direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C14×C4.4D4, (C2×C42)⋊9C14, C4.13(D4×C14), (C4×C28)⋊58C22, C42⋊17(C2×C14), C28.320(C2×D4), (C2×C28).430D4, (C22×Q8)⋊4C14, C24.16(C2×C14), (Q8×C14)⋊50C22, C22.62(D4×C14), (C2×C14).346C24, (C2×C28).659C23, (C22×D4).11C14, C14.185(C22×D4), C23.6(C22×C14), (D4×C14).317C22, C22.20(C23×C14), (C23×C14).13C22, (C22×C14).85C23, (C22×C28).508C22, (C2×C4×C28)⋊22C2, C2.9(D4×C2×C14), (Q8×C2×C14)⋊16C2, (D4×C2×C14).24C2, C2.9(C14×C4○D4), (C2×C4).86(C7×D4), (C2×Q8)⋊10(C2×C14), (C2×C22⋊C4)⋊11C14, (C14×C22⋊C4)⋊31C2, C22⋊C4⋊14(C2×C14), (C2×D4).62(C2×C14), C14.228(C2×C4○D4), (C2×C14).683(C2×D4), C22.32(C7×C4○D4), (C7×C22⋊C4)⋊68C22, (C2×C4).58(C22×C14), (C2×C14).232(C4○D4), (C22×C4).100(C2×C14), SmallGroup(448,1309)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 530 in 330 conjugacy classes, 178 normal (18 characteristic)
C1, C2, C2 [×6], C2 [×4], C4 [×4], C4 [×8], C22, C22 [×6], C22 [×20], C7, C2×C4 [×14], C2×C4 [×8], D4 [×8], Q8 [×8], C23, C23 [×4], C23 [×12], C14, C14 [×6], C14 [×4], C42 [×4], C22⋊C4 [×16], C22×C4, C22×C4 [×4], C2×D4 [×4], C2×D4 [×4], C2×Q8 [×4], C2×Q8 [×4], C24 [×2], C28 [×4], C28 [×8], C2×C14, C2×C14 [×6], C2×C14 [×20], C2×C42, C2×C22⋊C4 [×4], C4.4D4 [×8], C22×D4, C22×Q8, C2×C28 [×14], C2×C28 [×8], C7×D4 [×8], C7×Q8 [×8], C22×C14, C22×C14 [×4], C22×C14 [×12], C2×C4.4D4, C4×C28 [×4], C7×C22⋊C4 [×16], C22×C28, C22×C28 [×4], D4×C14 [×4], D4×C14 [×4], Q8×C14 [×4], Q8×C14 [×4], C23×C14 [×2], C2×C4×C28, C14×C22⋊C4 [×4], C7×C4.4D4 [×8], D4×C2×C14, Q8×C2×C14, C14×C4.4D4
Quotients:
C1, C2 [×15], C22 [×35], C7, D4 [×4], C23 [×15], C14 [×15], C2×D4 [×6], C4○D4 [×4], C24, C2×C14 [×35], C4.4D4 [×4], C22×D4, C2×C4○D4 [×2], C7×D4 [×4], C22×C14 [×15], C2×C4.4D4, D4×C14 [×6], C7×C4○D4 [×4], C23×C14, C7×C4.4D4 [×4], D4×C2×C14, C14×C4○D4 [×2], C14×C4.4D4
Generators and relations
G = < a,b,c,d | a14=b4=c4=1, d2=b2, ab=ba, ac=ca, ad=da, bc=cb, dbd-1=b-1, dcd-1=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 99 187 45)(2 100 188 46)(3 101 189 47)(4 102 190 48)(5 103 191 49)(6 104 192 50)(7 105 193 51)(8 106 194 52)(9 107 195 53)(10 108 196 54)(11 109 183 55)(12 110 184 56)(13 111 185 43)(14 112 186 44)(15 162 152 178)(16 163 153 179)(17 164 154 180)(18 165 141 181)(19 166 142 182)(20 167 143 169)(21 168 144 170)(22 155 145 171)(23 156 146 172)(24 157 147 173)(25 158 148 174)(26 159 149 175)(27 160 150 176)(28 161 151 177)(29 206 97 116)(30 207 98 117)(31 208 85 118)(32 209 86 119)(33 210 87 120)(34 197 88 121)(35 198 89 122)(36 199 90 123)(37 200 91 124)(38 201 92 125)(39 202 93 126)(40 203 94 113)(41 204 95 114)(42 205 96 115)(57 140 72 221)(58 127 73 222)(59 128 74 223)(60 129 75 224)(61 130 76 211)(62 131 77 212)(63 132 78 213)(64 133 79 214)(65 134 80 215)(66 135 81 216)(67 136 82 217)(68 137 83 218)(69 138 84 219)(70 139 71 220)
(1 197 73 181)(2 198 74 182)(3 199 75 169)(4 200 76 170)(5 201 77 171)(6 202 78 172)(7 203 79 173)(8 204 80 174)(9 205 81 175)(10 206 82 176)(11 207 83 177)(12 208 84 178)(13 209 71 179)(14 210 72 180)(15 110 85 219)(16 111 86 220)(17 112 87 221)(18 99 88 222)(19 100 89 223)(20 101 90 224)(21 102 91 211)(22 103 92 212)(23 104 93 213)(24 105 94 214)(25 106 95 215)(26 107 96 216)(27 108 97 217)(28 109 98 218)(29 136 150 54)(30 137 151 55)(31 138 152 56)(32 139 153 43)(33 140 154 44)(34 127 141 45)(35 128 142 46)(36 129 143 47)(37 130 144 48)(38 131 145 49)(39 132 146 50)(40 133 147 51)(41 134 148 52)(42 135 149 53)(57 164 186 120)(58 165 187 121)(59 166 188 122)(60 167 189 123)(61 168 190 124)(62 155 191 125)(63 156 192 126)(64 157 193 113)(65 158 194 114)(66 159 195 115)(67 160 196 116)(68 161 183 117)(69 162 184 118)(70 163 185 119)
(1 148 187 25)(2 149 188 26)(3 150 189 27)(4 151 190 28)(5 152 191 15)(6 153 192 16)(7 154 193 17)(8 141 194 18)(9 142 195 19)(10 143 196 20)(11 144 183 21)(12 145 184 22)(13 146 185 23)(14 147 186 24)(29 60 97 75)(30 61 98 76)(31 62 85 77)(32 63 86 78)(33 64 87 79)(34 65 88 80)(35 66 89 81)(36 67 90 82)(37 68 91 83)(38 69 92 84)(39 70 93 71)(40 57 94 72)(41 58 95 73)(42 59 96 74)(43 172 111 156)(44 173 112 157)(45 174 99 158)(46 175 100 159)(47 176 101 160)(48 177 102 161)(49 178 103 162)(50 179 104 163)(51 180 105 164)(52 181 106 165)(53 182 107 166)(54 169 108 167)(55 170 109 168)(56 171 110 155)(113 140 203 221)(114 127 204 222)(115 128 205 223)(116 129 206 224)(117 130 207 211)(118 131 208 212)(119 132 209 213)(120 133 210 214)(121 134 197 215)(122 135 198 216)(123 136 199 217)(124 137 200 218)(125 138 201 219)(126 139 202 220)
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), (1,99,187,45)(2,100,188,46)(3,101,189,47)(4,102,190,48)(5,103,191,49)(6,104,192,50)(7,105,193,51)(8,106,194,52)(9,107,195,53)(10,108,196,54)(11,109,183,55)(12,110,184,56)(13,111,185,43)(14,112,186,44)(15,162,152,178)(16,163,153,179)(17,164,154,180)(18,165,141,181)(19,166,142,182)(20,167,143,169)(21,168,144,170)(22,155,145,171)(23,156,146,172)(24,157,147,173)(25,158,148,174)(26,159,149,175)(27,160,150,176)(28,161,151,177)(29,206,97,116)(30,207,98,117)(31,208,85,118)(32,209,86,119)(33,210,87,120)(34,197,88,121)(35,198,89,122)(36,199,90,123)(37,200,91,124)(38,201,92,125)(39,202,93,126)(40,203,94,113)(41,204,95,114)(42,205,96,115)(57,140,72,221)(58,127,73,222)(59,128,74,223)(60,129,75,224)(61,130,76,211)(62,131,77,212)(63,132,78,213)(64,133,79,214)(65,134,80,215)(66,135,81,216)(67,136,82,217)(68,137,83,218)(69,138,84,219)(70,139,71,220), (1,197,73,181)(2,198,74,182)(3,199,75,169)(4,200,76,170)(5,201,77,171)(6,202,78,172)(7,203,79,173)(8,204,80,174)(9,205,81,175)(10,206,82,176)(11,207,83,177)(12,208,84,178)(13,209,71,179)(14,210,72,180)(15,110,85,219)(16,111,86,220)(17,112,87,221)(18,99,88,222)(19,100,89,223)(20,101,90,224)(21,102,91,211)(22,103,92,212)(23,104,93,213)(24,105,94,214)(25,106,95,215)(26,107,96,216)(27,108,97,217)(28,109,98,218)(29,136,150,54)(30,137,151,55)(31,138,152,56)(32,139,153,43)(33,140,154,44)(34,127,141,45)(35,128,142,46)(36,129,143,47)(37,130,144,48)(38,131,145,49)(39,132,146,50)(40,133,147,51)(41,134,148,52)(42,135,149,53)(57,164,186,120)(58,165,187,121)(59,166,188,122)(60,167,189,123)(61,168,190,124)(62,155,191,125)(63,156,192,126)(64,157,193,113)(65,158,194,114)(66,159,195,115)(67,160,196,116)(68,161,183,117)(69,162,184,118)(70,163,185,119), (1,148,187,25)(2,149,188,26)(3,150,189,27)(4,151,190,28)(5,152,191,15)(6,153,192,16)(7,154,193,17)(8,141,194,18)(9,142,195,19)(10,143,196,20)(11,144,183,21)(12,145,184,22)(13,146,185,23)(14,147,186,24)(29,60,97,75)(30,61,98,76)(31,62,85,77)(32,63,86,78)(33,64,87,79)(34,65,88,80)(35,66,89,81)(36,67,90,82)(37,68,91,83)(38,69,92,84)(39,70,93,71)(40,57,94,72)(41,58,95,73)(42,59,96,74)(43,172,111,156)(44,173,112,157)(45,174,99,158)(46,175,100,159)(47,176,101,160)(48,177,102,161)(49,178,103,162)(50,179,104,163)(51,180,105,164)(52,181,106,165)(53,182,107,166)(54,169,108,167)(55,170,109,168)(56,171,110,155)(113,140,203,221)(114,127,204,222)(115,128,205,223)(116,129,206,224)(117,130,207,211)(118,131,208,212)(119,132,209,213)(120,133,210,214)(121,134,197,215)(122,135,198,216)(123,136,199,217)(124,137,200,218)(125,138,201,219)(126,139,202,220)>;
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), (1,99,187,45)(2,100,188,46)(3,101,189,47)(4,102,190,48)(5,103,191,49)(6,104,192,50)(7,105,193,51)(8,106,194,52)(9,107,195,53)(10,108,196,54)(11,109,183,55)(12,110,184,56)(13,111,185,43)(14,112,186,44)(15,162,152,178)(16,163,153,179)(17,164,154,180)(18,165,141,181)(19,166,142,182)(20,167,143,169)(21,168,144,170)(22,155,145,171)(23,156,146,172)(24,157,147,173)(25,158,148,174)(26,159,149,175)(27,160,150,176)(28,161,151,177)(29,206,97,116)(30,207,98,117)(31,208,85,118)(32,209,86,119)(33,210,87,120)(34,197,88,121)(35,198,89,122)(36,199,90,123)(37,200,91,124)(38,201,92,125)(39,202,93,126)(40,203,94,113)(41,204,95,114)(42,205,96,115)(57,140,72,221)(58,127,73,222)(59,128,74,223)(60,129,75,224)(61,130,76,211)(62,131,77,212)(63,132,78,213)(64,133,79,214)(65,134,80,215)(66,135,81,216)(67,136,82,217)(68,137,83,218)(69,138,84,219)(70,139,71,220), (1,197,73,181)(2,198,74,182)(3,199,75,169)(4,200,76,170)(5,201,77,171)(6,202,78,172)(7,203,79,173)(8,204,80,174)(9,205,81,175)(10,206,82,176)(11,207,83,177)(12,208,84,178)(13,209,71,179)(14,210,72,180)(15,110,85,219)(16,111,86,220)(17,112,87,221)(18,99,88,222)(19,100,89,223)(20,101,90,224)(21,102,91,211)(22,103,92,212)(23,104,93,213)(24,105,94,214)(25,106,95,215)(26,107,96,216)(27,108,97,217)(28,109,98,218)(29,136,150,54)(30,137,151,55)(31,138,152,56)(32,139,153,43)(33,140,154,44)(34,127,141,45)(35,128,142,46)(36,129,143,47)(37,130,144,48)(38,131,145,49)(39,132,146,50)(40,133,147,51)(41,134,148,52)(42,135,149,53)(57,164,186,120)(58,165,187,121)(59,166,188,122)(60,167,189,123)(61,168,190,124)(62,155,191,125)(63,156,192,126)(64,157,193,113)(65,158,194,114)(66,159,195,115)(67,160,196,116)(68,161,183,117)(69,162,184,118)(70,163,185,119), (1,148,187,25)(2,149,188,26)(3,150,189,27)(4,151,190,28)(5,152,191,15)(6,153,192,16)(7,154,193,17)(8,141,194,18)(9,142,195,19)(10,143,196,20)(11,144,183,21)(12,145,184,22)(13,146,185,23)(14,147,186,24)(29,60,97,75)(30,61,98,76)(31,62,85,77)(32,63,86,78)(33,64,87,79)(34,65,88,80)(35,66,89,81)(36,67,90,82)(37,68,91,83)(38,69,92,84)(39,70,93,71)(40,57,94,72)(41,58,95,73)(42,59,96,74)(43,172,111,156)(44,173,112,157)(45,174,99,158)(46,175,100,159)(47,176,101,160)(48,177,102,161)(49,178,103,162)(50,179,104,163)(51,180,105,164)(52,181,106,165)(53,182,107,166)(54,169,108,167)(55,170,109,168)(56,171,110,155)(113,140,203,221)(114,127,204,222)(115,128,205,223)(116,129,206,224)(117,130,207,211)(118,131,208,212)(119,132,209,213)(120,133,210,214)(121,134,197,215)(122,135,198,216)(123,136,199,217)(124,137,200,218)(125,138,201,219)(126,139,202,220) );
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)], [(1,99,187,45),(2,100,188,46),(3,101,189,47),(4,102,190,48),(5,103,191,49),(6,104,192,50),(7,105,193,51),(8,106,194,52),(9,107,195,53),(10,108,196,54),(11,109,183,55),(12,110,184,56),(13,111,185,43),(14,112,186,44),(15,162,152,178),(16,163,153,179),(17,164,154,180),(18,165,141,181),(19,166,142,182),(20,167,143,169),(21,168,144,170),(22,155,145,171),(23,156,146,172),(24,157,147,173),(25,158,148,174),(26,159,149,175),(27,160,150,176),(28,161,151,177),(29,206,97,116),(30,207,98,117),(31,208,85,118),(32,209,86,119),(33,210,87,120),(34,197,88,121),(35,198,89,122),(36,199,90,123),(37,200,91,124),(38,201,92,125),(39,202,93,126),(40,203,94,113),(41,204,95,114),(42,205,96,115),(57,140,72,221),(58,127,73,222),(59,128,74,223),(60,129,75,224),(61,130,76,211),(62,131,77,212),(63,132,78,213),(64,133,79,214),(65,134,80,215),(66,135,81,216),(67,136,82,217),(68,137,83,218),(69,138,84,219),(70,139,71,220)], [(1,197,73,181),(2,198,74,182),(3,199,75,169),(4,200,76,170),(5,201,77,171),(6,202,78,172),(7,203,79,173),(8,204,80,174),(9,205,81,175),(10,206,82,176),(11,207,83,177),(12,208,84,178),(13,209,71,179),(14,210,72,180),(15,110,85,219),(16,111,86,220),(17,112,87,221),(18,99,88,222),(19,100,89,223),(20,101,90,224),(21,102,91,211),(22,103,92,212),(23,104,93,213),(24,105,94,214),(25,106,95,215),(26,107,96,216),(27,108,97,217),(28,109,98,218),(29,136,150,54),(30,137,151,55),(31,138,152,56),(32,139,153,43),(33,140,154,44),(34,127,141,45),(35,128,142,46),(36,129,143,47),(37,130,144,48),(38,131,145,49),(39,132,146,50),(40,133,147,51),(41,134,148,52),(42,135,149,53),(57,164,186,120),(58,165,187,121),(59,166,188,122),(60,167,189,123),(61,168,190,124),(62,155,191,125),(63,156,192,126),(64,157,193,113),(65,158,194,114),(66,159,195,115),(67,160,196,116),(68,161,183,117),(69,162,184,118),(70,163,185,119)], [(1,148,187,25),(2,149,188,26),(3,150,189,27),(4,151,190,28),(5,152,191,15),(6,153,192,16),(7,154,193,17),(8,141,194,18),(9,142,195,19),(10,143,196,20),(11,144,183,21),(12,145,184,22),(13,146,185,23),(14,147,186,24),(29,60,97,75),(30,61,98,76),(31,62,85,77),(32,63,86,78),(33,64,87,79),(34,65,88,80),(35,66,89,81),(36,67,90,82),(37,68,91,83),(38,69,92,84),(39,70,93,71),(40,57,94,72),(41,58,95,73),(42,59,96,74),(43,172,111,156),(44,173,112,157),(45,174,99,158),(46,175,100,159),(47,176,101,160),(48,177,102,161),(49,178,103,162),(50,179,104,163),(51,180,105,164),(52,181,106,165),(53,182,107,166),(54,169,108,167),(55,170,109,168),(56,171,110,155),(113,140,203,221),(114,127,204,222),(115,128,205,223),(116,129,206,224),(117,130,207,211),(118,131,208,212),(119,132,209,213),(120,133,210,214),(121,134,197,215),(122,135,198,216),(123,136,199,217),(124,137,200,218),(125,138,201,219),(126,139,202,220)])
Matrix representation ►G ⊆ GL5(𝔽29)
| 28 | 0 | 0 | 0 | 0 |
| 0 | 22 | 0 | 0 | 0 |
| 0 | 0 | 22 | 0 | 0 |
| 0 | 0 | 0 | 24 | 0 |
| 0 | 0 | 0 | 0 | 24 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 |
| 0 | 0 | 0 | 17 | 0 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 17 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 28 | 0 |
G:=sub<GL(5,GF(29))| [28,0,0,0,0,0,22,0,0,0,0,0,22,0,0,0,0,0,24,0,0,0,0,0,24],[1,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,0,17,0,0,0,17,0],[1,0,0,0,0,0,0,28,0,0,0,1,0,0,0,0,0,0,17,0,0,0,0,0,17],[1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,1,0] >;
196 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | ··· | 4L | 4M | 4N | 4O | 4P | 7A | ··· | 7F | 14A | ··· | 14AP | 14AQ | ··· | 14BN | 28A | ··· | 28BT | 28BU | ··· | 28CR |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | ··· | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 4 | 4 | 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 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | |||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C7 | C14 | C14 | C14 | C14 | C14 | D4 | C4○D4 | C7×D4 | C7×C4○D4 |
| kernel | C14×C4.4D4 | C2×C4×C28 | C14×C22⋊C4 | C7×C4.4D4 | D4×C2×C14 | Q8×C2×C14 | C2×C4.4D4 | C2×C42 | C2×C22⋊C4 | C4.4D4 | C22×D4 | C22×Q8 | C2×C28 | C2×C14 | C2×C4 | C22 |
| # reps | 1 | 1 | 4 | 8 | 1 | 1 | 6 | 6 | 24 | 48 | 6 | 6 | 4 | 8 | 24 | 48 |
In GAP, Magma, Sage, TeX
C_{14}\times C_4._4D_4 % in TeX
G:=Group("C14xC4.4D4"); // GroupNames label
G:=SmallGroup(448,1309);
// by ID
G=gap.SmallGroup(448,1309);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,1597,1576,4790,604]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^4=c^4=1,d^2=b^2,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=b^2*c^-1>;
// generators/relations
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ℤ
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