metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.237D14, C4⋊C4.206D14, (D7×C42)⋊11C2, C42.C2⋊16D7, D28⋊C4⋊35C2, D14⋊2Q8⋊36C2, C4.D28⋊24C2, C28⋊1D4.11C2, Dic7⋊3Q8⋊35C2, D14.10(C4○D4), D14.5D4⋊33C2, C28.128(C4○D4), (C2×C14).235C24, (C2×C28).506C23, (C4×C28).195C22, D14⋊C4.60C22, C4.19(Q8⋊2D7), Dic7.44(C4○D4), (C2×D28).163C22, Dic7⋊C4.51C22, C4⋊Dic7.241C22, C22.256(C23×D7), (C4×Dic7).142C22, (C2×Dic7).312C23, (C22×D7).101C23, C7⋊10(C23.36C23), (C2×Dic14).179C22, C2.86(D7×C4○D4), C4⋊C4⋊D7⋊33C2, C4⋊C4⋊7D7⋊35C2, (C7×C42.C2)⋊8C2, C14.197(C2×C4○D4), C2.22(C2×Q8⋊2D7), (C2×C4×D7).125C22, (C2×C4).79(C22×D7), (C7×C4⋊C4).190C22, SmallGroup(448,1144)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1084 in 234 conjugacy classes, 99 normal (43 characteristic)
C1, C2 [×3], C2 [×4], C4 [×2], C4 [×12], C22, C22 [×10], C7, C2×C4 [×3], C2×C4 [×4], C2×C4 [×15], D4 [×6], Q8 [×2], C23 [×3], D7 [×4], C14 [×3], C42, C42 [×5], C22⋊C4 [×10], C4⋊C4 [×2], C4⋊C4 [×4], C4⋊C4 [×4], C22×C4 [×5], C2×D4 [×3], C2×Q8, Dic7 [×2], Dic7 [×4], C28 [×2], C28 [×6], D14 [×2], D14 [×8], C2×C14, C2×C42, C42⋊C2 [×2], C4×D4 [×3], C4×Q8, C4⋊D4, C22⋊Q8, C22.D4 [×2], C4.4D4, C42.C2, C42⋊2C2 [×2], Dic14 [×2], C4×D7 [×10], D28 [×6], C2×Dic7 [×3], C2×Dic7 [×2], C2×C28 [×3], C2×C28 [×4], C22×D7, C22×D7 [×2], C23.36C23, C4×Dic7 [×3], C4×Dic7 [×2], Dic7⋊C4 [×2], C4⋊Dic7 [×2], D14⋊C4 [×10], C4×C28, C7×C4⋊C4 [×2], C7×C4⋊C4 [×4], C2×Dic14, C2×C4×D7 [×3], C2×C4×D7 [×2], C2×D28, C2×D28 [×2], D7×C42, C4.D28, Dic7⋊3Q8, C4⋊C4⋊7D7 [×2], D28⋊C4, D28⋊C4 [×2], D14.5D4 [×2], C28⋊1D4, D14⋊2Q8, C4⋊C4⋊D7 [×2], C7×C42.C2, C42.237D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×6], C24, D14 [×7], C2×C4○D4 [×3], C22×D7 [×7], C23.36C23, Q8⋊2D7 [×2], C23×D7, C2×Q8⋊2D7, D7×C4○D4 [×2], C42.237D14
Generators and relations
G = < a,b,c,d | a4=b4=d2=1, c14=a2, ab=ba, cac-1=dad=ab2, cbc-1=dbd=a2b, dcd=a2c13 >
►On 224 points
Generators in S224
(1 205 15 219)(2 169 16 183)(3 207 17 221)(4 171 18 185)(5 209 19 223)(6 173 20 187)(7 211 21 197)(8 175 22 189)(9 213 23 199)(10 177 24 191)(11 215 25 201)(12 179 26 193)(13 217 27 203)(14 181 28 195)(29 111 43 97)(30 58 44 72)(31 85 45 99)(32 60 46 74)(33 87 47 101)(34 62 48 76)(35 89 49 103)(36 64 50 78)(37 91 51 105)(38 66 52 80)(39 93 53 107)(40 68 54 82)(41 95 55 109)(42 70 56 84)(57 138 71 124)(59 140 73 126)(61 114 75 128)(63 116 77 130)(65 118 79 132)(67 120 81 134)(69 122 83 136)(86 113 100 127)(88 115 102 129)(90 117 104 131)(92 119 106 133)(94 121 108 135)(96 123 110 137)(98 125 112 139)(141 170 155 184)(142 208 156 222)(143 172 157 186)(144 210 158 224)(145 174 159 188)(146 212 160 198)(147 176 161 190)(148 214 162 200)(149 178 163 192)(150 216 164 202)(151 180 165 194)(152 218 166 204)(153 182 167 196)(154 220 168 206)
(1 122 167 55)(2 137 168 42)(3 124 141 29)(4 139 142 44)(5 126 143 31)(6 113 144 46)(7 128 145 33)(8 115 146 48)(9 130 147 35)(10 117 148 50)(11 132 149 37)(12 119 150 52)(13 134 151 39)(14 121 152 54)(15 136 153 41)(16 123 154 56)(17 138 155 43)(18 125 156 30)(19 140 157 45)(20 127 158 32)(21 114 159 47)(22 129 160 34)(23 116 161 49)(24 131 162 36)(25 118 163 51)(26 133 164 38)(27 120 165 53)(28 135 166 40)(57 170 111 207)(58 185 112 222)(59 172 85 209)(60 187 86 224)(61 174 87 211)(62 189 88 198)(63 176 89 213)(64 191 90 200)(65 178 91 215)(66 193 92 202)(67 180 93 217)(68 195 94 204)(69 182 95 219)(70 169 96 206)(71 184 97 221)(72 171 98 208)(73 186 99 223)(74 173 100 210)(75 188 101 197)(76 175 102 212)(77 190 103 199)(78 177 104 214)(79 192 105 201)(80 179 106 216)(81 194 107 203)(82 181 108 218)(83 196 109 205)(84 183 110 220)
(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)
(1 152)(2 151)(3 150)(4 149)(5 148)(6 147)(7 146)(8 145)(9 144)(10 143)(11 142)(12 141)(13 168)(14 167)(15 166)(16 165)(17 164)(18 163)(19 162)(20 161)(21 160)(22 159)(23 158)(24 157)(25 156)(26 155)(27 154)(28 153)(29 133)(30 132)(31 131)(32 130)(33 129)(34 128)(35 127)(36 126)(37 125)(38 124)(39 123)(40 122)(41 121)(42 120)(43 119)(44 118)(45 117)(46 116)(47 115)(48 114)(49 113)(50 140)(51 139)(52 138)(53 137)(54 136)(55 135)(56 134)(57 92)(58 91)(59 90)(60 89)(61 88)(62 87)(63 86)(64 85)(65 112)(66 111)(67 110)(68 109)(69 108)(70 107)(71 106)(72 105)(73 104)(74 103)(75 102)(76 101)(77 100)(78 99)(79 98)(80 97)(81 96)(82 95)(83 94)(84 93)(169 217)(170 216)(171 215)(172 214)(173 213)(174 212)(175 211)(176 210)(177 209)(178 208)(179 207)(180 206)(181 205)(182 204)(183 203)(184 202)(185 201)(186 200)(187 199)(188 198)(189 197)(190 224)(191 223)(192 222)(193 221)(194 220)(195 219)(196 218)
G:=sub<Sym(224)| (1,205,15,219)(2,169,16,183)(3,207,17,221)(4,171,18,185)(5,209,19,223)(6,173,20,187)(7,211,21,197)(8,175,22,189)(9,213,23,199)(10,177,24,191)(11,215,25,201)(12,179,26,193)(13,217,27,203)(14,181,28,195)(29,111,43,97)(30,58,44,72)(31,85,45,99)(32,60,46,74)(33,87,47,101)(34,62,48,76)(35,89,49,103)(36,64,50,78)(37,91,51,105)(38,66,52,80)(39,93,53,107)(40,68,54,82)(41,95,55,109)(42,70,56,84)(57,138,71,124)(59,140,73,126)(61,114,75,128)(63,116,77,130)(65,118,79,132)(67,120,81,134)(69,122,83,136)(86,113,100,127)(88,115,102,129)(90,117,104,131)(92,119,106,133)(94,121,108,135)(96,123,110,137)(98,125,112,139)(141,170,155,184)(142,208,156,222)(143,172,157,186)(144,210,158,224)(145,174,159,188)(146,212,160,198)(147,176,161,190)(148,214,162,200)(149,178,163,192)(150,216,164,202)(151,180,165,194)(152,218,166,204)(153,182,167,196)(154,220,168,206), (1,122,167,55)(2,137,168,42)(3,124,141,29)(4,139,142,44)(5,126,143,31)(6,113,144,46)(7,128,145,33)(8,115,146,48)(9,130,147,35)(10,117,148,50)(11,132,149,37)(12,119,150,52)(13,134,151,39)(14,121,152,54)(15,136,153,41)(16,123,154,56)(17,138,155,43)(18,125,156,30)(19,140,157,45)(20,127,158,32)(21,114,159,47)(22,129,160,34)(23,116,161,49)(24,131,162,36)(25,118,163,51)(26,133,164,38)(27,120,165,53)(28,135,166,40)(57,170,111,207)(58,185,112,222)(59,172,85,209)(60,187,86,224)(61,174,87,211)(62,189,88,198)(63,176,89,213)(64,191,90,200)(65,178,91,215)(66,193,92,202)(67,180,93,217)(68,195,94,204)(69,182,95,219)(70,169,96,206)(71,184,97,221)(72,171,98,208)(73,186,99,223)(74,173,100,210)(75,188,101,197)(76,175,102,212)(77,190,103,199)(78,177,104,214)(79,192,105,201)(80,179,106,216)(81,194,107,203)(82,181,108,218)(83,196,109,205)(84,183,110,220), (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), (1,152)(2,151)(3,150)(4,149)(5,148)(6,147)(7,146)(8,145)(9,144)(10,143)(11,142)(12,141)(13,168)(14,167)(15,166)(16,165)(17,164)(18,163)(19,162)(20,161)(21,160)(22,159)(23,158)(24,157)(25,156)(26,155)(27,154)(28,153)(29,133)(30,132)(31,131)(32,130)(33,129)(34,128)(35,127)(36,126)(37,125)(38,124)(39,123)(40,122)(41,121)(42,120)(43,119)(44,118)(45,117)(46,116)(47,115)(48,114)(49,113)(50,140)(51,139)(52,138)(53,137)(54,136)(55,135)(56,134)(57,92)(58,91)(59,90)(60,89)(61,88)(62,87)(63,86)(64,85)(65,112)(66,111)(67,110)(68,109)(69,108)(70,107)(71,106)(72,105)(73,104)(74,103)(75,102)(76,101)(77,100)(78,99)(79,98)(80,97)(81,96)(82,95)(83,94)(84,93)(169,217)(170,216)(171,215)(172,214)(173,213)(174,212)(175,211)(176,210)(177,209)(178,208)(179,207)(180,206)(181,205)(182,204)(183,203)(184,202)(185,201)(186,200)(187,199)(188,198)(189,197)(190,224)(191,223)(192,222)(193,221)(194,220)(195,219)(196,218)>;
G:=Group( (1,205,15,219)(2,169,16,183)(3,207,17,221)(4,171,18,185)(5,209,19,223)(6,173,20,187)(7,211,21,197)(8,175,22,189)(9,213,23,199)(10,177,24,191)(11,215,25,201)(12,179,26,193)(13,217,27,203)(14,181,28,195)(29,111,43,97)(30,58,44,72)(31,85,45,99)(32,60,46,74)(33,87,47,101)(34,62,48,76)(35,89,49,103)(36,64,50,78)(37,91,51,105)(38,66,52,80)(39,93,53,107)(40,68,54,82)(41,95,55,109)(42,70,56,84)(57,138,71,124)(59,140,73,126)(61,114,75,128)(63,116,77,130)(65,118,79,132)(67,120,81,134)(69,122,83,136)(86,113,100,127)(88,115,102,129)(90,117,104,131)(92,119,106,133)(94,121,108,135)(96,123,110,137)(98,125,112,139)(141,170,155,184)(142,208,156,222)(143,172,157,186)(144,210,158,224)(145,174,159,188)(146,212,160,198)(147,176,161,190)(148,214,162,200)(149,178,163,192)(150,216,164,202)(151,180,165,194)(152,218,166,204)(153,182,167,196)(154,220,168,206), (1,122,167,55)(2,137,168,42)(3,124,141,29)(4,139,142,44)(5,126,143,31)(6,113,144,46)(7,128,145,33)(8,115,146,48)(9,130,147,35)(10,117,148,50)(11,132,149,37)(12,119,150,52)(13,134,151,39)(14,121,152,54)(15,136,153,41)(16,123,154,56)(17,138,155,43)(18,125,156,30)(19,140,157,45)(20,127,158,32)(21,114,159,47)(22,129,160,34)(23,116,161,49)(24,131,162,36)(25,118,163,51)(26,133,164,38)(27,120,165,53)(28,135,166,40)(57,170,111,207)(58,185,112,222)(59,172,85,209)(60,187,86,224)(61,174,87,211)(62,189,88,198)(63,176,89,213)(64,191,90,200)(65,178,91,215)(66,193,92,202)(67,180,93,217)(68,195,94,204)(69,182,95,219)(70,169,96,206)(71,184,97,221)(72,171,98,208)(73,186,99,223)(74,173,100,210)(75,188,101,197)(76,175,102,212)(77,190,103,199)(78,177,104,214)(79,192,105,201)(80,179,106,216)(81,194,107,203)(82,181,108,218)(83,196,109,205)(84,183,110,220), (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), (1,152)(2,151)(3,150)(4,149)(5,148)(6,147)(7,146)(8,145)(9,144)(10,143)(11,142)(12,141)(13,168)(14,167)(15,166)(16,165)(17,164)(18,163)(19,162)(20,161)(21,160)(22,159)(23,158)(24,157)(25,156)(26,155)(27,154)(28,153)(29,133)(30,132)(31,131)(32,130)(33,129)(34,128)(35,127)(36,126)(37,125)(38,124)(39,123)(40,122)(41,121)(42,120)(43,119)(44,118)(45,117)(46,116)(47,115)(48,114)(49,113)(50,140)(51,139)(52,138)(53,137)(54,136)(55,135)(56,134)(57,92)(58,91)(59,90)(60,89)(61,88)(62,87)(63,86)(64,85)(65,112)(66,111)(67,110)(68,109)(69,108)(70,107)(71,106)(72,105)(73,104)(74,103)(75,102)(76,101)(77,100)(78,99)(79,98)(80,97)(81,96)(82,95)(83,94)(84,93)(169,217)(170,216)(171,215)(172,214)(173,213)(174,212)(175,211)(176,210)(177,209)(178,208)(179,207)(180,206)(181,205)(182,204)(183,203)(184,202)(185,201)(186,200)(187,199)(188,198)(189,197)(190,224)(191,223)(192,222)(193,221)(194,220)(195,219)(196,218) );
G=PermutationGroup([(1,205,15,219),(2,169,16,183),(3,207,17,221),(4,171,18,185),(5,209,19,223),(6,173,20,187),(7,211,21,197),(8,175,22,189),(9,213,23,199),(10,177,24,191),(11,215,25,201),(12,179,26,193),(13,217,27,203),(14,181,28,195),(29,111,43,97),(30,58,44,72),(31,85,45,99),(32,60,46,74),(33,87,47,101),(34,62,48,76),(35,89,49,103),(36,64,50,78),(37,91,51,105),(38,66,52,80),(39,93,53,107),(40,68,54,82),(41,95,55,109),(42,70,56,84),(57,138,71,124),(59,140,73,126),(61,114,75,128),(63,116,77,130),(65,118,79,132),(67,120,81,134),(69,122,83,136),(86,113,100,127),(88,115,102,129),(90,117,104,131),(92,119,106,133),(94,121,108,135),(96,123,110,137),(98,125,112,139),(141,170,155,184),(142,208,156,222),(143,172,157,186),(144,210,158,224),(145,174,159,188),(146,212,160,198),(147,176,161,190),(148,214,162,200),(149,178,163,192),(150,216,164,202),(151,180,165,194),(152,218,166,204),(153,182,167,196),(154,220,168,206)], [(1,122,167,55),(2,137,168,42),(3,124,141,29),(4,139,142,44),(5,126,143,31),(6,113,144,46),(7,128,145,33),(8,115,146,48),(9,130,147,35),(10,117,148,50),(11,132,149,37),(12,119,150,52),(13,134,151,39),(14,121,152,54),(15,136,153,41),(16,123,154,56),(17,138,155,43),(18,125,156,30),(19,140,157,45),(20,127,158,32),(21,114,159,47),(22,129,160,34),(23,116,161,49),(24,131,162,36),(25,118,163,51),(26,133,164,38),(27,120,165,53),(28,135,166,40),(57,170,111,207),(58,185,112,222),(59,172,85,209),(60,187,86,224),(61,174,87,211),(62,189,88,198),(63,176,89,213),(64,191,90,200),(65,178,91,215),(66,193,92,202),(67,180,93,217),(68,195,94,204),(69,182,95,219),(70,169,96,206),(71,184,97,221),(72,171,98,208),(73,186,99,223),(74,173,100,210),(75,188,101,197),(76,175,102,212),(77,190,103,199),(78,177,104,214),(79,192,105,201),(80,179,106,216),(81,194,107,203),(82,181,108,218),(83,196,109,205),(84,183,110,220)], [(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)], [(1,152),(2,151),(3,150),(4,149),(5,148),(6,147),(7,146),(8,145),(9,144),(10,143),(11,142),(12,141),(13,168),(14,167),(15,166),(16,165),(17,164),(18,163),(19,162),(20,161),(21,160),(22,159),(23,158),(24,157),(25,156),(26,155),(27,154),(28,153),(29,133),(30,132),(31,131),(32,130),(33,129),(34,128),(35,127),(36,126),(37,125),(38,124),(39,123),(40,122),(41,121),(42,120),(43,119),(44,118),(45,117),(46,116),(47,115),(48,114),(49,113),(50,140),(51,139),(52,138),(53,137),(54,136),(55,135),(56,134),(57,92),(58,91),(59,90),(60,89),(61,88),(62,87),(63,86),(64,85),(65,112),(66,111),(67,110),(68,109),(69,108),(70,107),(71,106),(72,105),(73,104),(74,103),(75,102),(76,101),(77,100),(78,99),(79,98),(80,97),(81,96),(82,95),(83,94),(84,93),(169,217),(170,216),(171,215),(172,214),(173,213),(174,212),(175,211),(176,210),(177,209),(178,208),(179,207),(180,206),(181,205),(182,204),(183,203),(184,202),(185,201),(186,200),(187,199),(188,198),(189,197),(190,224),(191,223),(192,222),(193,221),(194,220),(195,219),(196,218)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 17 | 0 | 0 | 0 | 0 | 0 |
| 18 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 24 |
| 0 | 0 | 0 | 0 | 17 | 12 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 18 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 1 | 11 | 0 | 0 | 0 | 0 |
| 13 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 10 | 0 | 0 |
| 0 | 0 | 19 | 22 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 27 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 1 | 11 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 10 | 0 | 0 |
| 0 | 0 | 22 | 19 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 2 |
| 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(6,GF(29))| [17,18,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,17,17,0,0,0,0,24,12],[17,18,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[1,13,0,0,0,0,11,28,0,0,0,0,0,0,10,19,0,0,0,0,10,22,0,0,0,0,0,0,1,0,0,0,0,0,27,28],[1,0,0,0,0,0,11,28,0,0,0,0,0,0,10,22,0,0,0,0,10,19,0,0,0,0,0,0,28,0,0,0,0,0,2,1] >;
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 | 28A | ··· | 28R | 28S | ··· | 28AD |
| 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 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 28 | 28 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 7 | 14 | 14 | 14 | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
70 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | C4○D4 | D14 | D14 | Q8⋊2D7 | D7×C4○D4 |
| kernel | C42.237D14 | D7×C42 | C4.D28 | Dic7⋊3Q8 | C4⋊C4⋊7D7 | D28⋊C4 | D14.5D4 | C28⋊1D4 | D14⋊2Q8 | C4⋊C4⋊D7 | C7×C42.C2 | C42.C2 | Dic7 | C28 | D14 | C42 | C4⋊C4 | C4 | C2 |
| # reps | 1 | 1 | 1 | 1 | 2 | 3 | 2 | 1 | 1 | 2 | 1 | 3 | 4 | 4 | 4 | 3 | 18 | 6 | 12 |
In GAP, Magma, Sage, TeX
C_4^2._{237}D_{14} % in TeX
G:=Group("C4^2.237D14"); // GroupNames label
G:=SmallGroup(448,1144);
// by ID
G=gap.SmallGroup(448,1144);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,100,1123,346,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=d^2=1,c^14=a^2,a*b=b*a,c*a*c^-1=d*a*d=a*b^2,c*b*c^-1=d*b*d=a^2*b,d*c*d=a^2*c^13>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀