metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.148D14, C14.952- (1+4), C14.1302+ (1+4), (C4×D7)⋊1Q8, C28⋊Q8⋊35C2, C4.39(Q8×D7), D14.4(C2×Q8), C42.C2⋊4D7, C28.50(C2×Q8), C4⋊C4.111D14, C28⋊2Q8⋊32C2, Dic7.6(C2×Q8), Dic7.Q8⋊32C2, (C2×C28).87C23, D14⋊Q8.2C2, C4.Dic14⋊33C2, C42⋊D7.6C2, C14.42(C22×Q8), (C4×C28).193C22, (C2×C14).233C24, D14⋊C4.39C22, D14⋊2Q8.11C2, C2.55(D4⋊8D14), C4⋊Dic7.240C22, C22.254(C23×D7), Dic7⋊C4.122C22, C7⋊4(C23.41C23), (C4×Dic7).140C22, (C2×Dic7).121C23, (C2×Dic14).40C22, (C22×D7).220C23, C2.57(D4.10D14), C2.25(C2×Q8×D7), (D7×C4⋊C4).11C2, (C7×C42.C2)⋊6C2, C4⋊C4⋊7D7.12C2, (C2×C4×D7).124C22, (C7×C4⋊C4).188C22, (C2×C4).203(C22×D7), SmallGroup(448,1142)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 892 in 206 conjugacy classes, 103 normal (43 characteristic)
C1, C2 [×3], C2 [×2], C4 [×2], C4 [×14], C22, C22 [×4], C7, C2×C4 [×3], C2×C4 [×4], C2×C4 [×13], Q8 [×4], C23, D7 [×2], C14 [×3], C42, C42 [×3], C22⋊C4 [×4], C4⋊C4 [×2], C4⋊C4 [×4], C4⋊C4 [×14], C22×C4 [×3], C2×Q8 [×4], Dic7 [×2], Dic7 [×6], C28 [×2], C28 [×6], D14 [×2], D14 [×2], C2×C14, C2×C4⋊C4, C42⋊C2 [×2], C22⋊Q8 [×4], C42.C2, C42.C2 [×3], C4⋊Q8 [×4], Dic14 [×4], C4×D7 [×4], C4×D7 [×2], C2×Dic7 [×3], C2×Dic7 [×4], C2×C28 [×3], C2×C28 [×4], C22×D7, C23.41C23, C4×Dic7, C4×Dic7 [×2], Dic7⋊C4 [×2], Dic7⋊C4 [×6], C4⋊Dic7 [×2], C4⋊Dic7 [×4], D14⋊C4 [×2], D14⋊C4 [×2], C4×C28, C7×C4⋊C4 [×2], C7×C4⋊C4 [×4], C2×Dic14 [×4], C2×C4×D7, C2×C4×D7 [×2], C28⋊2Q8, C42⋊D7, C28⋊Q8, C28⋊Q8 [×2], Dic7.Q8 [×2], C4.Dic14, D7×C4⋊C4, C4⋊C4⋊7D7, D14⋊Q8 [×2], D14⋊2Q8 [×2], C7×C42.C2, C42.148D14
Quotients:
C1, C2 [×15], C22 [×35], Q8 [×4], C23 [×15], D7, C2×Q8 [×6], C24, D14 [×7], C22×Q8, 2+ (1+4), 2- (1+4), C22×D7 [×7], C23.41C23, Q8×D7 [×2], C23×D7, C2×Q8×D7, D4⋊8D14, D4.10D14, C42.148D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=d2=b2, ab=ba, cac-1=dad-1=a-1, cbc-1=a2b-1, dbd-1=b-1, dcd-1=c13 >
►On 224 points
Generators in S224
(1 50 82 221)(2 222 83 51)(3 52 84 223)(4 224 57 53)(5 54 58 197)(6 198 59 55)(7 56 60 199)(8 200 61 29)(9 30 62 201)(10 202 63 31)(11 32 64 203)(12 204 65 33)(13 34 66 205)(14 206 67 35)(15 36 68 207)(16 208 69 37)(17 38 70 209)(18 210 71 39)(19 40 72 211)(20 212 73 41)(21 42 74 213)(22 214 75 43)(23 44 76 215)(24 216 77 45)(25 46 78 217)(26 218 79 47)(27 48 80 219)(28 220 81 49)(85 141 174 117)(86 118 175 142)(87 143 176 119)(88 120 177 144)(89 145 178 121)(90 122 179 146)(91 147 180 123)(92 124 181 148)(93 149 182 125)(94 126 183 150)(95 151 184 127)(96 128 185 152)(97 153 186 129)(98 130 187 154)(99 155 188 131)(100 132 189 156)(101 157 190 133)(102 134 191 158)(103 159 192 135)(104 136 193 160)(105 161 194 137)(106 138 195 162)(107 163 196 139)(108 140 169 164)(109 165 170 113)(110 114 171 166)(111 167 172 115)(112 116 173 168)
(1 103 15 89)(2 179 16 193)(3 105 17 91)(4 181 18 195)(5 107 19 93)(6 183 20 169)(7 109 21 95)(8 185 22 171)(9 111 23 97)(10 187 24 173)(11 85 25 99)(12 189 26 175)(13 87 27 101)(14 191 28 177)(29 128 43 114)(30 167 44 153)(31 130 45 116)(32 141 46 155)(33 132 47 118)(34 143 48 157)(35 134 49 120)(36 145 50 159)(37 136 51 122)(38 147 52 161)(39 138 53 124)(40 149 54 163)(41 140 55 126)(42 151 56 165)(57 92 71 106)(58 196 72 182)(59 94 73 108)(60 170 74 184)(61 96 75 110)(62 172 76 186)(63 98 77 112)(64 174 78 188)(65 100 79 86)(66 176 80 190)(67 102 81 88)(68 178 82 192)(69 104 83 90)(70 180 84 194)(113 213 127 199)(115 215 129 201)(117 217 131 203)(119 219 133 205)(121 221 135 207)(123 223 137 209)(125 197 139 211)(142 204 156 218)(144 206 158 220)(146 208 160 222)(148 210 162 224)(150 212 164 198)(152 214 166 200)(154 216 168 202)
(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 42 43 56)(30 55 44 41)(31 40 45 54)(32 53 46 39)(33 38 47 52)(34 51 48 37)(35 36 49 50)(57 78 71 64)(58 63 72 77)(59 76 73 62)(60 61 74 75)(65 70 79 84)(66 83 80 69)(67 68 81 82)(85 195 99 181)(86 180 100 194)(87 193 101 179)(88 178 102 192)(89 191 103 177)(90 176 104 190)(91 189 105 175)(92 174 106 188)(93 187 107 173)(94 172 108 186)(95 185 109 171)(96 170 110 184)(97 183 111 169)(98 196 112 182)(113 166 127 152)(114 151 128 165)(115 164 129 150)(116 149 130 163)(117 162 131 148)(118 147 132 161)(119 160 133 146)(120 145 134 159)(121 158 135 144)(122 143 136 157)(123 156 137 142)(124 141 138 155)(125 154 139 168)(126 167 140 153)(197 202 211 216)(198 215 212 201)(199 200 213 214)(203 224 217 210)(204 209 218 223)(205 222 219 208)(206 207 220 221)
G:=sub<Sym(224)| (1,50,82,221)(2,222,83,51)(3,52,84,223)(4,224,57,53)(5,54,58,197)(6,198,59,55)(7,56,60,199)(8,200,61,29)(9,30,62,201)(10,202,63,31)(11,32,64,203)(12,204,65,33)(13,34,66,205)(14,206,67,35)(15,36,68,207)(16,208,69,37)(17,38,70,209)(18,210,71,39)(19,40,72,211)(20,212,73,41)(21,42,74,213)(22,214,75,43)(23,44,76,215)(24,216,77,45)(25,46,78,217)(26,218,79,47)(27,48,80,219)(28,220,81,49)(85,141,174,117)(86,118,175,142)(87,143,176,119)(88,120,177,144)(89,145,178,121)(90,122,179,146)(91,147,180,123)(92,124,181,148)(93,149,182,125)(94,126,183,150)(95,151,184,127)(96,128,185,152)(97,153,186,129)(98,130,187,154)(99,155,188,131)(100,132,189,156)(101,157,190,133)(102,134,191,158)(103,159,192,135)(104,136,193,160)(105,161,194,137)(106,138,195,162)(107,163,196,139)(108,140,169,164)(109,165,170,113)(110,114,171,166)(111,167,172,115)(112,116,173,168), (1,103,15,89)(2,179,16,193)(3,105,17,91)(4,181,18,195)(5,107,19,93)(6,183,20,169)(7,109,21,95)(8,185,22,171)(9,111,23,97)(10,187,24,173)(11,85,25,99)(12,189,26,175)(13,87,27,101)(14,191,28,177)(29,128,43,114)(30,167,44,153)(31,130,45,116)(32,141,46,155)(33,132,47,118)(34,143,48,157)(35,134,49,120)(36,145,50,159)(37,136,51,122)(38,147,52,161)(39,138,53,124)(40,149,54,163)(41,140,55,126)(42,151,56,165)(57,92,71,106)(58,196,72,182)(59,94,73,108)(60,170,74,184)(61,96,75,110)(62,172,76,186)(63,98,77,112)(64,174,78,188)(65,100,79,86)(66,176,80,190)(67,102,81,88)(68,178,82,192)(69,104,83,90)(70,180,84,194)(113,213,127,199)(115,215,129,201)(117,217,131,203)(119,219,133,205)(121,221,135,207)(123,223,137,209)(125,197,139,211)(142,204,156,218)(144,206,158,220)(146,208,160,222)(148,210,162,224)(150,212,164,198)(152,214,166,200)(154,216,168,202), (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)(29,42,43,56)(30,55,44,41)(31,40,45,54)(32,53,46,39)(33,38,47,52)(34,51,48,37)(35,36,49,50)(57,78,71,64)(58,63,72,77)(59,76,73,62)(60,61,74,75)(65,70,79,84)(66,83,80,69)(67,68,81,82)(85,195,99,181)(86,180,100,194)(87,193,101,179)(88,178,102,192)(89,191,103,177)(90,176,104,190)(91,189,105,175)(92,174,106,188)(93,187,107,173)(94,172,108,186)(95,185,109,171)(96,170,110,184)(97,183,111,169)(98,196,112,182)(113,166,127,152)(114,151,128,165)(115,164,129,150)(116,149,130,163)(117,162,131,148)(118,147,132,161)(119,160,133,146)(120,145,134,159)(121,158,135,144)(122,143,136,157)(123,156,137,142)(124,141,138,155)(125,154,139,168)(126,167,140,153)(197,202,211,216)(198,215,212,201)(199,200,213,214)(203,224,217,210)(204,209,218,223)(205,222,219,208)(206,207,220,221)>;
G:=Group( (1,50,82,221)(2,222,83,51)(3,52,84,223)(4,224,57,53)(5,54,58,197)(6,198,59,55)(7,56,60,199)(8,200,61,29)(9,30,62,201)(10,202,63,31)(11,32,64,203)(12,204,65,33)(13,34,66,205)(14,206,67,35)(15,36,68,207)(16,208,69,37)(17,38,70,209)(18,210,71,39)(19,40,72,211)(20,212,73,41)(21,42,74,213)(22,214,75,43)(23,44,76,215)(24,216,77,45)(25,46,78,217)(26,218,79,47)(27,48,80,219)(28,220,81,49)(85,141,174,117)(86,118,175,142)(87,143,176,119)(88,120,177,144)(89,145,178,121)(90,122,179,146)(91,147,180,123)(92,124,181,148)(93,149,182,125)(94,126,183,150)(95,151,184,127)(96,128,185,152)(97,153,186,129)(98,130,187,154)(99,155,188,131)(100,132,189,156)(101,157,190,133)(102,134,191,158)(103,159,192,135)(104,136,193,160)(105,161,194,137)(106,138,195,162)(107,163,196,139)(108,140,169,164)(109,165,170,113)(110,114,171,166)(111,167,172,115)(112,116,173,168), (1,103,15,89)(2,179,16,193)(3,105,17,91)(4,181,18,195)(5,107,19,93)(6,183,20,169)(7,109,21,95)(8,185,22,171)(9,111,23,97)(10,187,24,173)(11,85,25,99)(12,189,26,175)(13,87,27,101)(14,191,28,177)(29,128,43,114)(30,167,44,153)(31,130,45,116)(32,141,46,155)(33,132,47,118)(34,143,48,157)(35,134,49,120)(36,145,50,159)(37,136,51,122)(38,147,52,161)(39,138,53,124)(40,149,54,163)(41,140,55,126)(42,151,56,165)(57,92,71,106)(58,196,72,182)(59,94,73,108)(60,170,74,184)(61,96,75,110)(62,172,76,186)(63,98,77,112)(64,174,78,188)(65,100,79,86)(66,176,80,190)(67,102,81,88)(68,178,82,192)(69,104,83,90)(70,180,84,194)(113,213,127,199)(115,215,129,201)(117,217,131,203)(119,219,133,205)(121,221,135,207)(123,223,137,209)(125,197,139,211)(142,204,156,218)(144,206,158,220)(146,208,160,222)(148,210,162,224)(150,212,164,198)(152,214,166,200)(154,216,168,202), (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)(29,42,43,56)(30,55,44,41)(31,40,45,54)(32,53,46,39)(33,38,47,52)(34,51,48,37)(35,36,49,50)(57,78,71,64)(58,63,72,77)(59,76,73,62)(60,61,74,75)(65,70,79,84)(66,83,80,69)(67,68,81,82)(85,195,99,181)(86,180,100,194)(87,193,101,179)(88,178,102,192)(89,191,103,177)(90,176,104,190)(91,189,105,175)(92,174,106,188)(93,187,107,173)(94,172,108,186)(95,185,109,171)(96,170,110,184)(97,183,111,169)(98,196,112,182)(113,166,127,152)(114,151,128,165)(115,164,129,150)(116,149,130,163)(117,162,131,148)(118,147,132,161)(119,160,133,146)(120,145,134,159)(121,158,135,144)(122,143,136,157)(123,156,137,142)(124,141,138,155)(125,154,139,168)(126,167,140,153)(197,202,211,216)(198,215,212,201)(199,200,213,214)(203,224,217,210)(204,209,218,223)(205,222,219,208)(206,207,220,221) );
G=PermutationGroup([(1,50,82,221),(2,222,83,51),(3,52,84,223),(4,224,57,53),(5,54,58,197),(6,198,59,55),(7,56,60,199),(8,200,61,29),(9,30,62,201),(10,202,63,31),(11,32,64,203),(12,204,65,33),(13,34,66,205),(14,206,67,35),(15,36,68,207),(16,208,69,37),(17,38,70,209),(18,210,71,39),(19,40,72,211),(20,212,73,41),(21,42,74,213),(22,214,75,43),(23,44,76,215),(24,216,77,45),(25,46,78,217),(26,218,79,47),(27,48,80,219),(28,220,81,49),(85,141,174,117),(86,118,175,142),(87,143,176,119),(88,120,177,144),(89,145,178,121),(90,122,179,146),(91,147,180,123),(92,124,181,148),(93,149,182,125),(94,126,183,150),(95,151,184,127),(96,128,185,152),(97,153,186,129),(98,130,187,154),(99,155,188,131),(100,132,189,156),(101,157,190,133),(102,134,191,158),(103,159,192,135),(104,136,193,160),(105,161,194,137),(106,138,195,162),(107,163,196,139),(108,140,169,164),(109,165,170,113),(110,114,171,166),(111,167,172,115),(112,116,173,168)], [(1,103,15,89),(2,179,16,193),(3,105,17,91),(4,181,18,195),(5,107,19,93),(6,183,20,169),(7,109,21,95),(8,185,22,171),(9,111,23,97),(10,187,24,173),(11,85,25,99),(12,189,26,175),(13,87,27,101),(14,191,28,177),(29,128,43,114),(30,167,44,153),(31,130,45,116),(32,141,46,155),(33,132,47,118),(34,143,48,157),(35,134,49,120),(36,145,50,159),(37,136,51,122),(38,147,52,161),(39,138,53,124),(40,149,54,163),(41,140,55,126),(42,151,56,165),(57,92,71,106),(58,196,72,182),(59,94,73,108),(60,170,74,184),(61,96,75,110),(62,172,76,186),(63,98,77,112),(64,174,78,188),(65,100,79,86),(66,176,80,190),(67,102,81,88),(68,178,82,192),(69,104,83,90),(70,180,84,194),(113,213,127,199),(115,215,129,201),(117,217,131,203),(119,219,133,205),(121,221,135,207),(123,223,137,209),(125,197,139,211),(142,204,156,218),(144,206,158,220),(146,208,160,222),(148,210,162,224),(150,212,164,198),(152,214,166,200),(154,216,168,202)], [(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),(29,42,43,56),(30,55,44,41),(31,40,45,54),(32,53,46,39),(33,38,47,52),(34,51,48,37),(35,36,49,50),(57,78,71,64),(58,63,72,77),(59,76,73,62),(60,61,74,75),(65,70,79,84),(66,83,80,69),(67,68,81,82),(85,195,99,181),(86,180,100,194),(87,193,101,179),(88,178,102,192),(89,191,103,177),(90,176,104,190),(91,189,105,175),(92,174,106,188),(93,187,107,173),(94,172,108,186),(95,185,109,171),(96,170,110,184),(97,183,111,169),(98,196,112,182),(113,166,127,152),(114,151,128,165),(115,164,129,150),(116,149,130,163),(117,162,131,148),(118,147,132,161),(119,160,133,146),(120,145,134,159),(121,158,135,144),(122,143,136,157),(123,156,137,142),(124,141,138,155),(125,154,139,168),(126,167,140,153),(197,202,211,216),(198,215,212,201),(199,200,213,214),(203,224,217,210),(204,209,218,223),(205,222,219,208),(206,207,220,221)])
Matrix representation ►G ⊆ GL8(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 25 | 19 | 21 | 19 |
| 0 | 0 | 0 | 0 | 23 | 21 | 7 | 27 |
| 0 | 0 | 0 | 0 | 15 | 24 | 25 | 2 |
| 0 | 0 | 0 | 0 | 16 | 16 | 11 | 16 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 16 | 23 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 13 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 1 | 21 | 23 |
| 0 | 0 | 0 | 0 | 9 | 23 | 6 | 8 |
| 13 | 19 | 0 | 0 | 0 | 0 | 0 | 0 |
| 10 | 19 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 10 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 10 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 22 | 16 | 10 | 24 |
| 0 | 0 | 0 | 0 | 14 | 4 | 16 | 13 |
| 0 | 0 | 0 | 0 | 10 | 24 | 6 | 9 |
| 0 | 0 | 0 | 0 | 10 | 27 | 26 | 26 |
| 0 | 17 | 0 | 0 | 0 | 0 | 0 | 0 |
| 17 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 27 | 5 | 24 | 10 |
| 0 | 0 | 0 | 0 | 15 | 25 | 13 | 16 |
| 0 | 0 | 0 | 0 | 9 | 3 | 9 | 6 |
| 0 | 0 | 0 | 0 | 11 | 19 | 26 | 26 |
G:=sub<GL(8,GF(29))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,25,23,15,16,0,0,0,0,19,21,24,16,0,0,0,0,21,7,25,11,0,0,0,0,19,27,2,16],[0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,16,9,2,9,0,0,0,0,23,13,1,23,0,0,0,0,0,0,21,6,0,0,0,0,0,0,23,8],[13,10,0,0,0,0,0,0,19,19,0,0,0,0,0,0,0,0,16,19,0,0,0,0,0,0,10,10,0,0,0,0,0,0,0,0,22,14,10,10,0,0,0,0,16,4,24,27,0,0,0,0,10,16,6,26,0,0,0,0,24,13,9,26],[0,17,0,0,0,0,0,0,17,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,27,15,9,11,0,0,0,0,5,25,3,19,0,0,0,0,24,13,9,26,0,0,0,0,10,16,6,26] >;
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | ··· | 4H | 4I | 4J | 4K | ··· | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | - | + | + | + | + | - | - | + | - |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | Q8 | D7 | D14 | D14 | 2+ (1+4) | 2- (1+4) | Q8×D7 | D4⋊8D14 | D4.10D14 |
| kernel | C42.148D14 | C28⋊2Q8 | C42⋊D7 | C28⋊Q8 | Dic7.Q8 | C4.Dic14 | D7×C4⋊C4 | C4⋊C4⋊7D7 | D14⋊Q8 | D14⋊2Q8 | C7×C42.C2 | C4×D7 | C42.C2 | C42 | C4⋊C4 | C14 | C14 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 3 | 2 | 1 | 1 | 1 | 2 | 2 | 1 | 4 | 3 | 3 | 18 | 1 | 1 | 6 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{148}D_{14} % in TeX
G:=Group("C4^2.148D14"); // GroupNames label
G:=SmallGroup(448,1142);
// by ID
G=gap.SmallGroup(448,1142);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,268,675,297,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=a^2*b^-1,d*b*d^-1=b^-1,d*c*d^-1=c^13>;
// generators/relations
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ℤ
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