direct product, metabelian, nilpotent (class 3), monomial, 2-elementary
Aliases: C14×C8.C22, C56.50C23, C28.83C24, Q16⋊3(C2×C14), C4.67(D4×C14), (C2×Q16)⋊11C14, (C14×Q16)⋊25C2, SD16⋊2(C2×C14), (C2×SD16)⋊5C14, (C2×C28).526D4, C28.330(C2×D4), C8.1(C22×C14), C4.6(C23×C14), (C22×Q8)⋊9C14, C23.51(C7×D4), (C14×SD16)⋊16C2, M4(2)⋊4(C2×C14), (C2×M4(2))⋊4C14, (C7×Q16)⋊17C22, (Q8×C14)⋊55C22, (C7×D4).36C23, D4.3(C22×C14), C22.24(D4×C14), (C7×Q8).37C23, Q8.3(C22×C14), (C14×M4(2))⋊14C2, (C2×C56).280C22, (C2×C28).976C23, (C7×SD16)⋊18C22, C14.204(C22×D4), (C22×C14).173D4, (D4×C14).329C22, (C7×M4(2))⋊30C22, (C22×C28).466C22, (Q8×C2×C14)⋊21C2, C2.28(D4×C2×C14), (C2×C8).32(C2×C14), (C2×Q8)⋊15(C2×C14), (C2×C4).137(C7×D4), (C14×C4○D4).26C2, (C2×C4○D4).12C14, C4○D4.13(C2×C14), (C2×D4).75(C2×C14), (C2×C14).420(C2×D4), (C22×C4).77(C2×C14), (C2×C4).46(C22×C14), (C7×C4○D4).58C22, SmallGroup(448,1357)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 370 in 258 conjugacy classes, 162 normal (30 characteristic)
C1, C2, C2 [×2], C2 [×4], C4 [×2], C4 [×2], C4 [×6], C22, C22 [×2], C22 [×6], C7, C8 [×4], C2×C4 [×2], C2×C4 [×4], C2×C4 [×11], D4 [×2], D4 [×5], Q8 [×6], Q8 [×7], C23, C23, C14, C14 [×2], C14 [×4], C2×C8 [×2], M4(2) [×4], SD16 [×8], Q16 [×8], C22×C4, C22×C4 [×2], C2×D4, C2×D4, C2×Q8, C2×Q8 [×6], C2×Q8 [×3], C4○D4 [×4], C4○D4 [×2], C28 [×2], C28 [×2], C28 [×6], C2×C14, C2×C14 [×2], C2×C14 [×6], C2×M4(2), C2×SD16 [×2], C2×Q16 [×2], C8.C22 [×8], C22×Q8, C2×C4○D4, C56 [×4], C2×C28 [×2], C2×C28 [×4], C2×C28 [×11], C7×D4 [×2], C7×D4 [×5], C7×Q8 [×6], C7×Q8 [×7], C22×C14, C22×C14, C2×C8.C22, C2×C56 [×2], C7×M4(2) [×4], C7×SD16 [×8], C7×Q16 [×8], C22×C28, C22×C28 [×2], D4×C14, D4×C14, Q8×C14, Q8×C14 [×6], Q8×C14 [×3], C7×C4○D4 [×4], C7×C4○D4 [×2], C14×M4(2), C14×SD16 [×2], C14×Q16 [×2], C7×C8.C22 [×8], Q8×C2×C14, C14×C4○D4, C14×C8.C22
Quotients:
C1, C2 [×15], C22 [×35], C7, D4 [×4], C23 [×15], C14 [×15], C2×D4 [×6], C24, C2×C14 [×35], C8.C22 [×2], C22×D4, C7×D4 [×4], C22×C14 [×15], C2×C8.C22, D4×C14 [×6], C23×C14, C7×C8.C22 [×2], D4×C2×C14, C14×C8.C22
Generators and relations
G = < a,b,c,d | a14=b8=c2=d2=1, ab=ba, ac=ca, ad=da, cbc=b3, dbd=b5, dcd=b4c >
►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)
(1 105 125 206 69 152 172 221)(2 106 126 207 70 153 173 222)(3 107 113 208 57 154 174 223)(4 108 114 209 58 141 175 224)(5 109 115 210 59 142 176 211)(6 110 116 197 60 143 177 212)(7 111 117 198 61 144 178 213)(8 112 118 199 62 145 179 214)(9 99 119 200 63 146 180 215)(10 100 120 201 64 147 181 216)(11 101 121 202 65 148 182 217)(12 102 122 203 66 149 169 218)(13 103 123 204 67 150 170 219)(14 104 124 205 68 151 171 220)(15 50 95 134 187 42 165 76)(16 51 96 135 188 29 166 77)(17 52 97 136 189 30 167 78)(18 53 98 137 190 31 168 79)(19 54 85 138 191 32 155 80)(20 55 86 139 192 33 156 81)(21 56 87 140 193 34 157 82)(22 43 88 127 194 35 158 83)(23 44 89 128 195 36 159 84)(24 45 90 129 196 37 160 71)(25 46 91 130 183 38 161 72)(26 47 92 131 184 39 162 73)(27 48 93 132 185 40 163 74)(28 49 94 133 186 41 164 75)
(1 27)(2 28)(3 15)(4 16)(5 17)(6 18)(7 19)(8 20)(9 21)(10 22)(11 23)(12 24)(13 25)(14 26)(29 224)(30 211)(31 212)(32 213)(33 214)(34 215)(35 216)(36 217)(37 218)(38 219)(39 220)(40 221)(41 222)(42 223)(43 201)(44 202)(45 203)(46 204)(47 205)(48 206)(49 207)(50 208)(51 209)(52 210)(53 197)(54 198)(55 199)(56 200)(57 187)(58 188)(59 189)(60 190)(61 191)(62 192)(63 193)(64 194)(65 195)(66 196)(67 183)(68 184)(69 185)(70 186)(71 149)(72 150)(73 151)(74 152)(75 153)(76 154)(77 141)(78 142)(79 143)(80 144)(81 145)(82 146)(83 147)(84 148)(85 178)(86 179)(87 180)(88 181)(89 182)(90 169)(91 170)(92 171)(93 172)(94 173)(95 174)(96 175)(97 176)(98 177)(99 140)(100 127)(101 128)(102 129)(103 130)(104 131)(105 132)(106 133)(107 134)(108 135)(109 136)(110 137)(111 138)(112 139)(113 165)(114 166)(115 167)(116 168)(117 155)(118 156)(119 157)(120 158)(121 159)(122 160)(123 161)(124 162)(125 163)(126 164)
(15 187)(16 188)(17 189)(18 190)(19 191)(20 192)(21 193)(22 194)(23 195)(24 196)(25 183)(26 184)(27 185)(28 186)(85 155)(86 156)(87 157)(88 158)(89 159)(90 160)(91 161)(92 162)(93 163)(94 164)(95 165)(96 166)(97 167)(98 168)(99 146)(100 147)(101 148)(102 149)(103 150)(104 151)(105 152)(106 153)(107 154)(108 141)(109 142)(110 143)(111 144)(112 145)(197 212)(198 213)(199 214)(200 215)(201 216)(202 217)(203 218)(204 219)(205 220)(206 221)(207 222)(208 223)(209 224)(210 211)
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), (1,105,125,206,69,152,172,221)(2,106,126,207,70,153,173,222)(3,107,113,208,57,154,174,223)(4,108,114,209,58,141,175,224)(5,109,115,210,59,142,176,211)(6,110,116,197,60,143,177,212)(7,111,117,198,61,144,178,213)(8,112,118,199,62,145,179,214)(9,99,119,200,63,146,180,215)(10,100,120,201,64,147,181,216)(11,101,121,202,65,148,182,217)(12,102,122,203,66,149,169,218)(13,103,123,204,67,150,170,219)(14,104,124,205,68,151,171,220)(15,50,95,134,187,42,165,76)(16,51,96,135,188,29,166,77)(17,52,97,136,189,30,167,78)(18,53,98,137,190,31,168,79)(19,54,85,138,191,32,155,80)(20,55,86,139,192,33,156,81)(21,56,87,140,193,34,157,82)(22,43,88,127,194,35,158,83)(23,44,89,128,195,36,159,84)(24,45,90,129,196,37,160,71)(25,46,91,130,183,38,161,72)(26,47,92,131,184,39,162,73)(27,48,93,132,185,40,163,74)(28,49,94,133,186,41,164,75), (1,27)(2,28)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(13,25)(14,26)(29,224)(30,211)(31,212)(32,213)(33,214)(34,215)(35,216)(36,217)(37,218)(38,219)(39,220)(40,221)(41,222)(42,223)(43,201)(44,202)(45,203)(46,204)(47,205)(48,206)(49,207)(50,208)(51,209)(52,210)(53,197)(54,198)(55,199)(56,200)(57,187)(58,188)(59,189)(60,190)(61,191)(62,192)(63,193)(64,194)(65,195)(66,196)(67,183)(68,184)(69,185)(70,186)(71,149)(72,150)(73,151)(74,152)(75,153)(76,154)(77,141)(78,142)(79,143)(80,144)(81,145)(82,146)(83,147)(84,148)(85,178)(86,179)(87,180)(88,181)(89,182)(90,169)(91,170)(92,171)(93,172)(94,173)(95,174)(96,175)(97,176)(98,177)(99,140)(100,127)(101,128)(102,129)(103,130)(104,131)(105,132)(106,133)(107,134)(108,135)(109,136)(110,137)(111,138)(112,139)(113,165)(114,166)(115,167)(116,168)(117,155)(118,156)(119,157)(120,158)(121,159)(122,160)(123,161)(124,162)(125,163)(126,164), (15,187)(16,188)(17,189)(18,190)(19,191)(20,192)(21,193)(22,194)(23,195)(24,196)(25,183)(26,184)(27,185)(28,186)(85,155)(86,156)(87,157)(88,158)(89,159)(90,160)(91,161)(92,162)(93,163)(94,164)(95,165)(96,166)(97,167)(98,168)(99,146)(100,147)(101,148)(102,149)(103,150)(104,151)(105,152)(106,153)(107,154)(108,141)(109,142)(110,143)(111,144)(112,145)(197,212)(198,213)(199,214)(200,215)(201,216)(202,217)(203,218)(204,219)(205,220)(206,221)(207,222)(208,223)(209,224)(210,211)>;
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), (1,105,125,206,69,152,172,221)(2,106,126,207,70,153,173,222)(3,107,113,208,57,154,174,223)(4,108,114,209,58,141,175,224)(5,109,115,210,59,142,176,211)(6,110,116,197,60,143,177,212)(7,111,117,198,61,144,178,213)(8,112,118,199,62,145,179,214)(9,99,119,200,63,146,180,215)(10,100,120,201,64,147,181,216)(11,101,121,202,65,148,182,217)(12,102,122,203,66,149,169,218)(13,103,123,204,67,150,170,219)(14,104,124,205,68,151,171,220)(15,50,95,134,187,42,165,76)(16,51,96,135,188,29,166,77)(17,52,97,136,189,30,167,78)(18,53,98,137,190,31,168,79)(19,54,85,138,191,32,155,80)(20,55,86,139,192,33,156,81)(21,56,87,140,193,34,157,82)(22,43,88,127,194,35,158,83)(23,44,89,128,195,36,159,84)(24,45,90,129,196,37,160,71)(25,46,91,130,183,38,161,72)(26,47,92,131,184,39,162,73)(27,48,93,132,185,40,163,74)(28,49,94,133,186,41,164,75), (1,27)(2,28)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(13,25)(14,26)(29,224)(30,211)(31,212)(32,213)(33,214)(34,215)(35,216)(36,217)(37,218)(38,219)(39,220)(40,221)(41,222)(42,223)(43,201)(44,202)(45,203)(46,204)(47,205)(48,206)(49,207)(50,208)(51,209)(52,210)(53,197)(54,198)(55,199)(56,200)(57,187)(58,188)(59,189)(60,190)(61,191)(62,192)(63,193)(64,194)(65,195)(66,196)(67,183)(68,184)(69,185)(70,186)(71,149)(72,150)(73,151)(74,152)(75,153)(76,154)(77,141)(78,142)(79,143)(80,144)(81,145)(82,146)(83,147)(84,148)(85,178)(86,179)(87,180)(88,181)(89,182)(90,169)(91,170)(92,171)(93,172)(94,173)(95,174)(96,175)(97,176)(98,177)(99,140)(100,127)(101,128)(102,129)(103,130)(104,131)(105,132)(106,133)(107,134)(108,135)(109,136)(110,137)(111,138)(112,139)(113,165)(114,166)(115,167)(116,168)(117,155)(118,156)(119,157)(120,158)(121,159)(122,160)(123,161)(124,162)(125,163)(126,164), (15,187)(16,188)(17,189)(18,190)(19,191)(20,192)(21,193)(22,194)(23,195)(24,196)(25,183)(26,184)(27,185)(28,186)(85,155)(86,156)(87,157)(88,158)(89,159)(90,160)(91,161)(92,162)(93,163)(94,164)(95,165)(96,166)(97,167)(98,168)(99,146)(100,147)(101,148)(102,149)(103,150)(104,151)(105,152)(106,153)(107,154)(108,141)(109,142)(110,143)(111,144)(112,145)(197,212)(198,213)(199,214)(200,215)(201,216)(202,217)(203,218)(204,219)(205,220)(206,221)(207,222)(208,223)(209,224)(210,211) );
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)], [(1,105,125,206,69,152,172,221),(2,106,126,207,70,153,173,222),(3,107,113,208,57,154,174,223),(4,108,114,209,58,141,175,224),(5,109,115,210,59,142,176,211),(6,110,116,197,60,143,177,212),(7,111,117,198,61,144,178,213),(8,112,118,199,62,145,179,214),(9,99,119,200,63,146,180,215),(10,100,120,201,64,147,181,216),(11,101,121,202,65,148,182,217),(12,102,122,203,66,149,169,218),(13,103,123,204,67,150,170,219),(14,104,124,205,68,151,171,220),(15,50,95,134,187,42,165,76),(16,51,96,135,188,29,166,77),(17,52,97,136,189,30,167,78),(18,53,98,137,190,31,168,79),(19,54,85,138,191,32,155,80),(20,55,86,139,192,33,156,81),(21,56,87,140,193,34,157,82),(22,43,88,127,194,35,158,83),(23,44,89,128,195,36,159,84),(24,45,90,129,196,37,160,71),(25,46,91,130,183,38,161,72),(26,47,92,131,184,39,162,73),(27,48,93,132,185,40,163,74),(28,49,94,133,186,41,164,75)], [(1,27),(2,28),(3,15),(4,16),(5,17),(6,18),(7,19),(8,20),(9,21),(10,22),(11,23),(12,24),(13,25),(14,26),(29,224),(30,211),(31,212),(32,213),(33,214),(34,215),(35,216),(36,217),(37,218),(38,219),(39,220),(40,221),(41,222),(42,223),(43,201),(44,202),(45,203),(46,204),(47,205),(48,206),(49,207),(50,208),(51,209),(52,210),(53,197),(54,198),(55,199),(56,200),(57,187),(58,188),(59,189),(60,190),(61,191),(62,192),(63,193),(64,194),(65,195),(66,196),(67,183),(68,184),(69,185),(70,186),(71,149),(72,150),(73,151),(74,152),(75,153),(76,154),(77,141),(78,142),(79,143),(80,144),(81,145),(82,146),(83,147),(84,148),(85,178),(86,179),(87,180),(88,181),(89,182),(90,169),(91,170),(92,171),(93,172),(94,173),(95,174),(96,175),(97,176),(98,177),(99,140),(100,127),(101,128),(102,129),(103,130),(104,131),(105,132),(106,133),(107,134),(108,135),(109,136),(110,137),(111,138),(112,139),(113,165),(114,166),(115,167),(116,168),(117,155),(118,156),(119,157),(120,158),(121,159),(122,160),(123,161),(124,162),(125,163),(126,164)], [(15,187),(16,188),(17,189),(18,190),(19,191),(20,192),(21,193),(22,194),(23,195),(24,196),(25,183),(26,184),(27,185),(28,186),(85,155),(86,156),(87,157),(88,158),(89,159),(90,160),(91,161),(92,162),(93,163),(94,164),(95,165),(96,166),(97,167),(98,168),(99,146),(100,147),(101,148),(102,149),(103,150),(104,151),(105,152),(106,153),(107,154),(108,141),(109,142),(110,143),(111,144),(112,145),(197,212),(198,213),(199,214),(200,215),(201,216),(202,217),(203,218),(204,219),(205,220),(206,221),(207,222),(208,223),(209,224),(210,211)])
Matrix representation ►G ⊆ GL6(𝔽113)
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 64 | 0 | 0 | 0 |
| 0 | 0 | 0 | 64 | 0 | 0 |
| 0 | 0 | 0 | 0 | 64 | 0 |
| 0 | 0 | 0 | 0 | 0 | 64 |
| 18 | 72 | 0 | 0 | 0 | 0 |
| 41 | 95 | 0 | 0 | 0 | 0 |
| 0 | 0 | 110 | 36 | 37 | 21 |
| 0 | 0 | 96 | 91 | 94 | 58 |
| 0 | 0 | 95 | 66 | 0 | 79 |
| 0 | 0 | 55 | 18 | 0 | 25 |
| 41 | 95 | 0 | 0 | 0 | 0 |
| 18 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 2 | 1 | 15 |
| 0 | 0 | 0 | 49 | 0 | 86 |
| 0 | 0 | 1 | 0 | 0 | 111 |
| 0 | 0 | 0 | 1 | 0 | 64 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 109 |
| 0 | 0 | 0 | 1 | 0 | 15 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
G:=sub<GL(6,GF(113))| [112,0,0,0,0,0,0,112,0,0,0,0,0,0,64,0,0,0,0,0,0,64,0,0,0,0,0,0,64,0,0,0,0,0,0,64],[18,41,0,0,0,0,72,95,0,0,0,0,0,0,110,96,95,55,0,0,36,91,66,18,0,0,37,94,0,0,0,0,21,58,79,25],[41,18,0,0,0,0,95,72,0,0,0,0,0,0,0,0,1,0,0,0,2,49,0,1,0,0,1,0,0,0,0,0,15,86,111,64],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,112,0,0,0,109,15,0,112] >;
154 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | ··· | 4J | 7A | ··· | 7F | 8A | 8B | 8C | 8D | 14A | ··· | 14R | 14S | ··· | 14AD | 14AE | ··· | 14AP | 28A | ··· | 28X | 28Y | ··· | 28BH | 56A | ··· | 56X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | ··· | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 1 | ··· | 1 | 4 | 4 | 4 | 4 | 1 | ··· | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
154 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | ||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C7 | C14 | C14 | C14 | C14 | C14 | C14 | D4 | D4 | C7×D4 | C7×D4 | C8.C22 | C7×C8.C22 |
| kernel | C14×C8.C22 | C14×M4(2) | C14×SD16 | C14×Q16 | C7×C8.C22 | Q8×C2×C14 | C14×C4○D4 | C2×C8.C22 | C2×M4(2) | C2×SD16 | C2×Q16 | C8.C22 | C22×Q8 | C2×C4○D4 | C2×C28 | C22×C14 | C2×C4 | C23 | C14 | C2 |
| # reps | 1 | 1 | 2 | 2 | 8 | 1 | 1 | 6 | 6 | 12 | 12 | 48 | 6 | 6 | 3 | 1 | 18 | 6 | 2 | 12 |
In GAP, Magma, Sage, TeX
C_{14}\times C_8.C_2^2 % in TeX
G:=Group("C14xC8.C2^2"); // GroupNames label
G:=SmallGroup(448,1357);
// by ID
G=gap.SmallGroup(448,1357);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,1597,1576,4790,14117,7068,124]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^8=c^2=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c=b^3,d*b*d=b^5,d*c*d=b^4*c>;
// generators/relations
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