metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.152D14, C14.962- (1+4), C42.C2⋊8D7, C4⋊C4.208D14, (C4×D28).25C2, D14⋊2Q8⋊38C2, (C4×Dic14)⋊48C2, (C2×C28).90C23, C4.Dic14⋊35C2, D14.25(C4○D4), C28.129(C4○D4), (C4×C28).197C22, (C2×C14).238C24, C4.38(Q8⋊2D7), D14.5D4.3C2, D14⋊C4.138C22, (C2×D28).225C22, C4⋊Dic7.243C22, C22.259(C23×D7), Dic7⋊C4.123C22, (C4×Dic7).144C22, (C2×Dic7).123C23, (C22×D7).103C23, C2.58(D4.10D14), C7⋊10(C22.46C24), (C2×Dic14).299C22, (D7×C4⋊C4)⋊38C2, C2.89(D7×C4○D4), C4⋊C4⋊D7⋊36C2, C4⋊C4⋊7D7⋊37C2, C14.200(C2×C4○D4), C2.23(C2×Q8⋊2D7), (C7×C42.C2)⋊11C2, (C2×C4×D7).128C22, (C2×C4).81(C22×D7), (C7×C4⋊C4).193C22, SmallGroup(448,1147)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 924 in 214 conjugacy classes, 97 normal (43 characteristic)
C1, C2 [×3], C2 [×3], C4 [×2], C4 [×12], C22, C22 [×7], C7, C2×C4 [×3], C2×C4 [×4], C2×C4 [×14], D4 [×2], Q8 [×2], C23 [×2], D7 [×3], C14 [×3], C42, C42 [×4], C22⋊C4 [×8], C4⋊C4 [×2], C4⋊C4 [×4], C4⋊C4 [×10], C22×C4 [×4], C2×D4, C2×Q8, Dic7 [×6], C28 [×2], C28 [×6], D14 [×2], D14 [×5], C2×C14, C2×C4⋊C4, C42⋊C2 [×3], C4×D4, C4×Q8, C22⋊Q8 [×2], C22.D4 [×2], C42.C2, C42.C2 [×2], C42⋊2C2 [×2], Dic14 [×2], C4×D7 [×8], D28 [×2], C2×Dic7 [×2], C2×Dic7 [×4], C2×C28 [×3], C2×C28 [×4], C22×D7 [×2], C22.46C24, C4×Dic7 [×4], Dic7⋊C4 [×4], C4⋊Dic7 [×2], C4⋊Dic7 [×4], D14⋊C4 [×2], D14⋊C4 [×6], C4×C28, C7×C4⋊C4 [×2], C7×C4⋊C4 [×4], C2×Dic14, C2×C4×D7 [×2], C2×C4×D7 [×2], C2×D28, C4×Dic14, C4×D28, C4.Dic14 [×2], D7×C4⋊C4, C4⋊C4⋊7D7, C4⋊C4⋊7D7 [×2], D14.5D4 [×2], D14⋊2Q8 [×2], C4⋊C4⋊D7 [×2], C7×C42.C2, C42.152D14
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], C22.46C24, Q8⋊2D7 [×2], C23×D7, C2×Q8⋊2D7, D7×C4○D4, D4.10D14, C42.152D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=d2=b2, ab=ba, cac-1=dad-1=a-1, cbc-1=a2b-1, dbd-1=a2b, dcd-1=c13 >
►On 224 points
Generators in S224
(1 116 44 217)(2 218 45 117)(3 118 46 219)(4 220 47 119)(5 120 48 221)(6 222 49 121)(7 122 50 223)(8 224 51 123)(9 124 52 197)(10 198 53 125)(11 126 54 199)(12 200 55 127)(13 128 56 201)(14 202 29 129)(15 130 30 203)(16 204 31 131)(17 132 32 205)(18 206 33 133)(19 134 34 207)(20 208 35 135)(21 136 36 209)(22 210 37 137)(23 138 38 211)(24 212 39 139)(25 140 40 213)(26 214 41 113)(27 114 42 215)(28 216 43 115)(57 179 165 97)(58 98 166 180)(59 181 167 99)(60 100 168 182)(61 183 141 101)(62 102 142 184)(63 185 143 103)(64 104 144 186)(65 187 145 105)(66 106 146 188)(67 189 147 107)(68 108 148 190)(69 191 149 109)(70 110 150 192)(71 193 151 111)(72 112 152 194)(73 195 153 85)(74 86 154 196)(75 169 155 87)(76 88 156 170)(77 171 157 89)(78 90 158 172)(79 173 159 91)(80 92 160 174)(81 175 161 93)(82 94 162 176)(83 177 163 95)(84 96 164 178)
(1 152 15 166)(2 59 16 73)(3 154 17 168)(4 61 18 75)(5 156 19 142)(6 63 20 77)(7 158 21 144)(8 65 22 79)(9 160 23 146)(10 67 24 81)(11 162 25 148)(12 69 26 83)(13 164 27 150)(14 71 28 57)(29 151 43 165)(30 58 44 72)(31 153 45 167)(32 60 46 74)(33 155 47 141)(34 62 48 76)(35 157 49 143)(36 64 50 78)(37 159 51 145)(38 66 52 80)(39 161 53 147)(40 68 54 82)(41 163 55 149)(42 70 56 84)(85 117 99 131)(86 205 100 219)(87 119 101 133)(88 207 102 221)(89 121 103 135)(90 209 104 223)(91 123 105 137)(92 211 106 197)(93 125 107 139)(94 213 108 199)(95 127 109 113)(96 215 110 201)(97 129 111 115)(98 217 112 203)(114 192 128 178)(116 194 130 180)(118 196 132 182)(120 170 134 184)(122 172 136 186)(124 174 138 188)(126 176 140 190)(169 220 183 206)(171 222 185 208)(173 224 187 210)(175 198 189 212)(177 200 191 214)(179 202 193 216)(181 204 195 218)
(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 14 15 28)(2 27 16 13)(3 12 17 26)(4 25 18 11)(5 10 19 24)(6 23 20 9)(7 8 21 22)(29 30 43 44)(31 56 45 42)(32 41 46 55)(33 54 47 40)(34 39 48 53)(35 52 49 38)(36 37 50 51)(57 72 71 58)(59 70 73 84)(60 83 74 69)(61 68 75 82)(62 81 76 67)(63 66 77 80)(64 79 78 65)(85 96 99 110)(86 109 100 95)(87 94 101 108)(88 107 102 93)(89 92 103 106)(90 105 104 91)(97 112 111 98)(113 118 127 132)(114 131 128 117)(115 116 129 130)(119 140 133 126)(120 125 134 139)(121 138 135 124)(122 123 136 137)(141 148 155 162)(142 161 156 147)(143 146 157 160)(144 159 158 145)(149 168 163 154)(150 153 164 167)(151 166 165 152)(169 176 183 190)(170 189 184 175)(171 174 185 188)(172 187 186 173)(177 196 191 182)(178 181 192 195)(179 194 193 180)(197 222 211 208)(198 207 212 221)(199 220 213 206)(200 205 214 219)(201 218 215 204)(202 203 216 217)(209 210 223 224)
G:=sub<Sym(224)| (1,116,44,217)(2,218,45,117)(3,118,46,219)(4,220,47,119)(5,120,48,221)(6,222,49,121)(7,122,50,223)(8,224,51,123)(9,124,52,197)(10,198,53,125)(11,126,54,199)(12,200,55,127)(13,128,56,201)(14,202,29,129)(15,130,30,203)(16,204,31,131)(17,132,32,205)(18,206,33,133)(19,134,34,207)(20,208,35,135)(21,136,36,209)(22,210,37,137)(23,138,38,211)(24,212,39,139)(25,140,40,213)(26,214,41,113)(27,114,42,215)(28,216,43,115)(57,179,165,97)(58,98,166,180)(59,181,167,99)(60,100,168,182)(61,183,141,101)(62,102,142,184)(63,185,143,103)(64,104,144,186)(65,187,145,105)(66,106,146,188)(67,189,147,107)(68,108,148,190)(69,191,149,109)(70,110,150,192)(71,193,151,111)(72,112,152,194)(73,195,153,85)(74,86,154,196)(75,169,155,87)(76,88,156,170)(77,171,157,89)(78,90,158,172)(79,173,159,91)(80,92,160,174)(81,175,161,93)(82,94,162,176)(83,177,163,95)(84,96,164,178), (1,152,15,166)(2,59,16,73)(3,154,17,168)(4,61,18,75)(5,156,19,142)(6,63,20,77)(7,158,21,144)(8,65,22,79)(9,160,23,146)(10,67,24,81)(11,162,25,148)(12,69,26,83)(13,164,27,150)(14,71,28,57)(29,151,43,165)(30,58,44,72)(31,153,45,167)(32,60,46,74)(33,155,47,141)(34,62,48,76)(35,157,49,143)(36,64,50,78)(37,159,51,145)(38,66,52,80)(39,161,53,147)(40,68,54,82)(41,163,55,149)(42,70,56,84)(85,117,99,131)(86,205,100,219)(87,119,101,133)(88,207,102,221)(89,121,103,135)(90,209,104,223)(91,123,105,137)(92,211,106,197)(93,125,107,139)(94,213,108,199)(95,127,109,113)(96,215,110,201)(97,129,111,115)(98,217,112,203)(114,192,128,178)(116,194,130,180)(118,196,132,182)(120,170,134,184)(122,172,136,186)(124,174,138,188)(126,176,140,190)(169,220,183,206)(171,222,185,208)(173,224,187,210)(175,198,189,212)(177,200,191,214)(179,202,193,216)(181,204,195,218), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,30,43,44)(31,56,45,42)(32,41,46,55)(33,54,47,40)(34,39,48,53)(35,52,49,38)(36,37,50,51)(57,72,71,58)(59,70,73,84)(60,83,74,69)(61,68,75,82)(62,81,76,67)(63,66,77,80)(64,79,78,65)(85,96,99,110)(86,109,100,95)(87,94,101,108)(88,107,102,93)(89,92,103,106)(90,105,104,91)(97,112,111,98)(113,118,127,132)(114,131,128,117)(115,116,129,130)(119,140,133,126)(120,125,134,139)(121,138,135,124)(122,123,136,137)(141,148,155,162)(142,161,156,147)(143,146,157,160)(144,159,158,145)(149,168,163,154)(150,153,164,167)(151,166,165,152)(169,176,183,190)(170,189,184,175)(171,174,185,188)(172,187,186,173)(177,196,191,182)(178,181,192,195)(179,194,193,180)(197,222,211,208)(198,207,212,221)(199,220,213,206)(200,205,214,219)(201,218,215,204)(202,203,216,217)(209,210,223,224)>;
G:=Group( (1,116,44,217)(2,218,45,117)(3,118,46,219)(4,220,47,119)(5,120,48,221)(6,222,49,121)(7,122,50,223)(8,224,51,123)(9,124,52,197)(10,198,53,125)(11,126,54,199)(12,200,55,127)(13,128,56,201)(14,202,29,129)(15,130,30,203)(16,204,31,131)(17,132,32,205)(18,206,33,133)(19,134,34,207)(20,208,35,135)(21,136,36,209)(22,210,37,137)(23,138,38,211)(24,212,39,139)(25,140,40,213)(26,214,41,113)(27,114,42,215)(28,216,43,115)(57,179,165,97)(58,98,166,180)(59,181,167,99)(60,100,168,182)(61,183,141,101)(62,102,142,184)(63,185,143,103)(64,104,144,186)(65,187,145,105)(66,106,146,188)(67,189,147,107)(68,108,148,190)(69,191,149,109)(70,110,150,192)(71,193,151,111)(72,112,152,194)(73,195,153,85)(74,86,154,196)(75,169,155,87)(76,88,156,170)(77,171,157,89)(78,90,158,172)(79,173,159,91)(80,92,160,174)(81,175,161,93)(82,94,162,176)(83,177,163,95)(84,96,164,178), (1,152,15,166)(2,59,16,73)(3,154,17,168)(4,61,18,75)(5,156,19,142)(6,63,20,77)(7,158,21,144)(8,65,22,79)(9,160,23,146)(10,67,24,81)(11,162,25,148)(12,69,26,83)(13,164,27,150)(14,71,28,57)(29,151,43,165)(30,58,44,72)(31,153,45,167)(32,60,46,74)(33,155,47,141)(34,62,48,76)(35,157,49,143)(36,64,50,78)(37,159,51,145)(38,66,52,80)(39,161,53,147)(40,68,54,82)(41,163,55,149)(42,70,56,84)(85,117,99,131)(86,205,100,219)(87,119,101,133)(88,207,102,221)(89,121,103,135)(90,209,104,223)(91,123,105,137)(92,211,106,197)(93,125,107,139)(94,213,108,199)(95,127,109,113)(96,215,110,201)(97,129,111,115)(98,217,112,203)(114,192,128,178)(116,194,130,180)(118,196,132,182)(120,170,134,184)(122,172,136,186)(124,174,138,188)(126,176,140,190)(169,220,183,206)(171,222,185,208)(173,224,187,210)(175,198,189,212)(177,200,191,214)(179,202,193,216)(181,204,195,218), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,30,43,44)(31,56,45,42)(32,41,46,55)(33,54,47,40)(34,39,48,53)(35,52,49,38)(36,37,50,51)(57,72,71,58)(59,70,73,84)(60,83,74,69)(61,68,75,82)(62,81,76,67)(63,66,77,80)(64,79,78,65)(85,96,99,110)(86,109,100,95)(87,94,101,108)(88,107,102,93)(89,92,103,106)(90,105,104,91)(97,112,111,98)(113,118,127,132)(114,131,128,117)(115,116,129,130)(119,140,133,126)(120,125,134,139)(121,138,135,124)(122,123,136,137)(141,148,155,162)(142,161,156,147)(143,146,157,160)(144,159,158,145)(149,168,163,154)(150,153,164,167)(151,166,165,152)(169,176,183,190)(170,189,184,175)(171,174,185,188)(172,187,186,173)(177,196,191,182)(178,181,192,195)(179,194,193,180)(197,222,211,208)(198,207,212,221)(199,220,213,206)(200,205,214,219)(201,218,215,204)(202,203,216,217)(209,210,223,224) );
G=PermutationGroup([(1,116,44,217),(2,218,45,117),(3,118,46,219),(4,220,47,119),(5,120,48,221),(6,222,49,121),(7,122,50,223),(8,224,51,123),(9,124,52,197),(10,198,53,125),(11,126,54,199),(12,200,55,127),(13,128,56,201),(14,202,29,129),(15,130,30,203),(16,204,31,131),(17,132,32,205),(18,206,33,133),(19,134,34,207),(20,208,35,135),(21,136,36,209),(22,210,37,137),(23,138,38,211),(24,212,39,139),(25,140,40,213),(26,214,41,113),(27,114,42,215),(28,216,43,115),(57,179,165,97),(58,98,166,180),(59,181,167,99),(60,100,168,182),(61,183,141,101),(62,102,142,184),(63,185,143,103),(64,104,144,186),(65,187,145,105),(66,106,146,188),(67,189,147,107),(68,108,148,190),(69,191,149,109),(70,110,150,192),(71,193,151,111),(72,112,152,194),(73,195,153,85),(74,86,154,196),(75,169,155,87),(76,88,156,170),(77,171,157,89),(78,90,158,172),(79,173,159,91),(80,92,160,174),(81,175,161,93),(82,94,162,176),(83,177,163,95),(84,96,164,178)], [(1,152,15,166),(2,59,16,73),(3,154,17,168),(4,61,18,75),(5,156,19,142),(6,63,20,77),(7,158,21,144),(8,65,22,79),(9,160,23,146),(10,67,24,81),(11,162,25,148),(12,69,26,83),(13,164,27,150),(14,71,28,57),(29,151,43,165),(30,58,44,72),(31,153,45,167),(32,60,46,74),(33,155,47,141),(34,62,48,76),(35,157,49,143),(36,64,50,78),(37,159,51,145),(38,66,52,80),(39,161,53,147),(40,68,54,82),(41,163,55,149),(42,70,56,84),(85,117,99,131),(86,205,100,219),(87,119,101,133),(88,207,102,221),(89,121,103,135),(90,209,104,223),(91,123,105,137),(92,211,106,197),(93,125,107,139),(94,213,108,199),(95,127,109,113),(96,215,110,201),(97,129,111,115),(98,217,112,203),(114,192,128,178),(116,194,130,180),(118,196,132,182),(120,170,134,184),(122,172,136,186),(124,174,138,188),(126,176,140,190),(169,220,183,206),(171,222,185,208),(173,224,187,210),(175,198,189,212),(177,200,191,214),(179,202,193,216),(181,204,195,218)], [(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)], [(1,14,15,28),(2,27,16,13),(3,12,17,26),(4,25,18,11),(5,10,19,24),(6,23,20,9),(7,8,21,22),(29,30,43,44),(31,56,45,42),(32,41,46,55),(33,54,47,40),(34,39,48,53),(35,52,49,38),(36,37,50,51),(57,72,71,58),(59,70,73,84),(60,83,74,69),(61,68,75,82),(62,81,76,67),(63,66,77,80),(64,79,78,65),(85,96,99,110),(86,109,100,95),(87,94,101,108),(88,107,102,93),(89,92,103,106),(90,105,104,91),(97,112,111,98),(113,118,127,132),(114,131,128,117),(115,116,129,130),(119,140,133,126),(120,125,134,139),(121,138,135,124),(122,123,136,137),(141,148,155,162),(142,161,156,147),(143,146,157,160),(144,159,158,145),(149,168,163,154),(150,153,164,167),(151,166,165,152),(169,176,183,190),(170,189,184,175),(171,174,185,188),(172,187,186,173),(177,196,191,182),(178,181,192,195),(179,194,193,180),(197,222,211,208),(198,207,212,221),(199,220,213,206),(200,205,214,219),(201,218,215,204),(202,203,216,217),(209,210,223,224)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 12 | 28 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 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 | 1 |
| 28 | 17 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 12 | 28 | 0 | 0 | 0 | 0 |
| 27 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 10 | 0 | 0 |
| 0 | 0 | 19 | 22 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 12 | 28 | 0 | 0 | 0 | 0 |
| 27 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 10 | 0 | 0 |
| 0 | 0 | 22 | 19 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,28,17,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[28,0,0,0,0,0,17,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,0,28,0,0,0,0,1,0],[12,27,0,0,0,0,28,17,0,0,0,0,0,0,10,19,0,0,0,0,10,22,0,0,0,0,0,0,12,0,0,0,0,0,0,17],[12,27,0,0,0,0,28,17,0,0,0,0,0,0,10,22,0,0,0,0,10,19,0,0,0,0,0,0,12,0,0,0,0,0,0,12] >;
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | ··· | 4I | 4J | ··· | 4O | 4P | 4Q | 4R | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 28 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | 2- (1+4) | Q8⋊2D7 | D7×C4○D4 | D4.10D14 |
| kernel | C42.152D14 | C4×Dic14 | C4×D28 | C4.Dic14 | D7×C4⋊C4 | C4⋊C4⋊7D7 | D14.5D4 | D14⋊2Q8 | C4⋊C4⋊D7 | C7×C42.C2 | C42.C2 | C28 | D14 | C42 | C4⋊C4 | C14 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 1 | 3 | 2 | 2 | 2 | 1 | 3 | 4 | 4 | 3 | 18 | 1 | 6 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{152}D_{14} % in TeX
G:=Group("C4^2.152D14"); // GroupNames label
G:=SmallGroup(448,1147);
// by ID
G=gap.SmallGroup(448,1147);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,268,1571,297,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=a^2*b^-1,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations
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