metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4⋊C4.197D14, (D4×Dic7)⋊27C2, (C2×D4).159D14, Dic7.Q8⋊24C2, (C2×C28).67C23, C22⋊C4.66D14, Dic7⋊3Q8⋊30C2, Dic7⋊4D4⋊17C2, (C2×C14).193C24, D14⋊C4.31C22, Dic7.8(C4○D4), Dic7⋊D4.1C2, C22.D4⋊17D7, (C22×C4).321D14, C23.24(C22×D7), Dic7.D4⋊30C2, C22⋊Dic14⋊28C2, (D4×C14).131C22, C23.D14⋊27C2, Dic7⋊C4.38C22, C4⋊Dic7.224C22, (C22×C14).29C23, (C2×Dic7).98C23, (C22×D7).84C23, C22.214(C23×D7), C23.D7.39C22, C23.23D14⋊19C2, C22.11(D4⋊2D7), C23.11D14⋊11C2, (C22×C28).367C22, C7⋊8(C23.36C23), (C4×Dic7).120C22, (C2×Dic14).166C22, (C22×Dic7).226C22, (C2×C4×Dic7)⋊36C2, C2.57(D7×C4○D4), C4⋊C4⋊D7⋊26C2, C4⋊C4⋊7D7⋊31C2, C14.169(C2×C4○D4), C2.51(C2×D4⋊2D7), (C2×C4×D7).109C22, (C2×C4).58(C22×D7), (C2×C14).45(C4○D4), (C7×C4⋊C4).173C22, (C7×C22.D4)⋊3C2, (C2×C7⋊D4).45C22, (C7×C22⋊C4).48C22, SmallGroup(448,1102)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 940 in 234 conjugacy classes, 99 normal (91 characteristic)
C1, C2 [×3], C2 [×4], C4 [×14], C22, C22 [×2], C22 [×8], C7, C2×C4 [×5], C2×C4 [×17], D4 [×6], Q8 [×2], C23 [×2], C23, D7, C14 [×3], C14 [×3], C42 [×6], C22⋊C4 [×3], C22⋊C4 [×7], C4⋊C4 [×2], C4⋊C4 [×8], C22×C4, C22×C4 [×4], C2×D4, C2×D4 [×2], C2×Q8, Dic7 [×4], Dic7 [×5], C28 [×5], D14 [×3], C2×C14, C2×C14 [×2], C2×C14 [×5], C2×C42, C42⋊C2 [×2], C4×D4 [×3], C4×Q8, C4⋊D4, C22⋊Q8, C22.D4, C22.D4, C4.4D4, C42.C2, C42⋊2C2 [×2], Dic14 [×2], C4×D7 [×2], C2×Dic7 [×7], C2×Dic7 [×6], C7⋊D4 [×4], C2×C28 [×5], C2×C28 [×2], C7×D4 [×2], C22×D7, C22×C14 [×2], C23.36C23, C4×Dic7 [×6], Dic7⋊C4 [×6], C4⋊Dic7 [×2], D14⋊C4 [×4], C23.D7 [×3], C7×C22⋊C4 [×3], C7×C4⋊C4 [×2], C2×Dic14, C2×C4×D7, C22×Dic7 [×3], C2×C7⋊D4 [×2], C22×C28, D4×C14, C23.11D14, C22⋊Dic14, C23.D14, Dic7⋊4D4 [×2], Dic7.D4, Dic7⋊3Q8, Dic7.Q8, C4⋊C4⋊7D7, C4⋊C4⋊D7, C2×C4×Dic7, C23.23D14, D4×Dic7, Dic7⋊D4, C7×C22.D4, C4⋊C4.197D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×6], C24, D14 [×7], C2×C4○D4 [×3], C22×D7 [×7], C23.36C23, D4⋊2D7 [×2], C23×D7, C2×D4⋊2D7, D7×C4○D4 [×2], C4⋊C4.197D14
Generators and relations
G = < a,b,c,d | a4=b4=c14=1, d2=a2, bab-1=a-1, cac-1=dad-1=ab2, bc=cb, bd=db, dcd-1=c-1 >
►On 224 points
Generators in S224
(1 29 8 166)(2 160 9 37)(3 31 10 168)(4 162 11 39)(5 33 12 156)(6 164 13 41)(7 35 14 158)(15 223 22 138)(16 132 23 217)(17 211 24 140)(18 134 25 219)(19 213 26 128)(20 136 27 221)(21 215 28 130)(30 56 167 49)(32 44 155 51)(34 46 157 53)(36 48 159 55)(38 50 161 43)(40 52 163 45)(42 54 165 47)(57 106 171 99)(58 191 172 184)(59 108 173 101)(60 193 174 186)(61 110 175 103)(62 195 176 188)(63 112 177 105)(64 183 178 190)(65 100 179 107)(66 185 180 192)(67 102 181 109)(68 187 182 194)(69 104 169 111)(70 189 170 196)(71 145 78 91)(72 85 79 153)(73 147 80 93)(74 87 81 141)(75 149 82 95)(76 89 83 143)(77 151 84 97)(86 202 154 209)(88 204 142 197)(90 206 144 199)(92 208 146 201)(94 210 148 203)(96 198 150 205)(98 200 152 207)(113 127 120 212)(114 220 121 135)(115 129 122 214)(116 222 123 137)(117 131 124 216)(118 224 125 139)(119 133 126 218)
(1 100 48 184)(2 101 49 185)(3 102 50 186)(4 103 51 187)(5 104 52 188)(6 105 53 189)(7 106 54 190)(8 107 55 191)(9 108 56 192)(10 109 43 193)(11 110 44 194)(12 111 45 195)(13 112 46 196)(14 99 47 183)(15 83 117 205)(16 84 118 206)(17 71 119 207)(18 72 120 208)(19 73 121 209)(20 74 122 210)(21 75 123 197)(22 76 124 198)(23 77 125 199)(24 78 126 200)(25 79 113 201)(26 80 114 202)(27 81 115 203)(28 82 116 204)(29 65 159 172)(30 66 160 173)(31 67 161 174)(32 68 162 175)(33 69 163 176)(34 70 164 177)(35 57 165 178)(36 58 166 179)(37 59 167 180)(38 60 168 181)(39 61 155 182)(40 62 156 169)(41 63 157 170)(42 64 158 171)(85 127 146 219)(86 128 147 220)(87 129 148 221)(88 130 149 222)(89 131 150 223)(90 132 151 224)(91 133 152 211)(92 134 153 212)(93 135 154 213)(94 136 141 214)(95 137 142 215)(96 138 143 216)(97 139 144 217)(98 140 145 218)
(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)
(1 117 8 124)(2 116 9 123)(3 115 10 122)(4 114 11 121)(5 113 12 120)(6 126 13 119)(7 125 14 118)(15 55 22 48)(16 54 23 47)(17 53 24 46)(18 52 25 45)(19 51 26 44)(20 50 27 43)(21 49 28 56)(29 223 166 138)(30 222 167 137)(31 221 168 136)(32 220 155 135)(33 219 156 134)(34 218 157 133)(35 217 158 132)(36 216 159 131)(37 215 160 130)(38 214 161 129)(39 213 162 128)(40 212 163 127)(41 211 164 140)(42 224 165 139)(57 97 171 151)(58 96 172 150)(59 95 173 149)(60 94 174 148)(61 93 175 147)(62 92 176 146)(63 91 177 145)(64 90 178 144)(65 89 179 143)(66 88 180 142)(67 87 181 141)(68 86 182 154)(69 85 169 153)(70 98 170 152)(71 189 78 196)(72 188 79 195)(73 187 80 194)(74 186 81 193)(75 185 82 192)(76 184 83 191)(77 183 84 190)(99 206 106 199)(100 205 107 198)(101 204 108 197)(102 203 109 210)(103 202 110 209)(104 201 111 208)(105 200 112 207)
G:=sub<Sym(224)| (1,29,8,166)(2,160,9,37)(3,31,10,168)(4,162,11,39)(5,33,12,156)(6,164,13,41)(7,35,14,158)(15,223,22,138)(16,132,23,217)(17,211,24,140)(18,134,25,219)(19,213,26,128)(20,136,27,221)(21,215,28,130)(30,56,167,49)(32,44,155,51)(34,46,157,53)(36,48,159,55)(38,50,161,43)(40,52,163,45)(42,54,165,47)(57,106,171,99)(58,191,172,184)(59,108,173,101)(60,193,174,186)(61,110,175,103)(62,195,176,188)(63,112,177,105)(64,183,178,190)(65,100,179,107)(66,185,180,192)(67,102,181,109)(68,187,182,194)(69,104,169,111)(70,189,170,196)(71,145,78,91)(72,85,79,153)(73,147,80,93)(74,87,81,141)(75,149,82,95)(76,89,83,143)(77,151,84,97)(86,202,154,209)(88,204,142,197)(90,206,144,199)(92,208,146,201)(94,210,148,203)(96,198,150,205)(98,200,152,207)(113,127,120,212)(114,220,121,135)(115,129,122,214)(116,222,123,137)(117,131,124,216)(118,224,125,139)(119,133,126,218), (1,100,48,184)(2,101,49,185)(3,102,50,186)(4,103,51,187)(5,104,52,188)(6,105,53,189)(7,106,54,190)(8,107,55,191)(9,108,56,192)(10,109,43,193)(11,110,44,194)(12,111,45,195)(13,112,46,196)(14,99,47,183)(15,83,117,205)(16,84,118,206)(17,71,119,207)(18,72,120,208)(19,73,121,209)(20,74,122,210)(21,75,123,197)(22,76,124,198)(23,77,125,199)(24,78,126,200)(25,79,113,201)(26,80,114,202)(27,81,115,203)(28,82,116,204)(29,65,159,172)(30,66,160,173)(31,67,161,174)(32,68,162,175)(33,69,163,176)(34,70,164,177)(35,57,165,178)(36,58,166,179)(37,59,167,180)(38,60,168,181)(39,61,155,182)(40,62,156,169)(41,63,157,170)(42,64,158,171)(85,127,146,219)(86,128,147,220)(87,129,148,221)(88,130,149,222)(89,131,150,223)(90,132,151,224)(91,133,152,211)(92,134,153,212)(93,135,154,213)(94,136,141,214)(95,137,142,215)(96,138,143,216)(97,139,144,217)(98,140,145,218), (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), (1,117,8,124)(2,116,9,123)(3,115,10,122)(4,114,11,121)(5,113,12,120)(6,126,13,119)(7,125,14,118)(15,55,22,48)(16,54,23,47)(17,53,24,46)(18,52,25,45)(19,51,26,44)(20,50,27,43)(21,49,28,56)(29,223,166,138)(30,222,167,137)(31,221,168,136)(32,220,155,135)(33,219,156,134)(34,218,157,133)(35,217,158,132)(36,216,159,131)(37,215,160,130)(38,214,161,129)(39,213,162,128)(40,212,163,127)(41,211,164,140)(42,224,165,139)(57,97,171,151)(58,96,172,150)(59,95,173,149)(60,94,174,148)(61,93,175,147)(62,92,176,146)(63,91,177,145)(64,90,178,144)(65,89,179,143)(66,88,180,142)(67,87,181,141)(68,86,182,154)(69,85,169,153)(70,98,170,152)(71,189,78,196)(72,188,79,195)(73,187,80,194)(74,186,81,193)(75,185,82,192)(76,184,83,191)(77,183,84,190)(99,206,106,199)(100,205,107,198)(101,204,108,197)(102,203,109,210)(103,202,110,209)(104,201,111,208)(105,200,112,207)>;
G:=Group( (1,29,8,166)(2,160,9,37)(3,31,10,168)(4,162,11,39)(5,33,12,156)(6,164,13,41)(7,35,14,158)(15,223,22,138)(16,132,23,217)(17,211,24,140)(18,134,25,219)(19,213,26,128)(20,136,27,221)(21,215,28,130)(30,56,167,49)(32,44,155,51)(34,46,157,53)(36,48,159,55)(38,50,161,43)(40,52,163,45)(42,54,165,47)(57,106,171,99)(58,191,172,184)(59,108,173,101)(60,193,174,186)(61,110,175,103)(62,195,176,188)(63,112,177,105)(64,183,178,190)(65,100,179,107)(66,185,180,192)(67,102,181,109)(68,187,182,194)(69,104,169,111)(70,189,170,196)(71,145,78,91)(72,85,79,153)(73,147,80,93)(74,87,81,141)(75,149,82,95)(76,89,83,143)(77,151,84,97)(86,202,154,209)(88,204,142,197)(90,206,144,199)(92,208,146,201)(94,210,148,203)(96,198,150,205)(98,200,152,207)(113,127,120,212)(114,220,121,135)(115,129,122,214)(116,222,123,137)(117,131,124,216)(118,224,125,139)(119,133,126,218), (1,100,48,184)(2,101,49,185)(3,102,50,186)(4,103,51,187)(5,104,52,188)(6,105,53,189)(7,106,54,190)(8,107,55,191)(9,108,56,192)(10,109,43,193)(11,110,44,194)(12,111,45,195)(13,112,46,196)(14,99,47,183)(15,83,117,205)(16,84,118,206)(17,71,119,207)(18,72,120,208)(19,73,121,209)(20,74,122,210)(21,75,123,197)(22,76,124,198)(23,77,125,199)(24,78,126,200)(25,79,113,201)(26,80,114,202)(27,81,115,203)(28,82,116,204)(29,65,159,172)(30,66,160,173)(31,67,161,174)(32,68,162,175)(33,69,163,176)(34,70,164,177)(35,57,165,178)(36,58,166,179)(37,59,167,180)(38,60,168,181)(39,61,155,182)(40,62,156,169)(41,63,157,170)(42,64,158,171)(85,127,146,219)(86,128,147,220)(87,129,148,221)(88,130,149,222)(89,131,150,223)(90,132,151,224)(91,133,152,211)(92,134,153,212)(93,135,154,213)(94,136,141,214)(95,137,142,215)(96,138,143,216)(97,139,144,217)(98,140,145,218), (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), (1,117,8,124)(2,116,9,123)(3,115,10,122)(4,114,11,121)(5,113,12,120)(6,126,13,119)(7,125,14,118)(15,55,22,48)(16,54,23,47)(17,53,24,46)(18,52,25,45)(19,51,26,44)(20,50,27,43)(21,49,28,56)(29,223,166,138)(30,222,167,137)(31,221,168,136)(32,220,155,135)(33,219,156,134)(34,218,157,133)(35,217,158,132)(36,216,159,131)(37,215,160,130)(38,214,161,129)(39,213,162,128)(40,212,163,127)(41,211,164,140)(42,224,165,139)(57,97,171,151)(58,96,172,150)(59,95,173,149)(60,94,174,148)(61,93,175,147)(62,92,176,146)(63,91,177,145)(64,90,178,144)(65,89,179,143)(66,88,180,142)(67,87,181,141)(68,86,182,154)(69,85,169,153)(70,98,170,152)(71,189,78,196)(72,188,79,195)(73,187,80,194)(74,186,81,193)(75,185,82,192)(76,184,83,191)(77,183,84,190)(99,206,106,199)(100,205,107,198)(101,204,108,197)(102,203,109,210)(103,202,110,209)(104,201,111,208)(105,200,112,207) );
G=PermutationGroup([(1,29,8,166),(2,160,9,37),(3,31,10,168),(4,162,11,39),(5,33,12,156),(6,164,13,41),(7,35,14,158),(15,223,22,138),(16,132,23,217),(17,211,24,140),(18,134,25,219),(19,213,26,128),(20,136,27,221),(21,215,28,130),(30,56,167,49),(32,44,155,51),(34,46,157,53),(36,48,159,55),(38,50,161,43),(40,52,163,45),(42,54,165,47),(57,106,171,99),(58,191,172,184),(59,108,173,101),(60,193,174,186),(61,110,175,103),(62,195,176,188),(63,112,177,105),(64,183,178,190),(65,100,179,107),(66,185,180,192),(67,102,181,109),(68,187,182,194),(69,104,169,111),(70,189,170,196),(71,145,78,91),(72,85,79,153),(73,147,80,93),(74,87,81,141),(75,149,82,95),(76,89,83,143),(77,151,84,97),(86,202,154,209),(88,204,142,197),(90,206,144,199),(92,208,146,201),(94,210,148,203),(96,198,150,205),(98,200,152,207),(113,127,120,212),(114,220,121,135),(115,129,122,214),(116,222,123,137),(117,131,124,216),(118,224,125,139),(119,133,126,218)], [(1,100,48,184),(2,101,49,185),(3,102,50,186),(4,103,51,187),(5,104,52,188),(6,105,53,189),(7,106,54,190),(8,107,55,191),(9,108,56,192),(10,109,43,193),(11,110,44,194),(12,111,45,195),(13,112,46,196),(14,99,47,183),(15,83,117,205),(16,84,118,206),(17,71,119,207),(18,72,120,208),(19,73,121,209),(20,74,122,210),(21,75,123,197),(22,76,124,198),(23,77,125,199),(24,78,126,200),(25,79,113,201),(26,80,114,202),(27,81,115,203),(28,82,116,204),(29,65,159,172),(30,66,160,173),(31,67,161,174),(32,68,162,175),(33,69,163,176),(34,70,164,177),(35,57,165,178),(36,58,166,179),(37,59,167,180),(38,60,168,181),(39,61,155,182),(40,62,156,169),(41,63,157,170),(42,64,158,171),(85,127,146,219),(86,128,147,220),(87,129,148,221),(88,130,149,222),(89,131,150,223),(90,132,151,224),(91,133,152,211),(92,134,153,212),(93,135,154,213),(94,136,141,214),(95,137,142,215),(96,138,143,216),(97,139,144,217),(98,140,145,218)], [(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)], [(1,117,8,124),(2,116,9,123),(3,115,10,122),(4,114,11,121),(5,113,12,120),(6,126,13,119),(7,125,14,118),(15,55,22,48),(16,54,23,47),(17,53,24,46),(18,52,25,45),(19,51,26,44),(20,50,27,43),(21,49,28,56),(29,223,166,138),(30,222,167,137),(31,221,168,136),(32,220,155,135),(33,219,156,134),(34,218,157,133),(35,217,158,132),(36,216,159,131),(37,215,160,130),(38,214,161,129),(39,213,162,128),(40,212,163,127),(41,211,164,140),(42,224,165,139),(57,97,171,151),(58,96,172,150),(59,95,173,149),(60,94,174,148),(61,93,175,147),(62,92,176,146),(63,91,177,145),(64,90,178,144),(65,89,179,143),(66,88,180,142),(67,87,181,141),(68,86,182,154),(69,85,169,153),(70,98,170,152),(71,189,78,196),(72,188,79,195),(73,187,80,194),(74,186,81,193),(75,185,82,192),(76,184,83,191),(77,183,84,190),(99,206,106,199),(100,205,107,198),(101,204,108,197),(102,203,109,210),(103,202,110,209),(104,201,111,208),(105,200,112,207)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 17 | 21 | 0 | 0 | 0 | 0 |
| 7 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 1 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 27 | 12 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 26 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 25 | 0 | 0 |
| 0 | 0 | 4 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 24 | 1 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 3 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 28 | 0 | 0 |
| 0 | 0 | 4 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 27 | 12 |
G:=sub<GL(6,GF(29))| [17,7,0,0,0,0,21,12,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,12,0,0,0,0,0,1,17],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,17,27,0,0,0,0,0,12],[1,26,0,0,0,0,0,28,0,0,0,0,0,0,25,4,0,0,0,0,25,11,0,0,0,0,0,0,28,24,0,0,0,0,0,1],[28,3,0,0,0,0,0,1,0,0,0,0,0,0,18,4,0,0,0,0,28,11,0,0,0,0,0,0,17,27,0,0,0,0,0,12] >;
70 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | ··· | 4Q | 4R | 4S | 4T | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 14P | 14Q | 14R | 28A | ··· | 28L | 28M | ··· | 28U |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 7 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
70 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | D14 | D4⋊2D7 | D7×C4○D4 |
| kernel | C4⋊C4.197D14 | C23.11D14 | C22⋊Dic14 | C23.D14 | Dic7⋊4D4 | Dic7.D4 | Dic7⋊3Q8 | Dic7.Q8 | C4⋊C4⋊7D7 | C4⋊C4⋊D7 | C2×C4×Dic7 | C23.23D14 | D4×Dic7 | Dic7⋊D4 | C7×C22.D4 | C22.D4 | Dic7 | C2×C14 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C22 | C2 |
| # reps | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 8 | 4 | 9 | 6 | 3 | 3 | 6 | 12 |
In GAP, Magma, Sage, TeX
C_4\rtimes C_4._{197}D_{14} % in TeX
G:=Group("C4:C4.197D14"); // GroupNames label
G:=SmallGroup(448,1102);
// by ID
G=gap.SmallGroup(448,1102);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,100,346,297,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2,b*a*b^-1=a^-1,c*a*c^-1=d*a*d^-1=a*b^2,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations
×
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ℤ
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