metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.114D14, C14.202+ 1+4, (C4×D4)⋊21D7, (D4×C28)⋊23C2, C4⋊C4.319D14, C28⋊D4.7C2, D28⋊C4⋊16C2, (C4×Dic14)⋊34C2, (C2×D4).220D14, D14.D4⋊8C2, C4.16(C4○D28), C4.D28⋊19C2, C28.17D4⋊9C2, (C22×C4).48D14, Dic7⋊3Q8⋊16C2, C28.111(C4○D4), (C2×C28).701C23, (C4×C28).158C22, (C2×C14).103C24, D14⋊C4.87C22, C22⋊C4.116D14, Dic7.D4⋊8C2, C2.21(D4⋊6D14), Dic7.35(C4○D4), (D4×C14).263C22, (C2×D28).139C22, Dic7⋊C4.66C22, C4⋊Dic7.301C22, (C4×Dic7).76C22, (C2×Dic7).44C23, (C22×D7).37C23, C22.128(C23×D7), C23.100(C22×D7), C23.23D14⋊18C2, (C22×C14).173C23, (C22×C28).365C22, C7⋊1(C22.53C24), C23.D7.107C22, (C2×Dic14).145C22, (C4×C7⋊D4)⋊45C2, C2.26(D7×C4○D4), C2.52(C2×C4○D28), C14.45(C2×C4○D4), (C2×C4×D7).202C22, (C7×C4⋊C4).332C22, (C2×C4).286(C22×D7), (C2×C7⋊D4).116C22, (C7×C22⋊C4).127C22, SmallGroup(448,1012)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.114D14
G = < a,b,c,d | a4=b4=1, c14=d2=b2, ab=ba, cac-1=a-1b2, dad-1=a-1, bc=cb, dbd-1=a2b, dcd-1=c13 >
Subgroups: 1076 in 236 conjugacy classes, 97 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, Dic7, Dic7, C28, C28, D14, C2×C14, C2×C14, C4×D4, C4×D4, C4×Q8, C22.D4, C4.4D4, C4⋊1D4, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C22.53C24, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C2×C7⋊D4, C22×C28, D4×C14, C4×Dic14, C4.D28, D14.D4, Dic7.D4, Dic7⋊3Q8, D28⋊C4, C4×C7⋊D4, C23.23D14, C28.17D4, C28⋊D4, D4×C28, C42.114D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.53C24, C4○D28, C23×D7, C2×C4○D28, D4⋊6D14, D7×C4○D4, C42.114D14
►On 224 points
Generators in S224
(1 88 35 164)(2 151 36 103)(3 90 37 166)(4 153 38 105)(5 92 39 168)(6 155 40 107)(7 94 41 142)(8 157 42 109)(9 96 43 144)(10 159 44 111)(11 98 45 146)(12 161 46 85)(13 100 47 148)(14 163 48 87)(15 102 49 150)(16 165 50 89)(17 104 51 152)(18 167 52 91)(19 106 53 154)(20 141 54 93)(21 108 55 156)(22 143 56 95)(23 110 29 158)(24 145 30 97)(25 112 31 160)(26 147 32 99)(27 86 33 162)(28 149 34 101)(57 131 189 223)(58 210 190 118)(59 133 191 197)(60 212 192 120)(61 135 193 199)(62 214 194 122)(63 137 195 201)(64 216 196 124)(65 139 169 203)(66 218 170 126)(67 113 171 205)(68 220 172 128)(69 115 173 207)(70 222 174 130)(71 117 175 209)(72 224 176 132)(73 119 177 211)(74 198 178 134)(75 121 179 213)(76 200 180 136)(77 123 181 215)(78 202 182 138)(79 125 183 217)(80 204 184 140)(81 127 185 219)(82 206 186 114)(83 129 187 221)(84 208 188 116)
(1 221 15 207)(2 222 16 208)(3 223 17 209)(4 224 18 210)(5 197 19 211)(6 198 20 212)(7 199 21 213)(8 200 22 214)(9 201 23 215)(10 202 24 216)(11 203 25 217)(12 204 26 218)(13 205 27 219)(14 206 28 220)(29 123 43 137)(30 124 44 138)(31 125 45 139)(32 126 46 140)(33 127 47 113)(34 128 48 114)(35 129 49 115)(36 130 50 116)(37 131 51 117)(38 132 52 118)(39 133 53 119)(40 134 54 120)(41 135 55 121)(42 136 56 122)(57 104 71 90)(58 105 72 91)(59 106 73 92)(60 107 74 93)(61 108 75 94)(62 109 76 95)(63 110 77 96)(64 111 78 97)(65 112 79 98)(66 85 80 99)(67 86 81 100)(68 87 82 101)(69 88 83 102)(70 89 84 103)(141 192 155 178)(142 193 156 179)(143 194 157 180)(144 195 158 181)(145 196 159 182)(146 169 160 183)(147 170 161 184)(148 171 162 185)(149 172 163 186)(150 173 164 187)(151 174 165 188)(152 175 166 189)(153 176 167 190)(154 177 168 191)
(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)
(1 186 15 172)(2 171 16 185)(3 184 17 170)(4 169 18 183)(5 182 19 196)(6 195 20 181)(7 180 21 194)(8 193 22 179)(9 178 23 192)(10 191 24 177)(11 176 25 190)(12 189 26 175)(13 174 27 188)(14 187 28 173)(29 60 43 74)(30 73 44 59)(31 58 45 72)(32 71 46 57)(33 84 47 70)(34 69 48 83)(35 82 49 68)(36 67 50 81)(37 80 51 66)(38 65 52 79)(39 78 53 64)(40 63 54 77)(41 76 55 62)(42 61 56 75)(85 223 99 209)(86 208 100 222)(87 221 101 207)(88 206 102 220)(89 219 103 205)(90 204 104 218)(91 217 105 203)(92 202 106 216)(93 215 107 201)(94 200 108 214)(95 213 109 199)(96 198 110 212)(97 211 111 197)(98 224 112 210)(113 165 127 151)(114 150 128 164)(115 163 129 149)(116 148 130 162)(117 161 131 147)(118 146 132 160)(119 159 133 145)(120 144 134 158)(121 157 135 143)(122 142 136 156)(123 155 137 141)(124 168 138 154)(125 153 139 167)(126 166 140 152)
G:=sub<Sym(224)| (1,88,35,164)(2,151,36,103)(3,90,37,166)(4,153,38,105)(5,92,39,168)(6,155,40,107)(7,94,41,142)(8,157,42,109)(9,96,43,144)(10,159,44,111)(11,98,45,146)(12,161,46,85)(13,100,47,148)(14,163,48,87)(15,102,49,150)(16,165,50,89)(17,104,51,152)(18,167,52,91)(19,106,53,154)(20,141,54,93)(21,108,55,156)(22,143,56,95)(23,110,29,158)(24,145,30,97)(25,112,31,160)(26,147,32,99)(27,86,33,162)(28,149,34,101)(57,131,189,223)(58,210,190,118)(59,133,191,197)(60,212,192,120)(61,135,193,199)(62,214,194,122)(63,137,195,201)(64,216,196,124)(65,139,169,203)(66,218,170,126)(67,113,171,205)(68,220,172,128)(69,115,173,207)(70,222,174,130)(71,117,175,209)(72,224,176,132)(73,119,177,211)(74,198,178,134)(75,121,179,213)(76,200,180,136)(77,123,181,215)(78,202,182,138)(79,125,183,217)(80,204,184,140)(81,127,185,219)(82,206,186,114)(83,129,187,221)(84,208,188,116), (1,221,15,207)(2,222,16,208)(3,223,17,209)(4,224,18,210)(5,197,19,211)(6,198,20,212)(7,199,21,213)(8,200,22,214)(9,201,23,215)(10,202,24,216)(11,203,25,217)(12,204,26,218)(13,205,27,219)(14,206,28,220)(29,123,43,137)(30,124,44,138)(31,125,45,139)(32,126,46,140)(33,127,47,113)(34,128,48,114)(35,129,49,115)(36,130,50,116)(37,131,51,117)(38,132,52,118)(39,133,53,119)(40,134,54,120)(41,135,55,121)(42,136,56,122)(57,104,71,90)(58,105,72,91)(59,106,73,92)(60,107,74,93)(61,108,75,94)(62,109,76,95)(63,110,77,96)(64,111,78,97)(65,112,79,98)(66,85,80,99)(67,86,81,100)(68,87,82,101)(69,88,83,102)(70,89,84,103)(141,192,155,178)(142,193,156,179)(143,194,157,180)(144,195,158,181)(145,196,159,182)(146,169,160,183)(147,170,161,184)(148,171,162,185)(149,172,163,186)(150,173,164,187)(151,174,165,188)(152,175,166,189)(153,176,167,190)(154,177,168,191), (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), (1,186,15,172)(2,171,16,185)(3,184,17,170)(4,169,18,183)(5,182,19,196)(6,195,20,181)(7,180,21,194)(8,193,22,179)(9,178,23,192)(10,191,24,177)(11,176,25,190)(12,189,26,175)(13,174,27,188)(14,187,28,173)(29,60,43,74)(30,73,44,59)(31,58,45,72)(32,71,46,57)(33,84,47,70)(34,69,48,83)(35,82,49,68)(36,67,50,81)(37,80,51,66)(38,65,52,79)(39,78,53,64)(40,63,54,77)(41,76,55,62)(42,61,56,75)(85,223,99,209)(86,208,100,222)(87,221,101,207)(88,206,102,220)(89,219,103,205)(90,204,104,218)(91,217,105,203)(92,202,106,216)(93,215,107,201)(94,200,108,214)(95,213,109,199)(96,198,110,212)(97,211,111,197)(98,224,112,210)(113,165,127,151)(114,150,128,164)(115,163,129,149)(116,148,130,162)(117,161,131,147)(118,146,132,160)(119,159,133,145)(120,144,134,158)(121,157,135,143)(122,142,136,156)(123,155,137,141)(124,168,138,154)(125,153,139,167)(126,166,140,152)>;
G:=Group( (1,88,35,164)(2,151,36,103)(3,90,37,166)(4,153,38,105)(5,92,39,168)(6,155,40,107)(7,94,41,142)(8,157,42,109)(9,96,43,144)(10,159,44,111)(11,98,45,146)(12,161,46,85)(13,100,47,148)(14,163,48,87)(15,102,49,150)(16,165,50,89)(17,104,51,152)(18,167,52,91)(19,106,53,154)(20,141,54,93)(21,108,55,156)(22,143,56,95)(23,110,29,158)(24,145,30,97)(25,112,31,160)(26,147,32,99)(27,86,33,162)(28,149,34,101)(57,131,189,223)(58,210,190,118)(59,133,191,197)(60,212,192,120)(61,135,193,199)(62,214,194,122)(63,137,195,201)(64,216,196,124)(65,139,169,203)(66,218,170,126)(67,113,171,205)(68,220,172,128)(69,115,173,207)(70,222,174,130)(71,117,175,209)(72,224,176,132)(73,119,177,211)(74,198,178,134)(75,121,179,213)(76,200,180,136)(77,123,181,215)(78,202,182,138)(79,125,183,217)(80,204,184,140)(81,127,185,219)(82,206,186,114)(83,129,187,221)(84,208,188,116), (1,221,15,207)(2,222,16,208)(3,223,17,209)(4,224,18,210)(5,197,19,211)(6,198,20,212)(7,199,21,213)(8,200,22,214)(9,201,23,215)(10,202,24,216)(11,203,25,217)(12,204,26,218)(13,205,27,219)(14,206,28,220)(29,123,43,137)(30,124,44,138)(31,125,45,139)(32,126,46,140)(33,127,47,113)(34,128,48,114)(35,129,49,115)(36,130,50,116)(37,131,51,117)(38,132,52,118)(39,133,53,119)(40,134,54,120)(41,135,55,121)(42,136,56,122)(57,104,71,90)(58,105,72,91)(59,106,73,92)(60,107,74,93)(61,108,75,94)(62,109,76,95)(63,110,77,96)(64,111,78,97)(65,112,79,98)(66,85,80,99)(67,86,81,100)(68,87,82,101)(69,88,83,102)(70,89,84,103)(141,192,155,178)(142,193,156,179)(143,194,157,180)(144,195,158,181)(145,196,159,182)(146,169,160,183)(147,170,161,184)(148,171,162,185)(149,172,163,186)(150,173,164,187)(151,174,165,188)(152,175,166,189)(153,176,167,190)(154,177,168,191), (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), (1,186,15,172)(2,171,16,185)(3,184,17,170)(4,169,18,183)(5,182,19,196)(6,195,20,181)(7,180,21,194)(8,193,22,179)(9,178,23,192)(10,191,24,177)(11,176,25,190)(12,189,26,175)(13,174,27,188)(14,187,28,173)(29,60,43,74)(30,73,44,59)(31,58,45,72)(32,71,46,57)(33,84,47,70)(34,69,48,83)(35,82,49,68)(36,67,50,81)(37,80,51,66)(38,65,52,79)(39,78,53,64)(40,63,54,77)(41,76,55,62)(42,61,56,75)(85,223,99,209)(86,208,100,222)(87,221,101,207)(88,206,102,220)(89,219,103,205)(90,204,104,218)(91,217,105,203)(92,202,106,216)(93,215,107,201)(94,200,108,214)(95,213,109,199)(96,198,110,212)(97,211,111,197)(98,224,112,210)(113,165,127,151)(114,150,128,164)(115,163,129,149)(116,148,130,162)(117,161,131,147)(118,146,132,160)(119,159,133,145)(120,144,134,158)(121,157,135,143)(122,142,136,156)(123,155,137,141)(124,168,138,154)(125,153,139,167)(126,166,140,152) );
G=PermutationGroup([[(1,88,35,164),(2,151,36,103),(3,90,37,166),(4,153,38,105),(5,92,39,168),(6,155,40,107),(7,94,41,142),(8,157,42,109),(9,96,43,144),(10,159,44,111),(11,98,45,146),(12,161,46,85),(13,100,47,148),(14,163,48,87),(15,102,49,150),(16,165,50,89),(17,104,51,152),(18,167,52,91),(19,106,53,154),(20,141,54,93),(21,108,55,156),(22,143,56,95),(23,110,29,158),(24,145,30,97),(25,112,31,160),(26,147,32,99),(27,86,33,162),(28,149,34,101),(57,131,189,223),(58,210,190,118),(59,133,191,197),(60,212,192,120),(61,135,193,199),(62,214,194,122),(63,137,195,201),(64,216,196,124),(65,139,169,203),(66,218,170,126),(67,113,171,205),(68,220,172,128),(69,115,173,207),(70,222,174,130),(71,117,175,209),(72,224,176,132),(73,119,177,211),(74,198,178,134),(75,121,179,213),(76,200,180,136),(77,123,181,215),(78,202,182,138),(79,125,183,217),(80,204,184,140),(81,127,185,219),(82,206,186,114),(83,129,187,221),(84,208,188,116)], [(1,221,15,207),(2,222,16,208),(3,223,17,209),(4,224,18,210),(5,197,19,211),(6,198,20,212),(7,199,21,213),(8,200,22,214),(9,201,23,215),(10,202,24,216),(11,203,25,217),(12,204,26,218),(13,205,27,219),(14,206,28,220),(29,123,43,137),(30,124,44,138),(31,125,45,139),(32,126,46,140),(33,127,47,113),(34,128,48,114),(35,129,49,115),(36,130,50,116),(37,131,51,117),(38,132,52,118),(39,133,53,119),(40,134,54,120),(41,135,55,121),(42,136,56,122),(57,104,71,90),(58,105,72,91),(59,106,73,92),(60,107,74,93),(61,108,75,94),(62,109,76,95),(63,110,77,96),(64,111,78,97),(65,112,79,98),(66,85,80,99),(67,86,81,100),(68,87,82,101),(69,88,83,102),(70,89,84,103),(141,192,155,178),(142,193,156,179),(143,194,157,180),(144,195,158,181),(145,196,159,182),(146,169,160,183),(147,170,161,184),(148,171,162,185),(149,172,163,186),(150,173,164,187),(151,174,165,188),(152,175,166,189),(153,176,167,190),(154,177,168,191)], [(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)], [(1,186,15,172),(2,171,16,185),(3,184,17,170),(4,169,18,183),(5,182,19,196),(6,195,20,181),(7,180,21,194),(8,193,22,179),(9,178,23,192),(10,191,24,177),(11,176,25,190),(12,189,26,175),(13,174,27,188),(14,187,28,173),(29,60,43,74),(30,73,44,59),(31,58,45,72),(32,71,46,57),(33,84,47,70),(34,69,48,83),(35,82,49,68),(36,67,50,81),(37,80,51,66),(38,65,52,79),(39,78,53,64),(40,63,54,77),(41,76,55,62),(42,61,56,75),(85,223,99,209),(86,208,100,222),(87,221,101,207),(88,206,102,220),(89,219,103,205),(90,204,104,218),(91,217,105,203),(92,202,106,216),(93,215,107,201),(94,200,108,214),(95,213,109,199),(96,198,110,212),(97,211,111,197),(98,224,112,210),(113,165,127,151),(114,150,128,164),(115,163,129,149),(116,148,130,162),(117,161,131,147),(118,146,132,160),(119,159,133,145),(120,144,134,158),(121,157,135,143),(122,142,136,156),(123,155,137,141),(124,168,138,154),(125,153,139,167),(126,166,140,152)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| 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 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 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 | 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 | D14 | D14 | C4○D28 | 2+ 1+4 | D4⋊6D14 | D7×C4○D4 |
| kernel | C42.114D14 | C4×Dic14 | C4.D28 | D14.D4 | Dic7.D4 | Dic7⋊3Q8 | D28⋊C4 | C4×C7⋊D4 | C23.23D14 | C28.17D4 | C28⋊D4 | D4×C28 | C4×D4 | Dic7 | C28 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C4 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 3 | 4 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of C42.114D14 ►in GL6(𝔽29)
| 0 | 1 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 5 |
| 0 | 0 | 0 | 0 | 10 | 26 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 23 | 10 | 0 | 0 |
| 0 | 0 | 9 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 5 |
| 0 | 0 | 0 | 0 | 27 | 26 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 28 | 0 | 0 |
| 0 | 0 | 12 | 10 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
G:=sub<GL(6,GF(29))| [0,28,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,3,10,0,0,0,0,5,26],[0,28,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,17,0,0,0,0,0,0,17],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,23,9,0,0,0,0,10,9,0,0,0,0,0,0,3,27,0,0,0,0,5,26],[12,0,0,0,0,0,0,17,0,0,0,0,0,0,19,12,0,0,0,0,28,10,0,0,0,0,0,0,12,0,0,0,0,0,0,12] >;
C42.114D14 in GAP, Magma, Sage, TeX
C_4^2._{114}D_{14} % in TeX
G:=Group("C4^2.114D14"); // GroupNames label
G:=SmallGroup(448,1012);
// by ID
G=gap.SmallGroup(448,1012);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,219,1571,136,18822]);
// 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=a^-1*b^2,d*a*d^-1=a^-1,b*c=c*b,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations