(149,195)(150,196)(151,183)(152,184)(153,185)(154,186)(155,162)(156,163)(157,164)(158,165)(159,166)(160,167)(161,168)(197,204)(198,205)(199,206)(200,207)(201,208)(202,209)(203,210)>;
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), (1,152,217,30)(2,153,218,31)(3,154,219,32)(4,141,220,33)(5,142,221,34)(6,143,222,35)(7,144,223,36)(8,145,224,37)(9,146,211,38)(10,147,212,39)(11,148,213,40)(12,149,214,41)(13,150,215,42)(14,151,216,29)(15,75,137,108)(16,76,138,109)(17,77,139,110)(18,78,140,111)(19,79,127,112)(20,80,128,99)(21,81,129,100)(22,82,130,101)(23,83,131,102)(24,84,132,103)(25,71,133,104)(26,72,134,105)(27,73,135,106)(28,74,136,107)(43,121,191,70)(44,122,192,57)(45,123,193,58)(46,124,194,59)(47,125,195,60)(48,126,196,61)(49,113,183,62)(50,114,184,63)(51,115,185,64)(52,116,186,65)(53,117,187,66)(54,118,188,67)(55,119,189,68)(56,120,190,69)(85,197,182,160)(86,198,169,161)(87,199,170,162)(88,200,171,163)(89,201,172,164)(90,202,173,165)(91,203,174,166)(92,204,175,167)(93,205,176,168)(94,206,177,155)(95,207,178,156)(96,208,179,157)(97,209,180,158)(98,210,181,159), (1,128,70,182)(2,129,57,169)(3,130,58,170)(4,131,59,171)(5,132,60,172)(6,133,61,173)(7,134,62,174)(8,135,63,175)(9,136,64,176)(10,137,65,177)(11,138,66,178)(12,139,67,179)(13,140,68,180)(14,127,69,181)(15,116,94,212)(16,117,95,213)(17,118,96,214)(18,119,97,215)(19,120,98,216)(20,121,85,217)(21,122,86,218)(22,123,87,219)(23,124,88,220)(24,125,89,221)(25,126,90,222)(26,113,91,223)(27,114,92,224)(28,115,93,211)(29,79,190,210)(30,80,191,197)(31,81,192,198)(32,82,193,199)(33,83,194,200)(34,84,195,201)(35,71,196,202)(36,72,183,203)(37,73,184,204)(38,74,185,205)(39,75,186,206)(40,76,187,207)(41,77,188,208)(42,78,189,209)(43,160,152,99)(44,161,153,100)(45,162,154,101)(46,163,141,102)(47,164,142,103)(48,165,143,104)(49,166,144,105)(50,167,145,106)(51,168,146,107)(52,155,147,108)(53,156,148,109)(54,157,149,110)(55,158,150,111)(56,159,151,112), (1,224)(2,211)(3,212)(4,213)(5,214)(6,215)(7,216)(8,217)(9,218)(10,219)(11,220)(12,221)(13,222)(14,223)(15,87)(16,88)(17,89)(18,90)(19,91)(20,92)(21,93)(22,94)(23,95)(24,96)(25,97)(26,98)(27,85)(28,86)(29,49)(30,50)(31,51)(32,52)(33,53)(34,54)(35,55)(36,56)(37,43)(38,44)(39,45)(40,46)(41,47)(42,48)(57,115)(58,116)(59,117)(60,118)(61,119)(62,120)(63,121)(64,122)(65,123)(66,124)(67,125)(68,126)(69,113)(70,114)(71,78)(72,79)(73,80)(74,81)(75,82)(76,83)(77,84)(99,106)(100,107)(101,108)(102,109)(103,110)(104,111)(105,112)(127,174)(128,175)(129,176)(130,177)(131,178)(132,179)(133,180)(134,181)(135,182)(136,169)(137,170)(138,171)(139,172)(140,173)(141,187)(142,188)(143,189)(144,190)(145,191)(146,192)(147,193)(148,194)(149,195)(150,196)(151,183)(152,184)(153,185)(154,186)(155,162)(156,163)(157,164)(158,165)(159,166)(160,167)(161,168)(197,204)(198,205)(199,206)(200,207)(201,208)(202,209)(203,210) );
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)], [(1,152,217,30),(2,153,218,31),(3,154,219,32),(4,141,220,33),(5,142,221,34),(6,143,222,35),(7,144,223,36),(8,145,224,37),(9,146,211,38),(10,147,212,39),(11,148,213,40),(12,149,214,41),(13,150,215,42),(14,151,216,29),(15,75,137,108),(16,76,138,109),(17,77,139,110),(18,78,140,111),(19,79,127,112),(20,80,128,99),(21,81,129,100),(22,82,130,101),(23,83,131,102),(24,84,132,103),(25,71,133,104),(26,72,134,105),(27,73,135,106),(28,74,136,107),(43,121,191,70),(44,122,192,57),(45,123,193,58),(46,124,194,59),(47,125,195,60),(48,126,196,61),(49,113,183,62),(50,114,184,63),(51,115,185,64),(52,116,186,65),(53,117,187,66),(54,118,188,67),(55,119,189,68),(56,120,190,69),(85,197,182,160),(86,198,169,161),(87,199,170,162),(88,200,171,163),(89,201,172,164),(90,202,173,165),(91,203,174,166),(92,204,175,167),(93,205,176,168),(94,206,177,155),(95,207,178,156),(96,208,179,157),(97,209,180,158),(98,210,181,159)], [(1,128,70,182),(2,129,57,169),(3,130,58,170),(4,131,59,171),(5,132,60,172),(6,133,61,173),(7,134,62,174),(8,135,63,175),(9,136,64,176),(10,137,65,177),(11,138,66,178),(12,139,67,179),(13,140,68,180),(14,127,69,181),(15,116,94,212),(16,117,95,213),(17,118,96,214),(18,119,97,215),(19,120,98,216),(20,121,85,217),(21,122,86,218),(22,123,87,219),(23,124,88,220),(24,125,89,221),(25,126,90,222),(26,113,91,223),(27,114,92,224),(28,115,93,211),(29,79,190,210),(30,80,191,197),(31,81,192,198),(32,82,193,199),(33,83,194,200),(34,84,195,201),(35,71,196,202),(36,72,183,203),(37,73,184,204),(38,74,185,205),(39,75,186,206),(40,76,187,207),(41,77,188,208),(42,78,189,209),(43,160,152,99),(44,161,153,100),(45,162,154,101),(46,163,141,102),(47,164,142,103),(48,165,143,104),(49,166,144,105),(50,167,145,106),(51,168,146,107),(52,155,147,108),(53,156,148,109),(54,157,149,110),(55,158,150,111),(56,159,151,112)], [(1,224),(2,211),(3,212),(4,213),(5,214),(6,215),(7,216),(8,217),(9,218),(10,219),(11,220),(12,221),(13,222),(14,223),(15,87),(16,88),(17,89),(18,90),(19,91),(20,92),(21,93),(22,94),(23,95),(24,96),(25,97),(26,98),(27,85),(28,86),(29,49),(30,50),(31,51),(32,52),(33,53),(34,54),(35,55),(36,56),(37,43),(38,44),(39,45),(40,46),(41,47),(42,48),(57,115),(58,116),(59,117),(60,118),(61,119),(62,120),(63,121),(64,122),(65,123),(66,124),(67,125),(68,126),(69,113),(70,114),(71,78),(72,79),(73,80),(74,81),(75,82),(76,83),(77,84),(99,106),(100,107),(101,108),(102,109),(103,110),(104,111),(105,112),(127,174),(128,175),(129,176),(130,177),(131,178),(132,179),(133,180),(134,181),(135,182),(136,169),(137,170),(138,171),(139,172),(140,173),(141,187),(142,188),(143,189),(144,190),(145,191),(146,192),(147,193),(148,194),(149,195),(150,196),(151,183),(152,184),(153,185),(154,186),(155,162),(156,163),(157,164),(158,165),(159,166),(160,167),(161,168),(197,204),(198,205),(199,206),(200,207),(201,208),(202,209),(203,210)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 0 |
| 0 | 0 | 0 | 0 | 0 | 20 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 19 | 4 |
| 0 | 0 | 0 | 0 | 11 | 10 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 27 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 24 | 1 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,20,0,0,0,0,0,0,20],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,19,11,0,0,0,0,4,10],[1,27,0,0,0,0,0,28,0,0,0,0,0,0,0,28,0,0,0,0,28,0,0,0,0,0,0,0,17,0,0,0,0,0,0,17],[1,0,0,0,0,0,1,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,28,24,0,0,0,0,0,1] >;
196 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 4A | ··· | 4L | 4M | ··· | 4R | 7A | ··· | 7F | 14A | ··· | 14AP | 14AQ | ··· | 14BB | 28A | ··· | 28BT | 28BU | ··· | 28DD |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | ··· | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 4 | 4 | 2 | ··· | 2 | 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 | 2 | 2 |
| type | + | + | + | + | + | |||||||
| image | C1 | C2 | C2 | C2 | C2 | C7 | C14 | C14 | C14 | C14 | C4○D4 | C7×C4○D4 |
| kernel | C14×C42⋊2C2 | C2×C4×C28 | C14×C22⋊C4 | C14×C4⋊C4 | C7×C42⋊2C2 | C2×C42⋊2C2 | C2×C42 | C2×C22⋊C4 | C2×C4⋊C4 | C42⋊2C2 | C2×C14 | C22 |
| # reps | 1 | 1 | 3 | 3 | 8 | 6 | 6 | 18 | 18 | 48 | 12 | 72 |
In GAP, Magma, Sage, TeX
C_{14}\times C_4^2\rtimes_2C_2 % in TeX
G:=Group("C14xC4^2:2C2"); // GroupNames label
G:=SmallGroup(448,1311);
// by ID
G=gap.SmallGroup(448,1311);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,1597,2360,4790,604]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^4=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d=b*c^2,d*c*d=b^2*c^-1>;
// generators/relations
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