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