metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.122D14, C14.72- 1+4, (C4×Q8)⋊5D7, (Q8×C28)⋊5C2, C4⋊C4.291D14, D14⋊Q8⋊10C2, Dic7⋊Q8⋊9C2, (C4×Dic14)⋊36C2, C4.18(C4○D28), C42⋊D7⋊33C2, C42⋊2D7⋊17C2, (C2×Q8).176D14, Dic7⋊3Q8⋊17C2, D28⋊C4.10C2, C28.116(C4○D4), (C2×C28).621C23, (C4×C28).238C22, (C2×C14).112C24, D14⋊C4.68C22, C4.D28.10C2, C28.23D4.7C2, Dic7.21(C4○D4), (C2×D28).140C22, Dic7⋊C4.68C22, C4⋊Dic7.303C22, (Q8×C14).212C22, (C4×Dic7).81C22, (C22×D7).44C23, C22.137(C23×D7), C7⋊3(C22.50C24), (C2×Dic7).211C23, C2.10(Q8.10D14), (C2×Dic14).147C22, C2.27(D7×C4○D4), C4⋊C4⋊D7⋊10C2, C2.60(C2×C4○D28), C14.53(C2×C4○D4), (C2×C4×D7).206C22, (C7×C4⋊C4).340C22, (C2×C4).653(C22×D7), SmallGroup(448,1021)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.122D14
G = < a,b,c,d | a4=b4=d2=1, c14=b2, ab=ba, ac=ca, dad=ab2, cbc-1=dbd=a2b-1, dcd=c13 >
Subgroups: 900 in 212 conjugacy classes, 97 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C2×Q8, Dic7, Dic7, C28, C28, D14, C2×C14, C42⋊C2, C4×D4, C4×Q8, C4×Q8, C22⋊Q8, C4.4D4, C42⋊2C2, C4⋊Q8, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C22.50C24, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C4×C28, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, Q8×C14, C4×Dic14, C42⋊D7, C4.D28, C42⋊2D7, Dic7⋊3Q8, D28⋊C4, D14⋊Q8, C4⋊C4⋊D7, Dic7⋊Q8, C28.23D4, Q8×C28, C42.122D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2- 1+4, C22×D7, C22.50C24, C4○D28, C23×D7, C2×C4○D28, Q8.10D14, D7×C4○D4, C42.122D14
►On 224 points
Generators in S224
(1 185 163 75)(2 186 164 76)(3 187 165 77)(4 188 166 78)(5 189 167 79)(6 190 168 80)(7 191 141 81)(8 192 142 82)(9 193 143 83)(10 194 144 84)(11 195 145 57)(12 196 146 58)(13 169 147 59)(14 170 148 60)(15 171 149 61)(16 172 150 62)(17 173 151 63)(18 174 152 64)(19 175 153 65)(20 176 154 66)(21 177 155 67)(22 178 156 68)(23 179 157 69)(24 180 158 70)(25 181 159 71)(26 182 160 72)(27 183 161 73)(28 184 162 74)(29 86 125 220)(30 87 126 221)(31 88 127 222)(32 89 128 223)(33 90 129 224)(34 91 130 197)(35 92 131 198)(36 93 132 199)(37 94 133 200)(38 95 134 201)(39 96 135 202)(40 97 136 203)(41 98 137 204)(42 99 138 205)(43 100 139 206)(44 101 140 207)(45 102 113 208)(46 103 114 209)(47 104 115 210)(48 105 116 211)(49 106 117 212)(50 107 118 213)(51 108 119 214)(52 109 120 215)(53 110 121 216)(54 111 122 217)(55 112 123 218)(56 85 124 219)
(1 219 15 205)(2 100 16 86)(3 221 17 207)(4 102 18 88)(5 223 19 209)(6 104 20 90)(7 197 21 211)(8 106 22 92)(9 199 23 213)(10 108 24 94)(11 201 25 215)(12 110 26 96)(13 203 27 217)(14 112 28 98)(29 76 43 62)(30 173 44 187)(31 78 45 64)(32 175 46 189)(33 80 47 66)(34 177 48 191)(35 82 49 68)(36 179 50 193)(37 84 51 70)(38 181 52 195)(39 58 53 72)(40 183 54 169)(41 60 55 74)(42 185 56 171)(57 134 71 120)(59 136 73 122)(61 138 75 124)(63 140 77 126)(65 114 79 128)(67 116 81 130)(69 118 83 132)(85 149 99 163)(87 151 101 165)(89 153 103 167)(91 155 105 141)(93 157 107 143)(95 159 109 145)(97 161 111 147)(113 174 127 188)(115 176 129 190)(117 178 131 192)(119 180 133 194)(121 182 135 196)(123 184 137 170)(125 186 139 172)(142 212 156 198)(144 214 158 200)(146 216 160 202)(148 218 162 204)(150 220 164 206)(152 222 166 208)(154 224 168 210)
(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 21)(2 6)(3 19)(5 17)(7 15)(8 28)(9 13)(10 26)(12 24)(14 22)(16 20)(23 27)(29 129)(30 114)(31 127)(32 140)(33 125)(34 138)(35 123)(36 136)(37 121)(38 134)(39 119)(40 132)(41 117)(42 130)(43 115)(44 128)(45 113)(46 126)(47 139)(48 124)(49 137)(50 122)(51 135)(52 120)(53 133)(54 118)(55 131)(56 116)(57 71)(58 84)(59 69)(60 82)(61 67)(62 80)(63 65)(64 78)(66 76)(68 74)(70 72)(73 83)(75 81)(77 79)(85 197)(86 210)(87 223)(88 208)(89 221)(90 206)(91 219)(92 204)(93 217)(94 202)(95 215)(96 200)(97 213)(98 198)(99 211)(100 224)(101 209)(102 222)(103 207)(104 220)(105 205)(106 218)(107 203)(108 216)(109 201)(110 214)(111 199)(112 212)(141 149)(142 162)(143 147)(144 160)(146 158)(148 156)(150 154)(151 167)(153 165)(155 163)(157 161)(164 168)(169 179)(170 192)(171 177)(172 190)(173 175)(174 188)(176 186)(178 184)(180 182)(181 195)(183 193)(185 191)(187 189)(194 196)
G:=sub<Sym(224)| (1,185,163,75)(2,186,164,76)(3,187,165,77)(4,188,166,78)(5,189,167,79)(6,190,168,80)(7,191,141,81)(8,192,142,82)(9,193,143,83)(10,194,144,84)(11,195,145,57)(12,196,146,58)(13,169,147,59)(14,170,148,60)(15,171,149,61)(16,172,150,62)(17,173,151,63)(18,174,152,64)(19,175,153,65)(20,176,154,66)(21,177,155,67)(22,178,156,68)(23,179,157,69)(24,180,158,70)(25,181,159,71)(26,182,160,72)(27,183,161,73)(28,184,162,74)(29,86,125,220)(30,87,126,221)(31,88,127,222)(32,89,128,223)(33,90,129,224)(34,91,130,197)(35,92,131,198)(36,93,132,199)(37,94,133,200)(38,95,134,201)(39,96,135,202)(40,97,136,203)(41,98,137,204)(42,99,138,205)(43,100,139,206)(44,101,140,207)(45,102,113,208)(46,103,114,209)(47,104,115,210)(48,105,116,211)(49,106,117,212)(50,107,118,213)(51,108,119,214)(52,109,120,215)(53,110,121,216)(54,111,122,217)(55,112,123,218)(56,85,124,219), (1,219,15,205)(2,100,16,86)(3,221,17,207)(4,102,18,88)(5,223,19,209)(6,104,20,90)(7,197,21,211)(8,106,22,92)(9,199,23,213)(10,108,24,94)(11,201,25,215)(12,110,26,96)(13,203,27,217)(14,112,28,98)(29,76,43,62)(30,173,44,187)(31,78,45,64)(32,175,46,189)(33,80,47,66)(34,177,48,191)(35,82,49,68)(36,179,50,193)(37,84,51,70)(38,181,52,195)(39,58,53,72)(40,183,54,169)(41,60,55,74)(42,185,56,171)(57,134,71,120)(59,136,73,122)(61,138,75,124)(63,140,77,126)(65,114,79,128)(67,116,81,130)(69,118,83,132)(85,149,99,163)(87,151,101,165)(89,153,103,167)(91,155,105,141)(93,157,107,143)(95,159,109,145)(97,161,111,147)(113,174,127,188)(115,176,129,190)(117,178,131,192)(119,180,133,194)(121,182,135,196)(123,184,137,170)(125,186,139,172)(142,212,156,198)(144,214,158,200)(146,216,160,202)(148,218,162,204)(150,220,164,206)(152,222,166,208)(154,224,168,210), (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), (1,21)(2,6)(3,19)(5,17)(7,15)(8,28)(9,13)(10,26)(12,24)(14,22)(16,20)(23,27)(29,129)(30,114)(31,127)(32,140)(33,125)(34,138)(35,123)(36,136)(37,121)(38,134)(39,119)(40,132)(41,117)(42,130)(43,115)(44,128)(45,113)(46,126)(47,139)(48,124)(49,137)(50,122)(51,135)(52,120)(53,133)(54,118)(55,131)(56,116)(57,71)(58,84)(59,69)(60,82)(61,67)(62,80)(63,65)(64,78)(66,76)(68,74)(70,72)(73,83)(75,81)(77,79)(85,197)(86,210)(87,223)(88,208)(89,221)(90,206)(91,219)(92,204)(93,217)(94,202)(95,215)(96,200)(97,213)(98,198)(99,211)(100,224)(101,209)(102,222)(103,207)(104,220)(105,205)(106,218)(107,203)(108,216)(109,201)(110,214)(111,199)(112,212)(141,149)(142,162)(143,147)(144,160)(146,158)(148,156)(150,154)(151,167)(153,165)(155,163)(157,161)(164,168)(169,179)(170,192)(171,177)(172,190)(173,175)(174,188)(176,186)(178,184)(180,182)(181,195)(183,193)(185,191)(187,189)(194,196)>;
G:=Group( (1,185,163,75)(2,186,164,76)(3,187,165,77)(4,188,166,78)(5,189,167,79)(6,190,168,80)(7,191,141,81)(8,192,142,82)(9,193,143,83)(10,194,144,84)(11,195,145,57)(12,196,146,58)(13,169,147,59)(14,170,148,60)(15,171,149,61)(16,172,150,62)(17,173,151,63)(18,174,152,64)(19,175,153,65)(20,176,154,66)(21,177,155,67)(22,178,156,68)(23,179,157,69)(24,180,158,70)(25,181,159,71)(26,182,160,72)(27,183,161,73)(28,184,162,74)(29,86,125,220)(30,87,126,221)(31,88,127,222)(32,89,128,223)(33,90,129,224)(34,91,130,197)(35,92,131,198)(36,93,132,199)(37,94,133,200)(38,95,134,201)(39,96,135,202)(40,97,136,203)(41,98,137,204)(42,99,138,205)(43,100,139,206)(44,101,140,207)(45,102,113,208)(46,103,114,209)(47,104,115,210)(48,105,116,211)(49,106,117,212)(50,107,118,213)(51,108,119,214)(52,109,120,215)(53,110,121,216)(54,111,122,217)(55,112,123,218)(56,85,124,219), (1,219,15,205)(2,100,16,86)(3,221,17,207)(4,102,18,88)(5,223,19,209)(6,104,20,90)(7,197,21,211)(8,106,22,92)(9,199,23,213)(10,108,24,94)(11,201,25,215)(12,110,26,96)(13,203,27,217)(14,112,28,98)(29,76,43,62)(30,173,44,187)(31,78,45,64)(32,175,46,189)(33,80,47,66)(34,177,48,191)(35,82,49,68)(36,179,50,193)(37,84,51,70)(38,181,52,195)(39,58,53,72)(40,183,54,169)(41,60,55,74)(42,185,56,171)(57,134,71,120)(59,136,73,122)(61,138,75,124)(63,140,77,126)(65,114,79,128)(67,116,81,130)(69,118,83,132)(85,149,99,163)(87,151,101,165)(89,153,103,167)(91,155,105,141)(93,157,107,143)(95,159,109,145)(97,161,111,147)(113,174,127,188)(115,176,129,190)(117,178,131,192)(119,180,133,194)(121,182,135,196)(123,184,137,170)(125,186,139,172)(142,212,156,198)(144,214,158,200)(146,216,160,202)(148,218,162,204)(150,220,164,206)(152,222,166,208)(154,224,168,210), (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), (1,21)(2,6)(3,19)(5,17)(7,15)(8,28)(9,13)(10,26)(12,24)(14,22)(16,20)(23,27)(29,129)(30,114)(31,127)(32,140)(33,125)(34,138)(35,123)(36,136)(37,121)(38,134)(39,119)(40,132)(41,117)(42,130)(43,115)(44,128)(45,113)(46,126)(47,139)(48,124)(49,137)(50,122)(51,135)(52,120)(53,133)(54,118)(55,131)(56,116)(57,71)(58,84)(59,69)(60,82)(61,67)(62,80)(63,65)(64,78)(66,76)(68,74)(70,72)(73,83)(75,81)(77,79)(85,197)(86,210)(87,223)(88,208)(89,221)(90,206)(91,219)(92,204)(93,217)(94,202)(95,215)(96,200)(97,213)(98,198)(99,211)(100,224)(101,209)(102,222)(103,207)(104,220)(105,205)(106,218)(107,203)(108,216)(109,201)(110,214)(111,199)(112,212)(141,149)(142,162)(143,147)(144,160)(146,158)(148,156)(150,154)(151,167)(153,165)(155,163)(157,161)(164,168)(169,179)(170,192)(171,177)(172,190)(173,175)(174,188)(176,186)(178,184)(180,182)(181,195)(183,193)(185,191)(187,189)(194,196) );
G=PermutationGroup([[(1,185,163,75),(2,186,164,76),(3,187,165,77),(4,188,166,78),(5,189,167,79),(6,190,168,80),(7,191,141,81),(8,192,142,82),(9,193,143,83),(10,194,144,84),(11,195,145,57),(12,196,146,58),(13,169,147,59),(14,170,148,60),(15,171,149,61),(16,172,150,62),(17,173,151,63),(18,174,152,64),(19,175,153,65),(20,176,154,66),(21,177,155,67),(22,178,156,68),(23,179,157,69),(24,180,158,70),(25,181,159,71),(26,182,160,72),(27,183,161,73),(28,184,162,74),(29,86,125,220),(30,87,126,221),(31,88,127,222),(32,89,128,223),(33,90,129,224),(34,91,130,197),(35,92,131,198),(36,93,132,199),(37,94,133,200),(38,95,134,201),(39,96,135,202),(40,97,136,203),(41,98,137,204),(42,99,138,205),(43,100,139,206),(44,101,140,207),(45,102,113,208),(46,103,114,209),(47,104,115,210),(48,105,116,211),(49,106,117,212),(50,107,118,213),(51,108,119,214),(52,109,120,215),(53,110,121,216),(54,111,122,217),(55,112,123,218),(56,85,124,219)], [(1,219,15,205),(2,100,16,86),(3,221,17,207),(4,102,18,88),(5,223,19,209),(6,104,20,90),(7,197,21,211),(8,106,22,92),(9,199,23,213),(10,108,24,94),(11,201,25,215),(12,110,26,96),(13,203,27,217),(14,112,28,98),(29,76,43,62),(30,173,44,187),(31,78,45,64),(32,175,46,189),(33,80,47,66),(34,177,48,191),(35,82,49,68),(36,179,50,193),(37,84,51,70),(38,181,52,195),(39,58,53,72),(40,183,54,169),(41,60,55,74),(42,185,56,171),(57,134,71,120),(59,136,73,122),(61,138,75,124),(63,140,77,126),(65,114,79,128),(67,116,81,130),(69,118,83,132),(85,149,99,163),(87,151,101,165),(89,153,103,167),(91,155,105,141),(93,157,107,143),(95,159,109,145),(97,161,111,147),(113,174,127,188),(115,176,129,190),(117,178,131,192),(119,180,133,194),(121,182,135,196),(123,184,137,170),(125,186,139,172),(142,212,156,198),(144,214,158,200),(146,216,160,202),(148,218,162,204),(150,220,164,206),(152,222,166,208),(154,224,168,210)], [(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)], [(1,21),(2,6),(3,19),(5,17),(7,15),(8,28),(9,13),(10,26),(12,24),(14,22),(16,20),(23,27),(29,129),(30,114),(31,127),(32,140),(33,125),(34,138),(35,123),(36,136),(37,121),(38,134),(39,119),(40,132),(41,117),(42,130),(43,115),(44,128),(45,113),(46,126),(47,139),(48,124),(49,137),(50,122),(51,135),(52,120),(53,133),(54,118),(55,131),(56,116),(57,71),(58,84),(59,69),(60,82),(61,67),(62,80),(63,65),(64,78),(66,76),(68,74),(70,72),(73,83),(75,81),(77,79),(85,197),(86,210),(87,223),(88,208),(89,221),(90,206),(91,219),(92,204),(93,217),(94,202),(95,215),(96,200),(97,213),(98,198),(99,211),(100,224),(101,209),(102,222),(103,207),(104,220),(105,205),(106,218),(107,203),(108,216),(109,201),(110,214),(111,199),(112,212),(141,149),(142,162),(143,147),(144,160),(146,158),(148,156),(150,154),(151,167),(153,165),(155,163),(157,161),(164,168),(169,179),(170,192),(171,177),(172,190),(173,175),(174,188),(176,186),(178,184),(180,182),(181,195),(183,193),(185,191),(187,189),(194,196)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 4Q | 4R | 4S | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 2 | ··· | 2 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 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 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | C4○D28 | 2- 1+4 | Q8.10D14 | D7×C4○D4 |
| kernel | C42.122D14 | C4×Dic14 | C42⋊D7 | C4.D28 | C42⋊2D7 | Dic7⋊3Q8 | D28⋊C4 | D14⋊Q8 | C4⋊C4⋊D7 | Dic7⋊Q8 | C28.23D4 | Q8×C28 | C4×Q8 | Dic7 | C28 | C42 | C4⋊C4 | C2×Q8 | C4 | C14 | C2 | C2 |
| # reps | 1 | 1 | 2 | 1 | 2 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 3 | 4 | 4 | 9 | 9 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of C42.122D14 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 13 | 0 | 0 |
| 0 | 0 | 4 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 2 |
| 0 | 0 | 0 | 0 | 1 | 12 |
| 10 | 10 | 0 | 0 | 0 | 0 |
| 19 | 22 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 12 | 28 |
| 10 | 10 | 0 | 0 | 0 | 0 |
| 22 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 24 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 12 | 28 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,18,4,0,0,0,0,13,11,0,0,0,0,0,0,17,0,0,0,0,0,0,17],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,0,0,0,0,17,1,0,0,0,0,2,12],[10,19,0,0,0,0,10,22,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,1,12,0,0,0,0,0,28],[10,22,0,0,0,0,10,19,0,0,0,0,0,0,1,24,0,0,0,0,0,28,0,0,0,0,0,0,1,12,0,0,0,0,0,28] >;
C42.122D14 in GAP, Magma, Sage, TeX
C_4^2._{122}D_{14} % in TeX
G:=Group("C4^2.122D14"); // GroupNames label
G:=SmallGroup(448,1021);
// by ID
G=gap.SmallGroup(448,1021);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,232,758,100,794,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=d^2=1,c^14=b^2,a*b=b*a,a*c=c*a,d*a*d=a*b^2,c*b*c^-1=d*b*d=a^2*b^-1,d*c*d=c^13>;
// generators/relations