metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.115D14, C14.222+ 1+4, C14.622- 1+4, (C4×D4)⋊23D7, C28⋊Q8⋊16C2, (D4×C28)⋊25C2, C4⋊C4.286D14, D14⋊2Q8⋊16C2, (C4×Dic14)⋊35C2, (C2×D4).222D14, C4.45(C4○D28), C28⋊2D4.10C2, C42⋊D7⋊14C2, C28.112(C4○D4), C28.17D4⋊10C2, C28.48D4⋊12C2, (C2×C14).105C24, (C4×C28).159C22, (C2×C28).163C23, C22⋊C4.117D14, (C22×C4).213D14, C23.D14⋊9C2, C4⋊Dic7.40C22, C2.23(D4⋊6D14), D14⋊C4.123C22, Dic7.D4⋊10C2, (D4×C14).264C22, C23.23D14⋊3C2, (C22×C28).82C22, (C4×Dic7).77C22, (C2×Dic7).46C23, (C22×D7).39C23, C23.102(C22×D7), C22.130(C23×D7), C23.D7.15C22, Dic7⋊C4.135C22, (C22×C14).175C23, C7⋊2(C22.36C24), (C2×Dic14).27C22, C2.19(D4.10D14), C14.47(C2×C4○D4), C2.54(C2×C4○D28), (C2×C4×D7).67C22, (C7×C4⋊C4).333C22, (C2×C4).287(C22×D7), (C2×C7⋊D4).18C22, (C7×C22⋊C4).128C22, SmallGroup(448,1014)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.115D14
G = < a,b,c,d | a4=b4=c14=1, d2=b2, ab=ba, cac-1=dad-1=a-1, bc=cb, dbd-1=a2b, dcd-1=b2c-1 >
Subgroups: 916 in 216 conjugacy classes, 95 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, C28, C28, D14, C2×C14, C2×C14, C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22.D4, C4.4D4, C42⋊2C2, C4⋊Q8, Dic14, C4×D7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C22.36C24, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C2×C4×D7, C2×C7⋊D4, C22×C28, D4×C14, C4×Dic14, C42⋊D7, C23.D14, Dic7.D4, C28⋊Q8, D14⋊2Q8, C28.48D4, C23.23D14, C28.17D4, C28⋊2D4, D4×C28, C42.115D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, 2- 1+4, C22×D7, C22.36C24, C4○D28, C23×D7, C2×C4○D28, D4⋊6D14, D4.10D14, C42.115D14
►On 224 points
Generators in S224
(1 125 12 118)(2 119 13 126)(3 113 14 120)(4 121 8 114)(5 115 9 122)(6 123 10 116)(7 117 11 124)(15 175 27 182)(16 169 28 176)(17 177 22 170)(18 171 23 178)(19 179 24 172)(20 173 25 180)(21 181 26 174)(29 98 42 91)(30 92 36 85)(31 86 37 93)(32 94 38 87)(33 88 39 95)(34 96 40 89)(35 90 41 97)(43 70 50 63)(44 64 51 57)(45 58 52 65)(46 66 53 59)(47 60 54 67)(48 68 55 61)(49 62 56 69)(71 214 208 136)(72 137 209 215)(73 216 210 138)(74 139 197 217)(75 218 198 140)(76 127 199 219)(77 220 200 128)(78 129 201 221)(79 222 202 130)(80 131 203 223)(81 224 204 132)(82 133 205 211)(83 212 206 134)(84 135 207 213)(99 192 157 145)(100 146 158 193)(101 194 159 147)(102 148 160 195)(103 196 161 149)(104 150 162 183)(105 184 163 151)(106 152 164 185)(107 186 165 153)(108 154 166 187)(109 188 167 141)(110 142 168 189)(111 190 155 143)(112 144 156 191)
(1 43 21 30)(2 44 15 31)(3 45 16 32)(4 46 17 33)(5 47 18 34)(6 48 19 35)(7 49 20 29)(8 53 22 39)(9 54 23 40)(10 55 24 41)(11 56 25 42)(12 50 26 36)(13 51 27 37)(14 52 28 38)(57 182 93 126)(58 169 94 113)(59 170 95 114)(60 171 96 115)(61 172 97 116)(62 173 98 117)(63 174 85 118)(64 175 86 119)(65 176 87 120)(66 177 88 121)(67 178 89 122)(68 179 90 123)(69 180 91 124)(70 181 92 125)(71 185 201 145)(72 186 202 146)(73 187 203 147)(74 188 204 148)(75 189 205 149)(76 190 206 150)(77 191 207 151)(78 192 208 152)(79 193 209 153)(80 194 210 154)(81 195 197 141)(82 196 198 142)(83 183 199 143)(84 184 200 144)(99 214 106 221)(100 215 107 222)(101 216 108 223)(102 217 109 224)(103 218 110 211)(104 219 111 212)(105 220 112 213)(127 155 134 162)(128 156 135 163)(129 157 136 164)(130 158 137 165)(131 159 138 166)(132 160 139 167)(133 161 140 168)
(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)
(1 158 21 165)(2 164 15 157)(3 156 16 163)(4 162 17 155)(5 168 18 161)(6 160 19 167)(7 166 20 159)(8 104 22 111)(9 110 23 103)(10 102 24 109)(11 108 25 101)(12 100 26 107)(13 106 27 99)(14 112 28 105)(29 216 49 223)(30 222 43 215)(31 214 44 221)(32 220 45 213)(33 212 46 219)(34 218 47 211)(35 224 48 217)(36 130 50 137)(37 136 51 129)(38 128 52 135)(39 134 53 127)(40 140 54 133)(41 132 55 139)(42 138 56 131)(57 78 93 208)(58 207 94 77)(59 76 95 206)(60 205 96 75)(61 74 97 204)(62 203 98 73)(63 72 85 202)(64 201 86 71)(65 84 87 200)(66 199 88 83)(67 82 89 198)(68 197 90 81)(69 80 91 210)(70 209 92 79)(113 144 169 184)(114 183 170 143)(115 142 171 196)(116 195 172 141)(117 154 173 194)(118 193 174 153)(119 152 175 192)(120 191 176 151)(121 150 177 190)(122 189 178 149)(123 148 179 188)(124 187 180 147)(125 146 181 186)(126 185 182 145)
G:=sub<Sym(224)| (1,125,12,118)(2,119,13,126)(3,113,14,120)(4,121,8,114)(5,115,9,122)(6,123,10,116)(7,117,11,124)(15,175,27,182)(16,169,28,176)(17,177,22,170)(18,171,23,178)(19,179,24,172)(20,173,25,180)(21,181,26,174)(29,98,42,91)(30,92,36,85)(31,86,37,93)(32,94,38,87)(33,88,39,95)(34,96,40,89)(35,90,41,97)(43,70,50,63)(44,64,51,57)(45,58,52,65)(46,66,53,59)(47,60,54,67)(48,68,55,61)(49,62,56,69)(71,214,208,136)(72,137,209,215)(73,216,210,138)(74,139,197,217)(75,218,198,140)(76,127,199,219)(77,220,200,128)(78,129,201,221)(79,222,202,130)(80,131,203,223)(81,224,204,132)(82,133,205,211)(83,212,206,134)(84,135,207,213)(99,192,157,145)(100,146,158,193)(101,194,159,147)(102,148,160,195)(103,196,161,149)(104,150,162,183)(105,184,163,151)(106,152,164,185)(107,186,165,153)(108,154,166,187)(109,188,167,141)(110,142,168,189)(111,190,155,143)(112,144,156,191), (1,43,21,30)(2,44,15,31)(3,45,16,32)(4,46,17,33)(5,47,18,34)(6,48,19,35)(7,49,20,29)(8,53,22,39)(9,54,23,40)(10,55,24,41)(11,56,25,42)(12,50,26,36)(13,51,27,37)(14,52,28,38)(57,182,93,126)(58,169,94,113)(59,170,95,114)(60,171,96,115)(61,172,97,116)(62,173,98,117)(63,174,85,118)(64,175,86,119)(65,176,87,120)(66,177,88,121)(67,178,89,122)(68,179,90,123)(69,180,91,124)(70,181,92,125)(71,185,201,145)(72,186,202,146)(73,187,203,147)(74,188,204,148)(75,189,205,149)(76,190,206,150)(77,191,207,151)(78,192,208,152)(79,193,209,153)(80,194,210,154)(81,195,197,141)(82,196,198,142)(83,183,199,143)(84,184,200,144)(99,214,106,221)(100,215,107,222)(101,216,108,223)(102,217,109,224)(103,218,110,211)(104,219,111,212)(105,220,112,213)(127,155,134,162)(128,156,135,163)(129,157,136,164)(130,158,137,165)(131,159,138,166)(132,160,139,167)(133,161,140,168), (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), (1,158,21,165)(2,164,15,157)(3,156,16,163)(4,162,17,155)(5,168,18,161)(6,160,19,167)(7,166,20,159)(8,104,22,111)(9,110,23,103)(10,102,24,109)(11,108,25,101)(12,100,26,107)(13,106,27,99)(14,112,28,105)(29,216,49,223)(30,222,43,215)(31,214,44,221)(32,220,45,213)(33,212,46,219)(34,218,47,211)(35,224,48,217)(36,130,50,137)(37,136,51,129)(38,128,52,135)(39,134,53,127)(40,140,54,133)(41,132,55,139)(42,138,56,131)(57,78,93,208)(58,207,94,77)(59,76,95,206)(60,205,96,75)(61,74,97,204)(62,203,98,73)(63,72,85,202)(64,201,86,71)(65,84,87,200)(66,199,88,83)(67,82,89,198)(68,197,90,81)(69,80,91,210)(70,209,92,79)(113,144,169,184)(114,183,170,143)(115,142,171,196)(116,195,172,141)(117,154,173,194)(118,193,174,153)(119,152,175,192)(120,191,176,151)(121,150,177,190)(122,189,178,149)(123,148,179,188)(124,187,180,147)(125,146,181,186)(126,185,182,145)>;
G:=Group( (1,125,12,118)(2,119,13,126)(3,113,14,120)(4,121,8,114)(5,115,9,122)(6,123,10,116)(7,117,11,124)(15,175,27,182)(16,169,28,176)(17,177,22,170)(18,171,23,178)(19,179,24,172)(20,173,25,180)(21,181,26,174)(29,98,42,91)(30,92,36,85)(31,86,37,93)(32,94,38,87)(33,88,39,95)(34,96,40,89)(35,90,41,97)(43,70,50,63)(44,64,51,57)(45,58,52,65)(46,66,53,59)(47,60,54,67)(48,68,55,61)(49,62,56,69)(71,214,208,136)(72,137,209,215)(73,216,210,138)(74,139,197,217)(75,218,198,140)(76,127,199,219)(77,220,200,128)(78,129,201,221)(79,222,202,130)(80,131,203,223)(81,224,204,132)(82,133,205,211)(83,212,206,134)(84,135,207,213)(99,192,157,145)(100,146,158,193)(101,194,159,147)(102,148,160,195)(103,196,161,149)(104,150,162,183)(105,184,163,151)(106,152,164,185)(107,186,165,153)(108,154,166,187)(109,188,167,141)(110,142,168,189)(111,190,155,143)(112,144,156,191), (1,43,21,30)(2,44,15,31)(3,45,16,32)(4,46,17,33)(5,47,18,34)(6,48,19,35)(7,49,20,29)(8,53,22,39)(9,54,23,40)(10,55,24,41)(11,56,25,42)(12,50,26,36)(13,51,27,37)(14,52,28,38)(57,182,93,126)(58,169,94,113)(59,170,95,114)(60,171,96,115)(61,172,97,116)(62,173,98,117)(63,174,85,118)(64,175,86,119)(65,176,87,120)(66,177,88,121)(67,178,89,122)(68,179,90,123)(69,180,91,124)(70,181,92,125)(71,185,201,145)(72,186,202,146)(73,187,203,147)(74,188,204,148)(75,189,205,149)(76,190,206,150)(77,191,207,151)(78,192,208,152)(79,193,209,153)(80,194,210,154)(81,195,197,141)(82,196,198,142)(83,183,199,143)(84,184,200,144)(99,214,106,221)(100,215,107,222)(101,216,108,223)(102,217,109,224)(103,218,110,211)(104,219,111,212)(105,220,112,213)(127,155,134,162)(128,156,135,163)(129,157,136,164)(130,158,137,165)(131,159,138,166)(132,160,139,167)(133,161,140,168), (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), (1,158,21,165)(2,164,15,157)(3,156,16,163)(4,162,17,155)(5,168,18,161)(6,160,19,167)(7,166,20,159)(8,104,22,111)(9,110,23,103)(10,102,24,109)(11,108,25,101)(12,100,26,107)(13,106,27,99)(14,112,28,105)(29,216,49,223)(30,222,43,215)(31,214,44,221)(32,220,45,213)(33,212,46,219)(34,218,47,211)(35,224,48,217)(36,130,50,137)(37,136,51,129)(38,128,52,135)(39,134,53,127)(40,140,54,133)(41,132,55,139)(42,138,56,131)(57,78,93,208)(58,207,94,77)(59,76,95,206)(60,205,96,75)(61,74,97,204)(62,203,98,73)(63,72,85,202)(64,201,86,71)(65,84,87,200)(66,199,88,83)(67,82,89,198)(68,197,90,81)(69,80,91,210)(70,209,92,79)(113,144,169,184)(114,183,170,143)(115,142,171,196)(116,195,172,141)(117,154,173,194)(118,193,174,153)(119,152,175,192)(120,191,176,151)(121,150,177,190)(122,189,178,149)(123,148,179,188)(124,187,180,147)(125,146,181,186)(126,185,182,145) );
G=PermutationGroup([[(1,125,12,118),(2,119,13,126),(3,113,14,120),(4,121,8,114),(5,115,9,122),(6,123,10,116),(7,117,11,124),(15,175,27,182),(16,169,28,176),(17,177,22,170),(18,171,23,178),(19,179,24,172),(20,173,25,180),(21,181,26,174),(29,98,42,91),(30,92,36,85),(31,86,37,93),(32,94,38,87),(33,88,39,95),(34,96,40,89),(35,90,41,97),(43,70,50,63),(44,64,51,57),(45,58,52,65),(46,66,53,59),(47,60,54,67),(48,68,55,61),(49,62,56,69),(71,214,208,136),(72,137,209,215),(73,216,210,138),(74,139,197,217),(75,218,198,140),(76,127,199,219),(77,220,200,128),(78,129,201,221),(79,222,202,130),(80,131,203,223),(81,224,204,132),(82,133,205,211),(83,212,206,134),(84,135,207,213),(99,192,157,145),(100,146,158,193),(101,194,159,147),(102,148,160,195),(103,196,161,149),(104,150,162,183),(105,184,163,151),(106,152,164,185),(107,186,165,153),(108,154,166,187),(109,188,167,141),(110,142,168,189),(111,190,155,143),(112,144,156,191)], [(1,43,21,30),(2,44,15,31),(3,45,16,32),(4,46,17,33),(5,47,18,34),(6,48,19,35),(7,49,20,29),(8,53,22,39),(9,54,23,40),(10,55,24,41),(11,56,25,42),(12,50,26,36),(13,51,27,37),(14,52,28,38),(57,182,93,126),(58,169,94,113),(59,170,95,114),(60,171,96,115),(61,172,97,116),(62,173,98,117),(63,174,85,118),(64,175,86,119),(65,176,87,120),(66,177,88,121),(67,178,89,122),(68,179,90,123),(69,180,91,124),(70,181,92,125),(71,185,201,145),(72,186,202,146),(73,187,203,147),(74,188,204,148),(75,189,205,149),(76,190,206,150),(77,191,207,151),(78,192,208,152),(79,193,209,153),(80,194,210,154),(81,195,197,141),(82,196,198,142),(83,183,199,143),(84,184,200,144),(99,214,106,221),(100,215,107,222),(101,216,108,223),(102,217,109,224),(103,218,110,211),(104,219,111,212),(105,220,112,213),(127,155,134,162),(128,156,135,163),(129,157,136,164),(130,158,137,165),(131,159,138,166),(132,160,139,167),(133,161,140,168)], [(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)], [(1,158,21,165),(2,164,15,157),(3,156,16,163),(4,162,17,155),(5,168,18,161),(6,160,19,167),(7,166,20,159),(8,104,22,111),(9,110,23,103),(10,102,24,109),(11,108,25,101),(12,100,26,107),(13,106,27,99),(14,112,28,105),(29,216,49,223),(30,222,43,215),(31,214,44,221),(32,220,45,213),(33,212,46,219),(34,218,47,211),(35,224,48,217),(36,130,50,137),(37,136,51,129),(38,128,52,135),(39,134,53,127),(40,140,54,133),(41,132,55,139),(42,138,56,131),(57,78,93,208),(58,207,94,77),(59,76,95,206),(60,205,96,75),(61,74,97,204),(62,203,98,73),(63,72,85,202),(64,201,86,71),(65,84,87,200),(66,199,88,83),(67,82,89,198),(68,197,90,81),(69,80,91,210),(70,209,92,79),(113,144,169,184),(114,183,170,143),(115,142,171,196),(116,195,172,141),(117,154,173,194),(118,193,174,153),(119,152,175,192),(120,191,176,151),(121,150,177,190),(122,189,178,149),(123,148,179,188),(124,187,180,147),(125,146,181,186),(126,185,182,145)]])
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | ··· | 4F | 4G | 4H | 4I | ··· | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 2 | ··· | 2 | 4 | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | D14 | D14 | C4○D28 | 2+ 1+4 | 2- 1+4 | D4⋊6D14 | D4.10D14 |
| kernel | C42.115D14 | C4×Dic14 | C42⋊D7 | C23.D14 | Dic7.D4 | C28⋊Q8 | D14⋊2Q8 | C28.48D4 | C23.23D14 | C28.17D4 | C28⋊2D4 | D4×C28 | C4×D4 | C28 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C4 | C14 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 3 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 1 | 1 | 6 | 6 |
Matrix representation of C42.115D14 ►in GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 27 | 0 | 0 |
| 0 | 0 | 1 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 27 |
| 0 | 0 | 0 | 0 | 1 | 28 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 23 | 0 | 0 | 0 |
| 0 | 0 | 23 | 6 | 0 | 0 |
| 0 | 0 | 0 | 0 | 5 | 0 |
| 0 | 0 | 0 | 0 | 5 | 24 |
| 14 | 1 | 0 | 0 | 0 | 0 |
| 6 | 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 24 | 0 |
| 0 | 0 | 0 | 0 | 24 | 5 |
| 0 | 0 | 6 | 0 | 0 | 0 |
| 0 | 0 | 6 | 23 | 0 | 0 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,27,28,0,0,0,0,0,0,1,1,0,0,0,0,27,28],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,17,0,0,0,0,0,0,17],[1,1,0,0,0,0,0,28,0,0,0,0,0,0,23,23,0,0,0,0,0,6,0,0,0,0,0,0,5,5,0,0,0,0,0,24],[14,6,0,0,0,0,1,15,0,0,0,0,0,0,0,0,6,6,0,0,0,0,0,23,0,0,24,24,0,0,0,0,0,5,0,0] >;
C42.115D14 in GAP, Magma, Sage, TeX
C_4^2._{115}D_{14} % in TeX
G:=Group("C4^2.115D14"); // GroupNames label
G:=SmallGroup(448,1014);
// by ID
G=gap.SmallGroup(448,1014);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,100,675,570,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,b*c=c*b,d*b*d^-1=a^2*b,d*c*d^-1=b^2*c^-1>;
// generators/relations