metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.189D14, C4⋊C4.212D14, (D7×C42)⋊20C2, D28⋊C4⋊41C2, D14⋊Q8⋊42C2, D14⋊D4.3C2, C42⋊2C2⋊10D7, C42⋊2D7⋊14C2, Dic7.Q8⋊37C2, (C2×C28).95C23, C22⋊C4.78D14, D14.13(C4○D4), Dic7⋊3Q8⋊41C2, Dic7⋊4D4⋊35C2, D14.5D4⋊40C2, D14.D4⋊50C2, (C2×C14).250C24, (C4×C28).234C22, D14⋊C4.45C22, C23.56(C22×D7), Dic7.15(C4○D4), Dic7.D4⋊46C2, (C2×D28).168C22, Dic7⋊C4.72C22, C4⋊Dic7.246C22, (C22×C14).64C23, C22.271(C23×D7), C23.D7.66C22, C23.11D14⋊21C2, (C4×Dic7).150C22, (C2×Dic7).313C23, (C22×D7).224C23, C7⋊11(C23.36C23), (C2×Dic14).183C22, (C22×Dic7).150C22, C2.97(D7×C4○D4), C4⋊C4⋊7D7⋊40C2, (C7×C42⋊2C2)⋊5C2, C14.208(C2×C4○D4), (C2×C4×D7).300C22, (C2×C4).87(C22×D7), (C7×C4⋊C4).202C22, (C2×C7⋊D4).70C22, (C7×C22⋊C4).75C22, SmallGroup(448,1159)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1036 in 234 conjugacy classes, 97 normal (91 characteristic)
C1, C2 [×3], C2 [×4], C4 [×14], C22, C22 [×10], C7, C2×C4 [×6], C2×C4 [×16], D4 [×6], Q8 [×2], C23, C23 [×2], D7 [×3], C14 [×3], C14, C42, C42 [×5], C22⋊C4 [×3], C22⋊C4 [×7], C4⋊C4 [×3], C4⋊C4 [×7], C22×C4 [×5], C2×D4 [×3], C2×Q8, Dic7 [×4], Dic7 [×4], C28 [×6], D14 [×2], D14 [×5], C2×C14, C2×C14 [×3], C2×C42, C42⋊C2 [×2], C4×D4 [×3], C4×Q8, C4⋊D4, C22⋊Q8, C22.D4 [×2], C4.4D4, C42.C2, C42⋊2C2, C42⋊2C2, Dic14 [×2], C4×D7 [×8], D28 [×2], C2×Dic7 [×6], C2×Dic7 [×2], C7⋊D4 [×4], C2×C28 [×6], C22×D7 [×2], C22×C14, C23.36C23, C4×Dic7 [×5], Dic7⋊C4 [×6], C4⋊Dic7, D14⋊C4 [×6], C23.D7, C4×C28, C7×C22⋊C4 [×3], C7×C4⋊C4 [×3], C2×Dic14, C2×C4×D7 [×4], C2×D28, C22×Dic7, C2×C7⋊D4 [×2], D7×C42, C42⋊2D7, C23.11D14, Dic7⋊4D4 [×2], D14.D4, D14⋊D4, Dic7.D4, Dic7⋊3Q8, Dic7.Q8, C4⋊C4⋊7D7, D28⋊C4, D14.5D4, D14⋊Q8, C7×C42⋊2C2, C42.189D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×6], C24, D14 [×7], C2×C4○D4 [×3], C22×D7 [×7], C23.36C23, C23×D7, D7×C4○D4 [×3], C42.189D14
Generators and relations
G = < a,b,c,d | a4=b4=c14=1, d2=a2, ab=ba, cac-1=dad-1=a-1b2, cbc-1=dbd-1=a2b, dcd-1=a2c-1 >
►On 224 points
Generators in S224
(1 69 150 186)(2 54 151 71)(3 57 152 188)(4 56 153 73)(5 59 154 190)(6 44 141 75)(7 61 142 192)(8 46 143 77)(9 63 144 194)(10 48 145 79)(11 65 146 196)(12 50 147 81)(13 67 148 184)(14 52 149 83)(15 135 174 216)(16 91 175 122)(17 137 176 218)(18 93 177 124)(19 139 178 220)(20 95 179 126)(21 127 180 222)(22 97 181 114)(23 129 182 224)(24 85 169 116)(25 131 170 212)(26 87 171 118)(27 133 172 214)(28 89 173 120)(29 123 199 92)(30 219 200 138)(31 125 201 94)(32 221 202 140)(33 113 203 96)(34 223 204 128)(35 115 205 98)(36 211 206 130)(37 117 207 86)(38 213 208 132)(39 119 209 88)(40 215 210 134)(41 121 197 90)(42 217 198 136)(43 107 74 157)(45 109 76 159)(47 111 78 161)(49 99 80 163)(51 101 82 165)(53 103 84 167)(55 105 72 155)(58 106 189 156)(60 108 191 158)(62 110 193 160)(64 112 195 162)(66 100 183 164)(68 102 185 166)(70 104 187 168)
(1 36 103 24)(2 207 104 170)(3 38 105 26)(4 209 106 172)(5 40 107 28)(6 197 108 174)(7 42 109 16)(8 199 110 176)(9 30 111 18)(10 201 112 178)(11 32 99 20)(12 203 100 180)(13 34 101 22)(14 205 102 182)(15 141 41 158)(17 143 29 160)(19 145 31 162)(21 147 33 164)(23 149 35 166)(25 151 37 168)(27 153 39 156)(43 120 190 134)(44 90 191 216)(45 122 192 136)(46 92 193 218)(47 124 194 138)(48 94 195 220)(49 126 196 140)(50 96 183 222)(51 114 184 128)(52 98 185 224)(53 116 186 130)(54 86 187 212)(55 118 188 132)(56 88 189 214)(57 213 72 87)(58 133 73 119)(59 215 74 89)(60 135 75 121)(61 217 76 91)(62 137 77 123)(63 219 78 93)(64 139 79 125)(65 221 80 95)(66 127 81 113)(67 223 82 97)(68 129 83 115)(69 211 84 85)(70 131 71 117)(142 198 159 175)(144 200 161 177)(146 202 163 179)(148 204 165 181)(150 206 167 169)(152 208 155 171)(154 210 157 173)
(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)
(1 102 150 166)(2 165 151 101)(3 100 152 164)(4 163 153 99)(5 112 154 162)(6 161 141 111)(7 110 142 160)(8 159 143 109)(9 108 144 158)(10 157 145 107)(11 106 146 156)(12 155 147 105)(13 104 148 168)(14 167 149 103)(15 200 174 30)(16 29 175 199)(17 198 176 42)(18 41 177 197)(19 210 178 40)(20 39 179 209)(21 208 180 38)(22 37 181 207)(23 206 182 36)(24 35 169 205)(25 204 170 34)(26 33 171 203)(27 202 172 32)(28 31 173 201)(43 195 74 64)(44 63 75 194)(45 193 76 62)(46 61 77 192)(47 191 78 60)(48 59 79 190)(49 189 80 58)(50 57 81 188)(51 187 82 70)(52 69 83 186)(53 185 84 68)(54 67 71 184)(55 183 72 66)(56 65 73 196)(85 224 116 129)(86 128 117 223)(87 222 118 127)(88 140 119 221)(89 220 120 139)(90 138 121 219)(91 218 122 137)(92 136 123 217)(93 216 124 135)(94 134 125 215)(95 214 126 133)(96 132 113 213)(97 212 114 131)(98 130 115 211)
G:=sub<Sym(224)| (1,69,150,186)(2,54,151,71)(3,57,152,188)(4,56,153,73)(5,59,154,190)(6,44,141,75)(7,61,142,192)(8,46,143,77)(9,63,144,194)(10,48,145,79)(11,65,146,196)(12,50,147,81)(13,67,148,184)(14,52,149,83)(15,135,174,216)(16,91,175,122)(17,137,176,218)(18,93,177,124)(19,139,178,220)(20,95,179,126)(21,127,180,222)(22,97,181,114)(23,129,182,224)(24,85,169,116)(25,131,170,212)(26,87,171,118)(27,133,172,214)(28,89,173,120)(29,123,199,92)(30,219,200,138)(31,125,201,94)(32,221,202,140)(33,113,203,96)(34,223,204,128)(35,115,205,98)(36,211,206,130)(37,117,207,86)(38,213,208,132)(39,119,209,88)(40,215,210,134)(41,121,197,90)(42,217,198,136)(43,107,74,157)(45,109,76,159)(47,111,78,161)(49,99,80,163)(51,101,82,165)(53,103,84,167)(55,105,72,155)(58,106,189,156)(60,108,191,158)(62,110,193,160)(64,112,195,162)(66,100,183,164)(68,102,185,166)(70,104,187,168), (1,36,103,24)(2,207,104,170)(3,38,105,26)(4,209,106,172)(5,40,107,28)(6,197,108,174)(7,42,109,16)(8,199,110,176)(9,30,111,18)(10,201,112,178)(11,32,99,20)(12,203,100,180)(13,34,101,22)(14,205,102,182)(15,141,41,158)(17,143,29,160)(19,145,31,162)(21,147,33,164)(23,149,35,166)(25,151,37,168)(27,153,39,156)(43,120,190,134)(44,90,191,216)(45,122,192,136)(46,92,193,218)(47,124,194,138)(48,94,195,220)(49,126,196,140)(50,96,183,222)(51,114,184,128)(52,98,185,224)(53,116,186,130)(54,86,187,212)(55,118,188,132)(56,88,189,214)(57,213,72,87)(58,133,73,119)(59,215,74,89)(60,135,75,121)(61,217,76,91)(62,137,77,123)(63,219,78,93)(64,139,79,125)(65,221,80,95)(66,127,81,113)(67,223,82,97)(68,129,83,115)(69,211,84,85)(70,131,71,117)(142,198,159,175)(144,200,161,177)(146,202,163,179)(148,204,165,181)(150,206,167,169)(152,208,155,171)(154,210,157,173), (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), (1,102,150,166)(2,165,151,101)(3,100,152,164)(4,163,153,99)(5,112,154,162)(6,161,141,111)(7,110,142,160)(8,159,143,109)(9,108,144,158)(10,157,145,107)(11,106,146,156)(12,155,147,105)(13,104,148,168)(14,167,149,103)(15,200,174,30)(16,29,175,199)(17,198,176,42)(18,41,177,197)(19,210,178,40)(20,39,179,209)(21,208,180,38)(22,37,181,207)(23,206,182,36)(24,35,169,205)(25,204,170,34)(26,33,171,203)(27,202,172,32)(28,31,173,201)(43,195,74,64)(44,63,75,194)(45,193,76,62)(46,61,77,192)(47,191,78,60)(48,59,79,190)(49,189,80,58)(50,57,81,188)(51,187,82,70)(52,69,83,186)(53,185,84,68)(54,67,71,184)(55,183,72,66)(56,65,73,196)(85,224,116,129)(86,128,117,223)(87,222,118,127)(88,140,119,221)(89,220,120,139)(90,138,121,219)(91,218,122,137)(92,136,123,217)(93,216,124,135)(94,134,125,215)(95,214,126,133)(96,132,113,213)(97,212,114,131)(98,130,115,211)>;
G:=Group( (1,69,150,186)(2,54,151,71)(3,57,152,188)(4,56,153,73)(5,59,154,190)(6,44,141,75)(7,61,142,192)(8,46,143,77)(9,63,144,194)(10,48,145,79)(11,65,146,196)(12,50,147,81)(13,67,148,184)(14,52,149,83)(15,135,174,216)(16,91,175,122)(17,137,176,218)(18,93,177,124)(19,139,178,220)(20,95,179,126)(21,127,180,222)(22,97,181,114)(23,129,182,224)(24,85,169,116)(25,131,170,212)(26,87,171,118)(27,133,172,214)(28,89,173,120)(29,123,199,92)(30,219,200,138)(31,125,201,94)(32,221,202,140)(33,113,203,96)(34,223,204,128)(35,115,205,98)(36,211,206,130)(37,117,207,86)(38,213,208,132)(39,119,209,88)(40,215,210,134)(41,121,197,90)(42,217,198,136)(43,107,74,157)(45,109,76,159)(47,111,78,161)(49,99,80,163)(51,101,82,165)(53,103,84,167)(55,105,72,155)(58,106,189,156)(60,108,191,158)(62,110,193,160)(64,112,195,162)(66,100,183,164)(68,102,185,166)(70,104,187,168), (1,36,103,24)(2,207,104,170)(3,38,105,26)(4,209,106,172)(5,40,107,28)(6,197,108,174)(7,42,109,16)(8,199,110,176)(9,30,111,18)(10,201,112,178)(11,32,99,20)(12,203,100,180)(13,34,101,22)(14,205,102,182)(15,141,41,158)(17,143,29,160)(19,145,31,162)(21,147,33,164)(23,149,35,166)(25,151,37,168)(27,153,39,156)(43,120,190,134)(44,90,191,216)(45,122,192,136)(46,92,193,218)(47,124,194,138)(48,94,195,220)(49,126,196,140)(50,96,183,222)(51,114,184,128)(52,98,185,224)(53,116,186,130)(54,86,187,212)(55,118,188,132)(56,88,189,214)(57,213,72,87)(58,133,73,119)(59,215,74,89)(60,135,75,121)(61,217,76,91)(62,137,77,123)(63,219,78,93)(64,139,79,125)(65,221,80,95)(66,127,81,113)(67,223,82,97)(68,129,83,115)(69,211,84,85)(70,131,71,117)(142,198,159,175)(144,200,161,177)(146,202,163,179)(148,204,165,181)(150,206,167,169)(152,208,155,171)(154,210,157,173), (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), (1,102,150,166)(2,165,151,101)(3,100,152,164)(4,163,153,99)(5,112,154,162)(6,161,141,111)(7,110,142,160)(8,159,143,109)(9,108,144,158)(10,157,145,107)(11,106,146,156)(12,155,147,105)(13,104,148,168)(14,167,149,103)(15,200,174,30)(16,29,175,199)(17,198,176,42)(18,41,177,197)(19,210,178,40)(20,39,179,209)(21,208,180,38)(22,37,181,207)(23,206,182,36)(24,35,169,205)(25,204,170,34)(26,33,171,203)(27,202,172,32)(28,31,173,201)(43,195,74,64)(44,63,75,194)(45,193,76,62)(46,61,77,192)(47,191,78,60)(48,59,79,190)(49,189,80,58)(50,57,81,188)(51,187,82,70)(52,69,83,186)(53,185,84,68)(54,67,71,184)(55,183,72,66)(56,65,73,196)(85,224,116,129)(86,128,117,223)(87,222,118,127)(88,140,119,221)(89,220,120,139)(90,138,121,219)(91,218,122,137)(92,136,123,217)(93,216,124,135)(94,134,125,215)(95,214,126,133)(96,132,113,213)(97,212,114,131)(98,130,115,211) );
G=PermutationGroup([(1,69,150,186),(2,54,151,71),(3,57,152,188),(4,56,153,73),(5,59,154,190),(6,44,141,75),(7,61,142,192),(8,46,143,77),(9,63,144,194),(10,48,145,79),(11,65,146,196),(12,50,147,81),(13,67,148,184),(14,52,149,83),(15,135,174,216),(16,91,175,122),(17,137,176,218),(18,93,177,124),(19,139,178,220),(20,95,179,126),(21,127,180,222),(22,97,181,114),(23,129,182,224),(24,85,169,116),(25,131,170,212),(26,87,171,118),(27,133,172,214),(28,89,173,120),(29,123,199,92),(30,219,200,138),(31,125,201,94),(32,221,202,140),(33,113,203,96),(34,223,204,128),(35,115,205,98),(36,211,206,130),(37,117,207,86),(38,213,208,132),(39,119,209,88),(40,215,210,134),(41,121,197,90),(42,217,198,136),(43,107,74,157),(45,109,76,159),(47,111,78,161),(49,99,80,163),(51,101,82,165),(53,103,84,167),(55,105,72,155),(58,106,189,156),(60,108,191,158),(62,110,193,160),(64,112,195,162),(66,100,183,164),(68,102,185,166),(70,104,187,168)], [(1,36,103,24),(2,207,104,170),(3,38,105,26),(4,209,106,172),(5,40,107,28),(6,197,108,174),(7,42,109,16),(8,199,110,176),(9,30,111,18),(10,201,112,178),(11,32,99,20),(12,203,100,180),(13,34,101,22),(14,205,102,182),(15,141,41,158),(17,143,29,160),(19,145,31,162),(21,147,33,164),(23,149,35,166),(25,151,37,168),(27,153,39,156),(43,120,190,134),(44,90,191,216),(45,122,192,136),(46,92,193,218),(47,124,194,138),(48,94,195,220),(49,126,196,140),(50,96,183,222),(51,114,184,128),(52,98,185,224),(53,116,186,130),(54,86,187,212),(55,118,188,132),(56,88,189,214),(57,213,72,87),(58,133,73,119),(59,215,74,89),(60,135,75,121),(61,217,76,91),(62,137,77,123),(63,219,78,93),(64,139,79,125),(65,221,80,95),(66,127,81,113),(67,223,82,97),(68,129,83,115),(69,211,84,85),(70,131,71,117),(142,198,159,175),(144,200,161,177),(146,202,163,179),(148,204,165,181),(150,206,167,169),(152,208,155,171),(154,210,157,173)], [(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)], [(1,102,150,166),(2,165,151,101),(3,100,152,164),(4,163,153,99),(5,112,154,162),(6,161,141,111),(7,110,142,160),(8,159,143,109),(9,108,144,158),(10,157,145,107),(11,106,146,156),(12,155,147,105),(13,104,148,168),(14,167,149,103),(15,200,174,30),(16,29,175,199),(17,198,176,42),(18,41,177,197),(19,210,178,40),(20,39,179,209),(21,208,180,38),(22,37,181,207),(23,206,182,36),(24,35,169,205),(25,204,170,34),(26,33,171,203),(27,202,172,32),(28,31,173,201),(43,195,74,64),(44,63,75,194),(45,193,76,62),(46,61,77,192),(47,191,78,60),(48,59,79,190),(49,189,80,58),(50,57,81,188),(51,187,82,70),(52,69,83,186),(53,185,84,68),(54,67,71,184),(55,183,72,66),(56,65,73,196),(85,224,116,129),(86,128,117,223),(87,222,118,127),(88,140,119,221),(89,220,120,139),(90,138,121,219),(91,218,122,137),(92,136,123,217),(93,216,124,135),(94,134,125,215),(95,214,126,133),(96,132,113,213),(97,212,114,131),(98,130,115,211)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 12 | 12 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 28 | 28 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 24 | 25 | 0 | 0 |
| 0 | 0 | 8 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 27 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 18 | 0 | 0 |
| 0 | 0 | 3 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 2 |
| 0 | 0 | 0 | 0 | 28 | 28 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,17,12,0,0,0,0,0,12],[12,0,0,0,0,0,0,17,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,28,0,0,0,0,0,28],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,24,8,0,0,0,0,25,12,0,0,0,0,0,0,28,0,0,0,0,0,27,1],[0,28,0,0,0,0,1,0,0,0,0,0,0,0,18,3,0,0,0,0,18,11,0,0,0,0,0,0,1,28,0,0,0,0,2,28] >;
70 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 4Q | 4R | 4S | 4T | 7A | 7B | 7C | 14A | ··· | 14I | 14J | 14K | 14L | 28A | ··· | 28R | 28S | ··· | 28AA |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 14 | 14 | 28 | 2 | ··· | 2 | 4 | 4 | 4 | 7 | 7 | 7 | 7 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
70 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | D7×C4○D4 |
| kernel | C42.189D14 | D7×C42 | C42⋊2D7 | C23.11D14 | Dic7⋊4D4 | D14.D4 | D14⋊D4 | Dic7.D4 | Dic7⋊3Q8 | Dic7.Q8 | C4⋊C4⋊7D7 | D28⋊C4 | D14.5D4 | D14⋊Q8 | C7×C42⋊2C2 | C42⋊2C2 | Dic7 | D14 | C42 | C22⋊C4 | C4⋊C4 | C2 |
| # reps | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 8 | 4 | 3 | 9 | 9 | 18 |
In GAP, Magma, Sage, TeX
C_4^2._{189}D_{14} % in TeX
G:=Group("C4^2.189D14"); // GroupNames label
G:=SmallGroup(448,1159);
// by ID
G=gap.SmallGroup(448,1159);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,100,1123,794,297,18822]);
// 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^-1*b^2,c*b*c^-1=d*b*d^-1=a^2*b,d*c*d^-1=a^2*c^-1>;
// generators/relations
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