metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.143D14, C14.1272+ (1+4), (C4×D28)⋊46C2, (Q8×Dic7)⋊20C2, (D4×Dic7)⋊31C2, C28⋊D4.9C2, C4.4D4⋊14D7, (C4×Dic14)⋊46C2, (C2×D4).176D14, (C2×Q8).139D14, C22⋊C4.36D14, Dic7⋊4D4⋊34C2, D14.D4⋊46C2, C28.126(C4○D4), C28.23D4⋊23C2, C4.16(D4⋊2D7), (C4×C28).188C22, (C2×C14).225C24, (C2×C28).505C23, D14⋊C4.37C22, C2.51(D4⋊8D14), C23.47(C22×D7), Dic7.39(C4○D4), Dic7.D4⋊41C2, (D4×C14).158C22, (C2×D28).266C22, C22.D28⋊26C2, C4⋊Dic7.235C22, (C22×C14).55C23, (Q8×C14).129C22, (C22×D7).97C23, C22.246(C23×D7), C23.D7.58C22, Dic7⋊C4.142C22, C7⋊4(C22.53C24), (C2×Dic7).256C23, (C4×Dic7).135C22, (C2×Dic14).250C22, (C22×Dic7).145C22, C2.81(D7×C4○D4), C14.192(C2×C4○D4), (C7×C4.4D4)⋊17C2, C2.57(C2×D4⋊2D7), (C2×C4×D7).216C22, (C2×C4).198(C22×D7), (C2×C7⋊D4).63C22, (C7×C22⋊C4).67C22, SmallGroup(448,1134)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1100 in 236 conjugacy classes, 97 normal (43 characteristic)
C1, C2 [×3], C2 [×4], C4 [×2], C4 [×11], C22, C22 [×12], C7, C2×C4 [×3], C2×C4 [×2], C2×C4 [×10], D4 [×10], Q8 [×4], C23 [×2], C23 [×2], D7 [×2], C14 [×3], C14 [×2], C42, C42 [×4], C22⋊C4 [×4], C22⋊C4 [×8], C4⋊C4 [×6], C22×C4 [×4], C2×D4, C2×D4 [×5], C2×Q8, C2×Q8, Dic7 [×2], Dic7 [×5], C28 [×2], C28 [×4], D14 [×6], C2×C14, C2×C14 [×6], C4×D4 [×4], C4×Q8 [×2], C22.D4 [×4], C4.4D4, C4.4D4 [×3], C4⋊1D4, Dic14 [×2], C4×D7 [×2], D28 [×2], C2×Dic7 [×4], C2×Dic7 [×2], C2×Dic7 [×2], C7⋊D4 [×6], C2×C28 [×3], C2×C28 [×2], C7×D4 [×2], C7×Q8 [×2], C22×D7 [×2], C22×C14 [×2], C22.53C24, C4×Dic7 [×2], C4×Dic7 [×2], Dic7⋊C4 [×2], C4⋊Dic7 [×2], C4⋊Dic7 [×2], D14⋊C4 [×6], C23.D7 [×2], C4×C28, C7×C22⋊C4 [×4], C2×Dic14, C2×C4×D7 [×2], C2×D28, C22×Dic7 [×2], C2×C7⋊D4 [×4], D4×C14, Q8×C14, C4×Dic14, C4×D28, Dic7⋊4D4 [×2], D14.D4 [×2], Dic7.D4 [×2], C22.D28 [×2], D4×Dic7, C28⋊D4, Q8×Dic7, C28.23D4, C7×C4.4D4, C42.143D14
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], C22.53C24, D4⋊2D7 [×2], C23×D7, C2×D4⋊2D7, D7×C4○D4, D4⋊8D14, C42.143D14
Generators and relations
G = < a,b,c,d | a4=b4=c14=1, d2=a2, ab=ba, cac-1=dad-1=ab2, cbc-1=a2b, dbd-1=b-1, dcd-1=a2c-1 >
►On 224 points
Generators in S224
(1 102 122 207)(2 150 123 48)(3 104 124 209)(4 152 125 50)(5 106 126 197)(6 154 113 52)(7 108 114 199)(8 142 115 54)(9 110 116 201)(10 144 117 56)(11 112 118 203)(12 146 119 44)(13 100 120 205)(14 148 121 46)(15 133 174 62)(16 194 175 224)(17 135 176 64)(18 196 177 212)(19 137 178 66)(20 184 179 214)(21 139 180 68)(22 186 181 216)(23 127 182 70)(24 188 169 218)(25 129 170 58)(26 190 171 220)(27 131 172 60)(28 192 173 222)(29 51 79 153)(30 198 80 107)(31 53 81 141)(32 200 82 109)(33 55 83 143)(34 202 84 111)(35 43 71 145)(36 204 72 99)(37 45 73 147)(38 206 74 101)(39 47 75 149)(40 208 76 103)(41 49 77 151)(42 210 78 105)(57 97 128 159)(59 85 130 161)(61 87 132 163)(63 89 134 165)(65 91 136 167)(67 93 138 155)(69 95 140 157)(86 191 162 221)(88 193 164 223)(90 195 166 211)(92 183 168 213)(94 185 156 215)(96 187 158 217)(98 189 160 219)
(1 139 75 185)(2 69 76 216)(3 127 77 187)(4 57 78 218)(5 129 79 189)(6 59 80 220)(7 131 81 191)(8 61 82 222)(9 133 83 193)(10 63 84 224)(11 135 71 195)(12 65 72 212)(13 137 73 183)(14 67 74 214)(15 55 88 201)(16 144 89 111)(17 43 90 203)(18 146 91 99)(19 45 92 205)(20 148 93 101)(21 47 94 207)(22 150 95 103)(23 49 96 209)(24 152 97 105)(25 51 98 197)(26 154 85 107)(27 53 86 199)(28 142 87 109)(29 219 126 58)(30 190 113 130)(31 221 114 60)(32 192 115 132)(33 223 116 62)(34 194 117 134)(35 211 118 64)(36 196 119 136)(37 213 120 66)(38 184 121 138)(39 215 122 68)(40 186 123 140)(41 217 124 70)(42 188 125 128)(44 167 204 177)(46 155 206 179)(48 157 208 181)(50 159 210 169)(52 161 198 171)(54 163 200 173)(56 165 202 175)(100 178 147 168)(102 180 149 156)(104 182 151 158)(106 170 153 160)(108 172 141 162)(110 174 143 164)(112 176 145 166)
(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 93 122 155)(2 168 123 92)(3 91 124 167)(4 166 125 90)(5 89 126 165)(6 164 113 88)(7 87 114 163)(8 162 115 86)(9 85 116 161)(10 160 117 98)(11 97 118 159)(12 158 119 96)(13 95 120 157)(14 156 121 94)(15 80 174 30)(16 29 175 79)(17 78 176 42)(18 41 177 77)(19 76 178 40)(20 39 179 75)(21 74 180 38)(22 37 181 73)(23 72 182 36)(24 35 169 71)(25 84 170 34)(26 33 171 83)(27 82 172 32)(28 31 173 81)(43 57 145 128)(44 127 146 70)(45 69 147 140)(46 139 148 68)(47 67 149 138)(48 137 150 66)(49 65 151 136)(50 135 152 64)(51 63 153 134)(52 133 154 62)(53 61 141 132)(54 131 142 60)(55 59 143 130)(56 129 144 58)(99 217 204 187)(100 186 205 216)(101 215 206 185)(102 184 207 214)(103 213 208 183)(104 196 209 212)(105 211 210 195)(106 194 197 224)(107 223 198 193)(108 192 199 222)(109 221 200 191)(110 190 201 220)(111 219 202 189)(112 188 203 218)
G:=sub<Sym(224)| (1,102,122,207)(2,150,123,48)(3,104,124,209)(4,152,125,50)(5,106,126,197)(6,154,113,52)(7,108,114,199)(8,142,115,54)(9,110,116,201)(10,144,117,56)(11,112,118,203)(12,146,119,44)(13,100,120,205)(14,148,121,46)(15,133,174,62)(16,194,175,224)(17,135,176,64)(18,196,177,212)(19,137,178,66)(20,184,179,214)(21,139,180,68)(22,186,181,216)(23,127,182,70)(24,188,169,218)(25,129,170,58)(26,190,171,220)(27,131,172,60)(28,192,173,222)(29,51,79,153)(30,198,80,107)(31,53,81,141)(32,200,82,109)(33,55,83,143)(34,202,84,111)(35,43,71,145)(36,204,72,99)(37,45,73,147)(38,206,74,101)(39,47,75,149)(40,208,76,103)(41,49,77,151)(42,210,78,105)(57,97,128,159)(59,85,130,161)(61,87,132,163)(63,89,134,165)(65,91,136,167)(67,93,138,155)(69,95,140,157)(86,191,162,221)(88,193,164,223)(90,195,166,211)(92,183,168,213)(94,185,156,215)(96,187,158,217)(98,189,160,219), (1,139,75,185)(2,69,76,216)(3,127,77,187)(4,57,78,218)(5,129,79,189)(6,59,80,220)(7,131,81,191)(8,61,82,222)(9,133,83,193)(10,63,84,224)(11,135,71,195)(12,65,72,212)(13,137,73,183)(14,67,74,214)(15,55,88,201)(16,144,89,111)(17,43,90,203)(18,146,91,99)(19,45,92,205)(20,148,93,101)(21,47,94,207)(22,150,95,103)(23,49,96,209)(24,152,97,105)(25,51,98,197)(26,154,85,107)(27,53,86,199)(28,142,87,109)(29,219,126,58)(30,190,113,130)(31,221,114,60)(32,192,115,132)(33,223,116,62)(34,194,117,134)(35,211,118,64)(36,196,119,136)(37,213,120,66)(38,184,121,138)(39,215,122,68)(40,186,123,140)(41,217,124,70)(42,188,125,128)(44,167,204,177)(46,155,206,179)(48,157,208,181)(50,159,210,169)(52,161,198,171)(54,163,200,173)(56,165,202,175)(100,178,147,168)(102,180,149,156)(104,182,151,158)(106,170,153,160)(108,172,141,162)(110,174,143,164)(112,176,145,166), (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), (1,93,122,155)(2,168,123,92)(3,91,124,167)(4,166,125,90)(5,89,126,165)(6,164,113,88)(7,87,114,163)(8,162,115,86)(9,85,116,161)(10,160,117,98)(11,97,118,159)(12,158,119,96)(13,95,120,157)(14,156,121,94)(15,80,174,30)(16,29,175,79)(17,78,176,42)(18,41,177,77)(19,76,178,40)(20,39,179,75)(21,74,180,38)(22,37,181,73)(23,72,182,36)(24,35,169,71)(25,84,170,34)(26,33,171,83)(27,82,172,32)(28,31,173,81)(43,57,145,128)(44,127,146,70)(45,69,147,140)(46,139,148,68)(47,67,149,138)(48,137,150,66)(49,65,151,136)(50,135,152,64)(51,63,153,134)(52,133,154,62)(53,61,141,132)(54,131,142,60)(55,59,143,130)(56,129,144,58)(99,217,204,187)(100,186,205,216)(101,215,206,185)(102,184,207,214)(103,213,208,183)(104,196,209,212)(105,211,210,195)(106,194,197,224)(107,223,198,193)(108,192,199,222)(109,221,200,191)(110,190,201,220)(111,219,202,189)(112,188,203,218)>;
G:=Group( (1,102,122,207)(2,150,123,48)(3,104,124,209)(4,152,125,50)(5,106,126,197)(6,154,113,52)(7,108,114,199)(8,142,115,54)(9,110,116,201)(10,144,117,56)(11,112,118,203)(12,146,119,44)(13,100,120,205)(14,148,121,46)(15,133,174,62)(16,194,175,224)(17,135,176,64)(18,196,177,212)(19,137,178,66)(20,184,179,214)(21,139,180,68)(22,186,181,216)(23,127,182,70)(24,188,169,218)(25,129,170,58)(26,190,171,220)(27,131,172,60)(28,192,173,222)(29,51,79,153)(30,198,80,107)(31,53,81,141)(32,200,82,109)(33,55,83,143)(34,202,84,111)(35,43,71,145)(36,204,72,99)(37,45,73,147)(38,206,74,101)(39,47,75,149)(40,208,76,103)(41,49,77,151)(42,210,78,105)(57,97,128,159)(59,85,130,161)(61,87,132,163)(63,89,134,165)(65,91,136,167)(67,93,138,155)(69,95,140,157)(86,191,162,221)(88,193,164,223)(90,195,166,211)(92,183,168,213)(94,185,156,215)(96,187,158,217)(98,189,160,219), (1,139,75,185)(2,69,76,216)(3,127,77,187)(4,57,78,218)(5,129,79,189)(6,59,80,220)(7,131,81,191)(8,61,82,222)(9,133,83,193)(10,63,84,224)(11,135,71,195)(12,65,72,212)(13,137,73,183)(14,67,74,214)(15,55,88,201)(16,144,89,111)(17,43,90,203)(18,146,91,99)(19,45,92,205)(20,148,93,101)(21,47,94,207)(22,150,95,103)(23,49,96,209)(24,152,97,105)(25,51,98,197)(26,154,85,107)(27,53,86,199)(28,142,87,109)(29,219,126,58)(30,190,113,130)(31,221,114,60)(32,192,115,132)(33,223,116,62)(34,194,117,134)(35,211,118,64)(36,196,119,136)(37,213,120,66)(38,184,121,138)(39,215,122,68)(40,186,123,140)(41,217,124,70)(42,188,125,128)(44,167,204,177)(46,155,206,179)(48,157,208,181)(50,159,210,169)(52,161,198,171)(54,163,200,173)(56,165,202,175)(100,178,147,168)(102,180,149,156)(104,182,151,158)(106,170,153,160)(108,172,141,162)(110,174,143,164)(112,176,145,166), (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), (1,93,122,155)(2,168,123,92)(3,91,124,167)(4,166,125,90)(5,89,126,165)(6,164,113,88)(7,87,114,163)(8,162,115,86)(9,85,116,161)(10,160,117,98)(11,97,118,159)(12,158,119,96)(13,95,120,157)(14,156,121,94)(15,80,174,30)(16,29,175,79)(17,78,176,42)(18,41,177,77)(19,76,178,40)(20,39,179,75)(21,74,180,38)(22,37,181,73)(23,72,182,36)(24,35,169,71)(25,84,170,34)(26,33,171,83)(27,82,172,32)(28,31,173,81)(43,57,145,128)(44,127,146,70)(45,69,147,140)(46,139,148,68)(47,67,149,138)(48,137,150,66)(49,65,151,136)(50,135,152,64)(51,63,153,134)(52,133,154,62)(53,61,141,132)(54,131,142,60)(55,59,143,130)(56,129,144,58)(99,217,204,187)(100,186,205,216)(101,215,206,185)(102,184,207,214)(103,213,208,183)(104,196,209,212)(105,211,210,195)(106,194,197,224)(107,223,198,193)(108,192,199,222)(109,221,200,191)(110,190,201,220)(111,219,202,189)(112,188,203,218) );
G=PermutationGroup([(1,102,122,207),(2,150,123,48),(3,104,124,209),(4,152,125,50),(5,106,126,197),(6,154,113,52),(7,108,114,199),(8,142,115,54),(9,110,116,201),(10,144,117,56),(11,112,118,203),(12,146,119,44),(13,100,120,205),(14,148,121,46),(15,133,174,62),(16,194,175,224),(17,135,176,64),(18,196,177,212),(19,137,178,66),(20,184,179,214),(21,139,180,68),(22,186,181,216),(23,127,182,70),(24,188,169,218),(25,129,170,58),(26,190,171,220),(27,131,172,60),(28,192,173,222),(29,51,79,153),(30,198,80,107),(31,53,81,141),(32,200,82,109),(33,55,83,143),(34,202,84,111),(35,43,71,145),(36,204,72,99),(37,45,73,147),(38,206,74,101),(39,47,75,149),(40,208,76,103),(41,49,77,151),(42,210,78,105),(57,97,128,159),(59,85,130,161),(61,87,132,163),(63,89,134,165),(65,91,136,167),(67,93,138,155),(69,95,140,157),(86,191,162,221),(88,193,164,223),(90,195,166,211),(92,183,168,213),(94,185,156,215),(96,187,158,217),(98,189,160,219)], [(1,139,75,185),(2,69,76,216),(3,127,77,187),(4,57,78,218),(5,129,79,189),(6,59,80,220),(7,131,81,191),(8,61,82,222),(9,133,83,193),(10,63,84,224),(11,135,71,195),(12,65,72,212),(13,137,73,183),(14,67,74,214),(15,55,88,201),(16,144,89,111),(17,43,90,203),(18,146,91,99),(19,45,92,205),(20,148,93,101),(21,47,94,207),(22,150,95,103),(23,49,96,209),(24,152,97,105),(25,51,98,197),(26,154,85,107),(27,53,86,199),(28,142,87,109),(29,219,126,58),(30,190,113,130),(31,221,114,60),(32,192,115,132),(33,223,116,62),(34,194,117,134),(35,211,118,64),(36,196,119,136),(37,213,120,66),(38,184,121,138),(39,215,122,68),(40,186,123,140),(41,217,124,70),(42,188,125,128),(44,167,204,177),(46,155,206,179),(48,157,208,181),(50,159,210,169),(52,161,198,171),(54,163,200,173),(56,165,202,175),(100,178,147,168),(102,180,149,156),(104,182,151,158),(106,170,153,160),(108,172,141,162),(110,174,143,164),(112,176,145,166)], [(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)], [(1,93,122,155),(2,168,123,92),(3,91,124,167),(4,166,125,90),(5,89,126,165),(6,164,113,88),(7,87,114,163),(8,162,115,86),(9,85,116,161),(10,160,117,98),(11,97,118,159),(12,158,119,96),(13,95,120,157),(14,156,121,94),(15,80,174,30),(16,29,175,79),(17,78,176,42),(18,41,177,77),(19,76,178,40),(20,39,179,75),(21,74,180,38),(22,37,181,73),(23,72,182,36),(24,35,169,71),(25,84,170,34),(26,33,171,83),(27,82,172,32),(28,31,173,81),(43,57,145,128),(44,127,146,70),(45,69,147,140),(46,139,148,68),(47,67,149,138),(48,137,150,66),(49,65,151,136),(50,135,152,64),(51,63,153,134),(52,133,154,62),(53,61,141,132),(54,131,142,60),(55,59,143,130),(56,129,144,58),(99,217,204,187),(100,186,205,216),(101,215,206,185),(102,184,207,214),(103,213,208,183),(104,196,209,212),(105,211,210,195),(106,194,197,224),(107,223,198,193),(108,192,199,222),(109,221,200,191),(110,190,201,220),(111,219,202,189),(112,188,203,218)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 1 | 12 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 28 | 17 |
| 4 | 4 | 0 | 0 | 0 | 0 |
| 25 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 24 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 25 | 25 | 0 | 0 | 0 | 0 |
| 11 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 5 |
| 0 | 0 | 0 | 0 | 17 | 1 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,17,1,0,0,0,0,0,12],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,28,0,0,0,0,0,0,0,12,28,0,0,0,0,0,17],[4,25,0,0,0,0,4,18,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,24,28],[25,11,0,0,0,0,25,4,0,0,0,0,0,0,0,12,0,0,0,0,12,0,0,0,0,0,0,0,28,17,0,0,0,0,5,1] >;
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | ··· | 4O | 4P | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | D14 | 2+ (1+4) | D4⋊2D7 | D7×C4○D4 | D4⋊8D14 |
| kernel | C42.143D14 | C4×Dic14 | C4×D28 | Dic7⋊4D4 | D14.D4 | Dic7.D4 | C22.D28 | D4×Dic7 | C28⋊D4 | Q8×Dic7 | C28.23D4 | C7×C4.4D4 | C4.4D4 | Dic7 | C28 | C42 | C22⋊C4 | C2×D4 | C2×Q8 | C14 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 4 | 3 | 12 | 3 | 3 | 1 | 6 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{143}D_{14} % in TeX
G:=Group("C4^2.143D14"); // GroupNames label
G:=SmallGroup(448,1134);
// by ID
G=gap.SmallGroup(448,1134);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,219,1571,297,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a*b^2,c*b*c^-1=a^2*b,d*b*d^-1=b^-1,d*c*d^-1=a^2*c^-1>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀