metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.132D14, C14.122- (1+4), (C4×Q8)⋊14D7, (Q8×C28)⋊16C2, C4⋊C4.299D14, D14⋊3Q8⋊9C2, (C4×D28).22C2, Dic7.Q8⋊9C2, C4.68(C4○D28), C42⋊D7⋊34C2, C42⋊2D7⋊18C2, (C2×Q8).180D14, C28.6Q8⋊19C2, D14.18(C4○D4), C28.119(C4○D4), (C2×C14).125C24, (C4×C28).177C22, (C2×C28).623C23, D14⋊C4.89C22, D14.5D4.1C2, (C2×D28).218C22, Dic7⋊C4.76C22, C4⋊Dic7.309C22, (Q8×C14).225C22, (C2×Dic7).56C23, (C22×D7).47C23, C22.146(C23×D7), C7⋊5(C22.46C24), (C4×Dic7).209C22, C2.13(Q8.10D14), (D7×C4⋊C4)⋊19C2, C2.32(D7×C4○D4), C4⋊C4⋊7D7⋊17C2, C2.64(C2×C4○D28), (C2×C4×D7).75C22, C14.147(C2×C4○D4), (C7×C4⋊C4).353C22, (C2×C4).289(C22×D7), SmallGroup(448,1034)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 900 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 [×2], C42 [×2], C22⋊C4 [×8], C4⋊C4, C4⋊C4 [×2], C4⋊C4 [×13], 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 [×3], C42⋊2C2 [×2], C4×D7 [×8], D28 [×2], C2×Dic7 [×2], C2×Dic7 [×4], C2×C28 [×3], C2×C28 [×4], C7×Q8 [×2], C22×D7 [×2], C22.46C24, C4×Dic7 [×2], Dic7⋊C4 [×10], C4⋊Dic7 [×3], D14⋊C4 [×2], D14⋊C4 [×6], C4×C28, C4×C28 [×2], C7×C4⋊C4, C7×C4⋊C4 [×2], C2×C4×D7 [×2], C2×C4×D7 [×2], C2×D28, Q8×C14, C28.6Q8, C42⋊D7 [×2], C4×D28, C42⋊2D7 [×2], Dic7.Q8 [×2], D7×C4⋊C4, C4⋊C4⋊7D7, D14.5D4 [×2], D14⋊3Q8 [×2], Q8×C28, C42.132D14
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, C4○D28 [×2], C23×D7, C2×C4○D28, Q8.10D14, D7×C4○D4, C42.132D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=d2=a2b2, ab=ba, cac-1=dad-1=a-1, bc=cb, dbd-1=a2b-1, dcd-1=c13 >
►On 224 points
Generators in S224
(1 185 83 220)(2 221 84 186)(3 187 57 222)(4 223 58 188)(5 189 59 224)(6 197 60 190)(7 191 61 198)(8 199 62 192)(9 193 63 200)(10 201 64 194)(11 195 65 202)(12 203 66 196)(13 169 67 204)(14 205 68 170)(15 171 69 206)(16 207 70 172)(17 173 71 208)(18 209 72 174)(19 175 73 210)(20 211 74 176)(21 177 75 212)(22 213 76 178)(23 179 77 214)(24 215 78 180)(25 181 79 216)(26 217 80 182)(27 183 81 218)(28 219 82 184)(29 85 163 129)(30 130 164 86)(31 87 165 131)(32 132 166 88)(33 89 167 133)(34 134 168 90)(35 91 141 135)(36 136 142 92)(37 93 143 137)(38 138 144 94)(39 95 145 139)(40 140 146 96)(41 97 147 113)(42 114 148 98)(43 99 149 115)(44 116 150 100)(45 101 151 117)(46 118 152 102)(47 103 153 119)(48 120 154 104)(49 105 155 121)(50 122 156 106)(51 107 157 123)(52 124 158 108)(53 109 159 125)(54 126 160 110)(55 111 161 127)(56 128 162 112)
(1 111 69 113)(2 112 70 114)(3 85 71 115)(4 86 72 116)(5 87 73 117)(6 88 74 118)(7 89 75 119)(8 90 76 120)(9 91 77 121)(10 92 78 122)(11 93 79 123)(12 94 80 124)(13 95 81 125)(14 96 82 126)(15 97 83 127)(16 98 84 128)(17 99 57 129)(18 100 58 130)(19 101 59 131)(20 102 60 132)(21 103 61 133)(22 104 62 134)(23 105 63 135)(24 106 64 136)(25 107 65 137)(26 108 66 138)(27 109 67 139)(28 110 68 140)(29 173 149 222)(30 174 150 223)(31 175 151 224)(32 176 152 197)(33 177 153 198)(34 178 154 199)(35 179 155 200)(36 180 156 201)(37 181 157 202)(38 182 158 203)(39 183 159 204)(40 184 160 205)(41 185 161 206)(42 186 162 207)(43 187 163 208)(44 188 164 209)(45 189 165 210)(46 190 166 211)(47 191 167 212)(48 192 168 213)(49 193 141 214)(50 194 142 215)(51 195 143 216)(52 196 144 217)(53 169 145 218)(54 170 146 219)(55 171 147 220)(56 172 148 221)
(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 52 43 38)(30 37 44 51)(31 50 45 36)(32 35 46 49)(33 48 47 34)(39 42 53 56)(40 55 54 41)(57 66 71 80)(58 79 72 65)(59 64 73 78)(60 77 74 63)(61 62 75 76)(67 84 81 70)(68 69 82 83)(85 108 99 94)(86 93 100 107)(87 106 101 92)(88 91 102 105)(89 104 103 90)(95 98 109 112)(96 111 110 97)(113 140 127 126)(114 125 128 139)(115 138 129 124)(116 123 130 137)(117 136 131 122)(118 121 132 135)(119 134 133 120)(141 152 155 166)(142 165 156 151)(143 150 157 164)(144 163 158 149)(145 148 159 162)(146 161 160 147)(153 168 167 154)(169 186 183 172)(170 171 184 185)(173 182 187 196)(174 195 188 181)(175 180 189 194)(176 193 190 179)(177 178 191 192)(197 214 211 200)(198 199 212 213)(201 210 215 224)(202 223 216 209)(203 208 217 222)(204 221 218 207)(205 206 219 220)
G:=sub<Sym(224)| (1,185,83,220)(2,221,84,186)(3,187,57,222)(4,223,58,188)(5,189,59,224)(6,197,60,190)(7,191,61,198)(8,199,62,192)(9,193,63,200)(10,201,64,194)(11,195,65,202)(12,203,66,196)(13,169,67,204)(14,205,68,170)(15,171,69,206)(16,207,70,172)(17,173,71,208)(18,209,72,174)(19,175,73,210)(20,211,74,176)(21,177,75,212)(22,213,76,178)(23,179,77,214)(24,215,78,180)(25,181,79,216)(26,217,80,182)(27,183,81,218)(28,219,82,184)(29,85,163,129)(30,130,164,86)(31,87,165,131)(32,132,166,88)(33,89,167,133)(34,134,168,90)(35,91,141,135)(36,136,142,92)(37,93,143,137)(38,138,144,94)(39,95,145,139)(40,140,146,96)(41,97,147,113)(42,114,148,98)(43,99,149,115)(44,116,150,100)(45,101,151,117)(46,118,152,102)(47,103,153,119)(48,120,154,104)(49,105,155,121)(50,122,156,106)(51,107,157,123)(52,124,158,108)(53,109,159,125)(54,126,160,110)(55,111,161,127)(56,128,162,112), (1,111,69,113)(2,112,70,114)(3,85,71,115)(4,86,72,116)(5,87,73,117)(6,88,74,118)(7,89,75,119)(8,90,76,120)(9,91,77,121)(10,92,78,122)(11,93,79,123)(12,94,80,124)(13,95,81,125)(14,96,82,126)(15,97,83,127)(16,98,84,128)(17,99,57,129)(18,100,58,130)(19,101,59,131)(20,102,60,132)(21,103,61,133)(22,104,62,134)(23,105,63,135)(24,106,64,136)(25,107,65,137)(26,108,66,138)(27,109,67,139)(28,110,68,140)(29,173,149,222)(30,174,150,223)(31,175,151,224)(32,176,152,197)(33,177,153,198)(34,178,154,199)(35,179,155,200)(36,180,156,201)(37,181,157,202)(38,182,158,203)(39,183,159,204)(40,184,160,205)(41,185,161,206)(42,186,162,207)(43,187,163,208)(44,188,164,209)(45,189,165,210)(46,190,166,211)(47,191,167,212)(48,192,168,213)(49,193,141,214)(50,194,142,215)(51,195,143,216)(52,196,144,217)(53,169,145,218)(54,170,146,219)(55,171,147,220)(56,172,148,221), (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)(29,52,43,38)(30,37,44,51)(31,50,45,36)(32,35,46,49)(33,48,47,34)(39,42,53,56)(40,55,54,41)(57,66,71,80)(58,79,72,65)(59,64,73,78)(60,77,74,63)(61,62,75,76)(67,84,81,70)(68,69,82,83)(85,108,99,94)(86,93,100,107)(87,106,101,92)(88,91,102,105)(89,104,103,90)(95,98,109,112)(96,111,110,97)(113,140,127,126)(114,125,128,139)(115,138,129,124)(116,123,130,137)(117,136,131,122)(118,121,132,135)(119,134,133,120)(141,152,155,166)(142,165,156,151)(143,150,157,164)(144,163,158,149)(145,148,159,162)(146,161,160,147)(153,168,167,154)(169,186,183,172)(170,171,184,185)(173,182,187,196)(174,195,188,181)(175,180,189,194)(176,193,190,179)(177,178,191,192)(197,214,211,200)(198,199,212,213)(201,210,215,224)(202,223,216,209)(203,208,217,222)(204,221,218,207)(205,206,219,220)>;
G:=Group( (1,185,83,220)(2,221,84,186)(3,187,57,222)(4,223,58,188)(5,189,59,224)(6,197,60,190)(7,191,61,198)(8,199,62,192)(9,193,63,200)(10,201,64,194)(11,195,65,202)(12,203,66,196)(13,169,67,204)(14,205,68,170)(15,171,69,206)(16,207,70,172)(17,173,71,208)(18,209,72,174)(19,175,73,210)(20,211,74,176)(21,177,75,212)(22,213,76,178)(23,179,77,214)(24,215,78,180)(25,181,79,216)(26,217,80,182)(27,183,81,218)(28,219,82,184)(29,85,163,129)(30,130,164,86)(31,87,165,131)(32,132,166,88)(33,89,167,133)(34,134,168,90)(35,91,141,135)(36,136,142,92)(37,93,143,137)(38,138,144,94)(39,95,145,139)(40,140,146,96)(41,97,147,113)(42,114,148,98)(43,99,149,115)(44,116,150,100)(45,101,151,117)(46,118,152,102)(47,103,153,119)(48,120,154,104)(49,105,155,121)(50,122,156,106)(51,107,157,123)(52,124,158,108)(53,109,159,125)(54,126,160,110)(55,111,161,127)(56,128,162,112), (1,111,69,113)(2,112,70,114)(3,85,71,115)(4,86,72,116)(5,87,73,117)(6,88,74,118)(7,89,75,119)(8,90,76,120)(9,91,77,121)(10,92,78,122)(11,93,79,123)(12,94,80,124)(13,95,81,125)(14,96,82,126)(15,97,83,127)(16,98,84,128)(17,99,57,129)(18,100,58,130)(19,101,59,131)(20,102,60,132)(21,103,61,133)(22,104,62,134)(23,105,63,135)(24,106,64,136)(25,107,65,137)(26,108,66,138)(27,109,67,139)(28,110,68,140)(29,173,149,222)(30,174,150,223)(31,175,151,224)(32,176,152,197)(33,177,153,198)(34,178,154,199)(35,179,155,200)(36,180,156,201)(37,181,157,202)(38,182,158,203)(39,183,159,204)(40,184,160,205)(41,185,161,206)(42,186,162,207)(43,187,163,208)(44,188,164,209)(45,189,165,210)(46,190,166,211)(47,191,167,212)(48,192,168,213)(49,193,141,214)(50,194,142,215)(51,195,143,216)(52,196,144,217)(53,169,145,218)(54,170,146,219)(55,171,147,220)(56,172,148,221), (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)(29,52,43,38)(30,37,44,51)(31,50,45,36)(32,35,46,49)(33,48,47,34)(39,42,53,56)(40,55,54,41)(57,66,71,80)(58,79,72,65)(59,64,73,78)(60,77,74,63)(61,62,75,76)(67,84,81,70)(68,69,82,83)(85,108,99,94)(86,93,100,107)(87,106,101,92)(88,91,102,105)(89,104,103,90)(95,98,109,112)(96,111,110,97)(113,140,127,126)(114,125,128,139)(115,138,129,124)(116,123,130,137)(117,136,131,122)(118,121,132,135)(119,134,133,120)(141,152,155,166)(142,165,156,151)(143,150,157,164)(144,163,158,149)(145,148,159,162)(146,161,160,147)(153,168,167,154)(169,186,183,172)(170,171,184,185)(173,182,187,196)(174,195,188,181)(175,180,189,194)(176,193,190,179)(177,178,191,192)(197,214,211,200)(198,199,212,213)(201,210,215,224)(202,223,216,209)(203,208,217,222)(204,221,218,207)(205,206,219,220) );
G=PermutationGroup([(1,185,83,220),(2,221,84,186),(3,187,57,222),(4,223,58,188),(5,189,59,224),(6,197,60,190),(7,191,61,198),(8,199,62,192),(9,193,63,200),(10,201,64,194),(11,195,65,202),(12,203,66,196),(13,169,67,204),(14,205,68,170),(15,171,69,206),(16,207,70,172),(17,173,71,208),(18,209,72,174),(19,175,73,210),(20,211,74,176),(21,177,75,212),(22,213,76,178),(23,179,77,214),(24,215,78,180),(25,181,79,216),(26,217,80,182),(27,183,81,218),(28,219,82,184),(29,85,163,129),(30,130,164,86),(31,87,165,131),(32,132,166,88),(33,89,167,133),(34,134,168,90),(35,91,141,135),(36,136,142,92),(37,93,143,137),(38,138,144,94),(39,95,145,139),(40,140,146,96),(41,97,147,113),(42,114,148,98),(43,99,149,115),(44,116,150,100),(45,101,151,117),(46,118,152,102),(47,103,153,119),(48,120,154,104),(49,105,155,121),(50,122,156,106),(51,107,157,123),(52,124,158,108),(53,109,159,125),(54,126,160,110),(55,111,161,127),(56,128,162,112)], [(1,111,69,113),(2,112,70,114),(3,85,71,115),(4,86,72,116),(5,87,73,117),(6,88,74,118),(7,89,75,119),(8,90,76,120),(9,91,77,121),(10,92,78,122),(11,93,79,123),(12,94,80,124),(13,95,81,125),(14,96,82,126),(15,97,83,127),(16,98,84,128),(17,99,57,129),(18,100,58,130),(19,101,59,131),(20,102,60,132),(21,103,61,133),(22,104,62,134),(23,105,63,135),(24,106,64,136),(25,107,65,137),(26,108,66,138),(27,109,67,139),(28,110,68,140),(29,173,149,222),(30,174,150,223),(31,175,151,224),(32,176,152,197),(33,177,153,198),(34,178,154,199),(35,179,155,200),(36,180,156,201),(37,181,157,202),(38,182,158,203),(39,183,159,204),(40,184,160,205),(41,185,161,206),(42,186,162,207),(43,187,163,208),(44,188,164,209),(45,189,165,210),(46,190,166,211),(47,191,167,212),(48,192,168,213),(49,193,141,214),(50,194,142,215),(51,195,143,216),(52,196,144,217),(53,169,145,218),(54,170,146,219),(55,171,147,220),(56,172,148,221)], [(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),(29,52,43,38),(30,37,44,51),(31,50,45,36),(32,35,46,49),(33,48,47,34),(39,42,53,56),(40,55,54,41),(57,66,71,80),(58,79,72,65),(59,64,73,78),(60,77,74,63),(61,62,75,76),(67,84,81,70),(68,69,82,83),(85,108,99,94),(86,93,100,107),(87,106,101,92),(88,91,102,105),(89,104,103,90),(95,98,109,112),(96,111,110,97),(113,140,127,126),(114,125,128,139),(115,138,129,124),(116,123,130,137),(117,136,131,122),(118,121,132,135),(119,134,133,120),(141,152,155,166),(142,165,156,151),(143,150,157,164),(144,163,158,149),(145,148,159,162),(146,161,160,147),(153,168,167,154),(169,186,183,172),(170,171,184,185),(173,182,187,196),(174,195,188,181),(175,180,189,194),(176,193,190,179),(177,178,191,192),(197,214,211,200),(198,199,212,213),(201,210,215,224),(202,223,216,209),(203,208,217,222),(204,221,218,207),(205,206,219,220)])
Matrix representation ►G ⊆ GL4(𝔽29) generated by
| 28 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 12 | 27 |
| 0 | 0 | 0 | 17 |
| 21 | 18 | 0 | 0 |
| 27 | 8 | 0 | 0 |
| 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 12 |
| 4 | 9 | 0 | 0 |
| 28 | 12 | 0 | 0 |
| 0 | 0 | 12 | 27 |
| 0 | 0 | 28 | 17 |
| 3 | 22 | 0 | 0 |
| 18 | 26 | 0 | 0 |
| 0 | 0 | 12 | 27 |
| 0 | 0 | 28 | 17 |
G:=sub<GL(4,GF(29))| [28,0,0,0,0,28,0,0,0,0,12,0,0,0,27,17],[21,27,0,0,18,8,0,0,0,0,12,0,0,0,0,12],[4,28,0,0,9,12,0,0,0,0,12,28,0,0,27,17],[3,18,0,0,22,26,0,0,0,0,12,28,0,0,27,17] >;
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | ··· | 4R | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 4 | 4 | 4 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 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 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | C4○D28 | 2- (1+4) | Q8.10D14 | D7×C4○D4 |
| kernel | C42.132D14 | C28.6Q8 | C42⋊D7 | C4×D28 | C42⋊2D7 | Dic7.Q8 | D7×C4⋊C4 | C4⋊C4⋊7D7 | D14.5D4 | D14⋊3Q8 | Q8×C28 | C4×Q8 | C28 | D14 | C42 | C4⋊C4 | C2×Q8 | C4 | C14 | C2 | C2 |
| # reps | 1 | 1 | 2 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 3 | 4 | 4 | 9 | 9 | 3 | 24 | 1 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{132}D_{14} % in TeX
G:=Group("C4^2.132D14"); // GroupNames label
G:=SmallGroup(448,1034);
// by ID
G=gap.SmallGroup(448,1034);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,268,1571,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^2*b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,b*c=c*b,d*b*d^-1=a^2*b^-1,d*c*d^-1=c^13>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀