metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.119D14, C14.1072+ (1+4), (C4×D4)⋊27D7, (C4×D28)⋊35C2, (D4×C28)⋊29C2, C28⋊7D4⋊13C2, C4⋊C4.289D14, (C2×D4).226D14, C28.6Q8⋊17C2, Dic7⋊D4⋊28C2, Dic7⋊4D4⋊48C2, D14.D4⋊11C2, C28.293(C4○D4), (C2×C28).588C23, (C2×C14).109C24, (C4×C28).162C22, C22⋊C4.121D14, C22.2(C4○D28), (C22×C4).216D14, C4.119(D4⋊2D7), C2.20(D4⋊8D14), D14⋊C4.144C22, (D4×C14).310C22, (C2×D28).215C22, Dic7⋊C4.67C22, C4⋊Dic7.398C22, (C22×C28).84C22, (C2×Dic7).49C23, (C22×D7).43C23, C22.134(C23×D7), C23.106(C22×D7), C23.21D14⋊10C2, (C22×C14).179C23, C7⋊5(C22.47C24), (C4×Dic7).208C22, C23.D7.109C22, (C22×Dic7).101C22, C4⋊C4⋊D7⋊9C2, (C2×C4⋊Dic7)⋊26C2, C2.58(C2×C4○D28), C14.51(C2×C4○D4), C2.25(C2×D4⋊2D7), (C2×C4×D7).205C22, (C2×C14).19(C4○D4), (C7×C4⋊C4).337C22, (C2×C4).165(C22×D7), (C2×C7⋊D4).21C22, (C7×C22⋊C4).131C22, SmallGroup(448,1018)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1076 in 238 conjugacy classes, 99 normal (51 characteristic)
C1, C2 [×3], C2 [×5], C4 [×2], C4 [×10], C22, C22 [×2], C22 [×11], C7, C2×C4 [×5], C2×C4 [×14], D4 [×10], C23 [×2], C23 [×2], D7 [×2], C14 [×3], C14 [×3], C42, C42 [×2], C22⋊C4 [×2], C22⋊C4 [×8], C4⋊C4, C4⋊C4 [×9], C22×C4 [×2], C22×C4 [×4], C2×D4, C2×D4 [×5], Dic7 [×6], C28 [×2], C28 [×4], D14 [×6], C2×C14, C2×C14 [×2], C2×C14 [×5], C2×C4⋊C4, C42⋊C2, C4×D4, C4×D4 [×3], C4⋊D4 [×4], C22.D4 [×2], C42.C2, C42⋊2C2 [×2], C4×D7 [×2], D28 [×2], C2×Dic7 [×6], C2×Dic7 [×2], C7⋊D4 [×6], C2×C28 [×5], C2×C28 [×4], C7×D4 [×2], C22×D7 [×2], C22×C14 [×2], C22.47C24, C4×Dic7 [×2], Dic7⋊C4 [×4], C4⋊Dic7 [×3], C4⋊Dic7 [×2], D14⋊C4 [×6], C23.D7 [×2], C4×C28, C7×C22⋊C4 [×2], C7×C4⋊C4, C2×C4×D7 [×2], C2×D28, C22×Dic7 [×2], C2×C7⋊D4 [×4], C22×C28 [×2], D4×C14, C28.6Q8, C4×D28, Dic7⋊4D4 [×2], D14.D4 [×2], C4⋊C4⋊D7 [×2], C2×C4⋊Dic7, C23.21D14, C28⋊7D4 [×2], Dic7⋊D4 [×2], D4×C28, C42.119D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×4], C24, D14 [×7], C2×C4○D4 [×2], 2+ (1+4), C22×D7 [×7], C22.47C24, C4○D28 [×2], D4⋊2D7 [×2], C23×D7, C2×C4○D28, C2×D4⋊2D7, D4⋊8D14, C42.119D14
Generators and relations
G = < a,b,c,d | a4=b4=c14=1, d2=a2, ab=ba, cac-1=dad-1=a-1b2, bc=cb, dbd-1=b-1, dcd-1=a2c-1 >
►On 224 points
Generators in S224
(1 144 18 193)(2 60 19 55)(3 146 20 195)(4 62 21 43)(5 148 22 183)(6 64 23 45)(7 150 24 185)(8 66 25 47)(9 152 26 187)(10 68 27 49)(11 154 28 189)(12 70 15 51)(13 142 16 191)(14 58 17 53)(29 104 162 123)(30 212 163 81)(31 106 164 125)(32 214 165 83)(33 108 166 113)(34 216 167 71)(35 110 168 115)(36 218 155 73)(37 112 156 117)(38 220 157 75)(39 100 158 119)(40 222 159 77)(41 102 160 121)(42 224 161 79)(44 203 63 180)(46 205 65 182)(48 207 67 170)(50 209 69 172)(52 197 57 174)(54 199 59 176)(56 201 61 178)(72 86 217 139)(74 88 219 127)(76 90 221 129)(78 92 223 131)(80 94 211 133)(82 96 213 135)(84 98 215 137)(85 109 138 114)(87 111 140 116)(89 99 128 118)(91 101 130 120)(93 103 132 122)(95 105 134 124)(97 107 136 126)(141 173 190 210)(143 175 192 198)(145 177 194 200)(147 179 196 202)(149 181 184 204)(151 169 186 206)(153 171 188 208)
(1 66 176 186)(2 67 177 187)(3 68 178 188)(4 69 179 189)(5 70 180 190)(6 57 181 191)(7 58 182 192)(8 59 169 193)(9 60 170 194)(10 61 171 195)(11 62 172 196)(12 63 173 183)(13 64 174 184)(14 65 175 185)(15 44 210 148)(16 45 197 149)(17 46 198 150)(18 47 199 151)(19 48 200 152)(20 49 201 153)(21 50 202 154)(22 51 203 141)(23 52 204 142)(24 53 205 143)(25 54 206 144)(26 55 207 145)(27 56 208 146)(28 43 209 147)(29 218 133 116)(30 219 134 117)(31 220 135 118)(32 221 136 119)(33 222 137 120)(34 223 138 121)(35 224 139 122)(36 211 140 123)(37 212 127 124)(38 213 128 125)(39 214 129 126)(40 215 130 113)(41 216 131 114)(42 217 132 115)(71 92 109 160)(72 93 110 161)(73 94 111 162)(74 95 112 163)(75 96 99 164)(76 97 100 165)(77 98 101 166)(78 85 102 167)(79 86 103 168)(80 87 104 155)(81 88 105 156)(82 89 106 157)(83 90 107 158)(84 91 108 159)
(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 33 18 166)(2 165 19 32)(3 31 20 164)(4 163 21 30)(5 29 22 162)(6 161 23 42)(7 41 24 160)(8 159 25 40)(9 39 26 158)(10 157 27 38)(11 37 28 156)(12 155 15 36)(13 35 16 168)(14 167 17 34)(43 105 62 124)(44 123 63 104)(45 103 64 122)(46 121 65 102)(47 101 66 120)(48 119 67 100)(49 99 68 118)(50 117 69 112)(51 111 70 116)(52 115 57 110)(53 109 58 114)(54 113 59 108)(55 107 60 126)(56 125 61 106)(71 192 216 143)(72 142 217 191)(73 190 218 141)(74 154 219 189)(75 188 220 153)(76 152 221 187)(77 186 222 151)(78 150 223 185)(79 184 224 149)(80 148 211 183)(81 196 212 147)(82 146 213 195)(83 194 214 145)(84 144 215 193)(85 198 138 175)(86 174 139 197)(87 210 140 173)(88 172 127 209)(89 208 128 171)(90 170 129 207)(91 206 130 169)(92 182 131 205)(93 204 132 181)(94 180 133 203)(95 202 134 179)(96 178 135 201)(97 200 136 177)(98 176 137 199)
G:=sub<Sym(224)| (1,144,18,193)(2,60,19,55)(3,146,20,195)(4,62,21,43)(5,148,22,183)(6,64,23,45)(7,150,24,185)(8,66,25,47)(9,152,26,187)(10,68,27,49)(11,154,28,189)(12,70,15,51)(13,142,16,191)(14,58,17,53)(29,104,162,123)(30,212,163,81)(31,106,164,125)(32,214,165,83)(33,108,166,113)(34,216,167,71)(35,110,168,115)(36,218,155,73)(37,112,156,117)(38,220,157,75)(39,100,158,119)(40,222,159,77)(41,102,160,121)(42,224,161,79)(44,203,63,180)(46,205,65,182)(48,207,67,170)(50,209,69,172)(52,197,57,174)(54,199,59,176)(56,201,61,178)(72,86,217,139)(74,88,219,127)(76,90,221,129)(78,92,223,131)(80,94,211,133)(82,96,213,135)(84,98,215,137)(85,109,138,114)(87,111,140,116)(89,99,128,118)(91,101,130,120)(93,103,132,122)(95,105,134,124)(97,107,136,126)(141,173,190,210)(143,175,192,198)(145,177,194,200)(147,179,196,202)(149,181,184,204)(151,169,186,206)(153,171,188,208), (1,66,176,186)(2,67,177,187)(3,68,178,188)(4,69,179,189)(5,70,180,190)(6,57,181,191)(7,58,182,192)(8,59,169,193)(9,60,170,194)(10,61,171,195)(11,62,172,196)(12,63,173,183)(13,64,174,184)(14,65,175,185)(15,44,210,148)(16,45,197,149)(17,46,198,150)(18,47,199,151)(19,48,200,152)(20,49,201,153)(21,50,202,154)(22,51,203,141)(23,52,204,142)(24,53,205,143)(25,54,206,144)(26,55,207,145)(27,56,208,146)(28,43,209,147)(29,218,133,116)(30,219,134,117)(31,220,135,118)(32,221,136,119)(33,222,137,120)(34,223,138,121)(35,224,139,122)(36,211,140,123)(37,212,127,124)(38,213,128,125)(39,214,129,126)(40,215,130,113)(41,216,131,114)(42,217,132,115)(71,92,109,160)(72,93,110,161)(73,94,111,162)(74,95,112,163)(75,96,99,164)(76,97,100,165)(77,98,101,166)(78,85,102,167)(79,86,103,168)(80,87,104,155)(81,88,105,156)(82,89,106,157)(83,90,107,158)(84,91,108,159), (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), (1,33,18,166)(2,165,19,32)(3,31,20,164)(4,163,21,30)(5,29,22,162)(6,161,23,42)(7,41,24,160)(8,159,25,40)(9,39,26,158)(10,157,27,38)(11,37,28,156)(12,155,15,36)(13,35,16,168)(14,167,17,34)(43,105,62,124)(44,123,63,104)(45,103,64,122)(46,121,65,102)(47,101,66,120)(48,119,67,100)(49,99,68,118)(50,117,69,112)(51,111,70,116)(52,115,57,110)(53,109,58,114)(54,113,59,108)(55,107,60,126)(56,125,61,106)(71,192,216,143)(72,142,217,191)(73,190,218,141)(74,154,219,189)(75,188,220,153)(76,152,221,187)(77,186,222,151)(78,150,223,185)(79,184,224,149)(80,148,211,183)(81,196,212,147)(82,146,213,195)(83,194,214,145)(84,144,215,193)(85,198,138,175)(86,174,139,197)(87,210,140,173)(88,172,127,209)(89,208,128,171)(90,170,129,207)(91,206,130,169)(92,182,131,205)(93,204,132,181)(94,180,133,203)(95,202,134,179)(96,178,135,201)(97,200,136,177)(98,176,137,199)>;
G:=Group( (1,144,18,193)(2,60,19,55)(3,146,20,195)(4,62,21,43)(5,148,22,183)(6,64,23,45)(7,150,24,185)(8,66,25,47)(9,152,26,187)(10,68,27,49)(11,154,28,189)(12,70,15,51)(13,142,16,191)(14,58,17,53)(29,104,162,123)(30,212,163,81)(31,106,164,125)(32,214,165,83)(33,108,166,113)(34,216,167,71)(35,110,168,115)(36,218,155,73)(37,112,156,117)(38,220,157,75)(39,100,158,119)(40,222,159,77)(41,102,160,121)(42,224,161,79)(44,203,63,180)(46,205,65,182)(48,207,67,170)(50,209,69,172)(52,197,57,174)(54,199,59,176)(56,201,61,178)(72,86,217,139)(74,88,219,127)(76,90,221,129)(78,92,223,131)(80,94,211,133)(82,96,213,135)(84,98,215,137)(85,109,138,114)(87,111,140,116)(89,99,128,118)(91,101,130,120)(93,103,132,122)(95,105,134,124)(97,107,136,126)(141,173,190,210)(143,175,192,198)(145,177,194,200)(147,179,196,202)(149,181,184,204)(151,169,186,206)(153,171,188,208), (1,66,176,186)(2,67,177,187)(3,68,178,188)(4,69,179,189)(5,70,180,190)(6,57,181,191)(7,58,182,192)(8,59,169,193)(9,60,170,194)(10,61,171,195)(11,62,172,196)(12,63,173,183)(13,64,174,184)(14,65,175,185)(15,44,210,148)(16,45,197,149)(17,46,198,150)(18,47,199,151)(19,48,200,152)(20,49,201,153)(21,50,202,154)(22,51,203,141)(23,52,204,142)(24,53,205,143)(25,54,206,144)(26,55,207,145)(27,56,208,146)(28,43,209,147)(29,218,133,116)(30,219,134,117)(31,220,135,118)(32,221,136,119)(33,222,137,120)(34,223,138,121)(35,224,139,122)(36,211,140,123)(37,212,127,124)(38,213,128,125)(39,214,129,126)(40,215,130,113)(41,216,131,114)(42,217,132,115)(71,92,109,160)(72,93,110,161)(73,94,111,162)(74,95,112,163)(75,96,99,164)(76,97,100,165)(77,98,101,166)(78,85,102,167)(79,86,103,168)(80,87,104,155)(81,88,105,156)(82,89,106,157)(83,90,107,158)(84,91,108,159), (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), (1,33,18,166)(2,165,19,32)(3,31,20,164)(4,163,21,30)(5,29,22,162)(6,161,23,42)(7,41,24,160)(8,159,25,40)(9,39,26,158)(10,157,27,38)(11,37,28,156)(12,155,15,36)(13,35,16,168)(14,167,17,34)(43,105,62,124)(44,123,63,104)(45,103,64,122)(46,121,65,102)(47,101,66,120)(48,119,67,100)(49,99,68,118)(50,117,69,112)(51,111,70,116)(52,115,57,110)(53,109,58,114)(54,113,59,108)(55,107,60,126)(56,125,61,106)(71,192,216,143)(72,142,217,191)(73,190,218,141)(74,154,219,189)(75,188,220,153)(76,152,221,187)(77,186,222,151)(78,150,223,185)(79,184,224,149)(80,148,211,183)(81,196,212,147)(82,146,213,195)(83,194,214,145)(84,144,215,193)(85,198,138,175)(86,174,139,197)(87,210,140,173)(88,172,127,209)(89,208,128,171)(90,170,129,207)(91,206,130,169)(92,182,131,205)(93,204,132,181)(94,180,133,203)(95,202,134,179)(96,178,135,201)(97,200,136,177)(98,176,137,199) );
G=PermutationGroup([(1,144,18,193),(2,60,19,55),(3,146,20,195),(4,62,21,43),(5,148,22,183),(6,64,23,45),(7,150,24,185),(8,66,25,47),(9,152,26,187),(10,68,27,49),(11,154,28,189),(12,70,15,51),(13,142,16,191),(14,58,17,53),(29,104,162,123),(30,212,163,81),(31,106,164,125),(32,214,165,83),(33,108,166,113),(34,216,167,71),(35,110,168,115),(36,218,155,73),(37,112,156,117),(38,220,157,75),(39,100,158,119),(40,222,159,77),(41,102,160,121),(42,224,161,79),(44,203,63,180),(46,205,65,182),(48,207,67,170),(50,209,69,172),(52,197,57,174),(54,199,59,176),(56,201,61,178),(72,86,217,139),(74,88,219,127),(76,90,221,129),(78,92,223,131),(80,94,211,133),(82,96,213,135),(84,98,215,137),(85,109,138,114),(87,111,140,116),(89,99,128,118),(91,101,130,120),(93,103,132,122),(95,105,134,124),(97,107,136,126),(141,173,190,210),(143,175,192,198),(145,177,194,200),(147,179,196,202),(149,181,184,204),(151,169,186,206),(153,171,188,208)], [(1,66,176,186),(2,67,177,187),(3,68,178,188),(4,69,179,189),(5,70,180,190),(6,57,181,191),(7,58,182,192),(8,59,169,193),(9,60,170,194),(10,61,171,195),(11,62,172,196),(12,63,173,183),(13,64,174,184),(14,65,175,185),(15,44,210,148),(16,45,197,149),(17,46,198,150),(18,47,199,151),(19,48,200,152),(20,49,201,153),(21,50,202,154),(22,51,203,141),(23,52,204,142),(24,53,205,143),(25,54,206,144),(26,55,207,145),(27,56,208,146),(28,43,209,147),(29,218,133,116),(30,219,134,117),(31,220,135,118),(32,221,136,119),(33,222,137,120),(34,223,138,121),(35,224,139,122),(36,211,140,123),(37,212,127,124),(38,213,128,125),(39,214,129,126),(40,215,130,113),(41,216,131,114),(42,217,132,115),(71,92,109,160),(72,93,110,161),(73,94,111,162),(74,95,112,163),(75,96,99,164),(76,97,100,165),(77,98,101,166),(78,85,102,167),(79,86,103,168),(80,87,104,155),(81,88,105,156),(82,89,106,157),(83,90,107,158),(84,91,108,159)], [(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)], [(1,33,18,166),(2,165,19,32),(3,31,20,164),(4,163,21,30),(5,29,22,162),(6,161,23,42),(7,41,24,160),(8,159,25,40),(9,39,26,158),(10,157,27,38),(11,37,28,156),(12,155,15,36),(13,35,16,168),(14,167,17,34),(43,105,62,124),(44,123,63,104),(45,103,64,122),(46,121,65,102),(47,101,66,120),(48,119,67,100),(49,99,68,118),(50,117,69,112),(51,111,70,116),(52,115,57,110),(53,109,58,114),(54,113,59,108),(55,107,60,126),(56,125,61,106),(71,192,216,143),(72,142,217,191),(73,190,218,141),(74,154,219,189),(75,188,220,153),(76,152,221,187),(77,186,222,151),(78,150,223,185),(79,184,224,149),(80,148,211,183),(81,196,212,147),(82,146,213,195),(83,194,214,145),(84,144,215,193),(85,198,138,175),(86,174,139,197),(87,210,140,173),(88,172,127,209),(89,208,128,171),(90,170,129,207),(91,206,130,169),(92,182,131,205),(93,204,132,181),(94,180,133,203),(95,202,134,179),(96,178,135,201),(97,200,136,177),(98,176,137,199)])
Matrix representation ►G ⊆ GL4(𝔽29) generated by
| 12 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 28 |
| 0 | 0 | 1 | 0 |
| 13 | 18 | 0 | 0 |
| 26 | 16 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 28 |
| 2 | 28 | 0 | 0 |
| 5 | 26 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
| 17 | 12 | 0 | 0 |
| 0 | 12 | 0 | 0 |
| 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 17 |
G:=sub<GL(4,GF(29))| [12,0,0,0,0,12,0,0,0,0,0,1,0,0,28,0],[13,26,0,0,18,16,0,0,0,0,28,0,0,0,0,28],[2,5,0,0,28,26,0,0,0,0,0,1,0,0,1,0],[17,0,0,0,12,12,0,0,0,0,12,0,0,0,0,17] >;
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 28 | 28 | 2 | ··· | 2 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 1 | 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 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | D14 | D14 | C4○D28 | 2+ (1+4) | D4⋊2D7 | D4⋊8D14 |
| kernel | C42.119D14 | C28.6Q8 | C4×D28 | Dic7⋊4D4 | D14.D4 | C4⋊C4⋊D7 | C2×C4⋊Dic7 | C23.21D14 | C28⋊7D4 | Dic7⋊D4 | D4×C28 | C4×D4 | C28 | C2×C14 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C22 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 3 | 4 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 1 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{119}D_{14} % in TeX
G:=Group("C4^2.119D14"); // GroupNames label
G:=SmallGroup(448,1018);
// by ID
G=gap.SmallGroup(448,1018);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,219,1571,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1*b^2,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=a^2*c^-1>;
// generators/relations
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