metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.102D14, (C4×D4)⋊5D7, (D4×C28)⋊6C2, C4⋊C4.277D14, (C4×Dic14)⋊25C2, (C2×D4).207D14, C42⋊D7⋊10C2, Dic7.Q8⋊45C2, (C2×C14).82C24, C28.309(C4○D4), (C2×C28).584C23, (C4×C28).145C22, D14⋊C4.97C22, C22⋊C4.105D14, Dic7.3(C4○D4), Dic7⋊D4.6C2, C22.5(C4○D28), (C22×C4).320D14, C4.136(D4⋊2D7), C23.91(C22×D7), Dic7.D4⋊49C2, C22⋊Dic14⋊49C2, (D4×C14).301C22, C23.21D14⋊5C2, C22.D28⋊33C2, C23.D14⋊49C2, C4⋊Dic7.295C22, (C22×D7).28C23, C22.110(C23×D7), C23.18D14⋊33C2, Dic7⋊C4.107C22, (C22×C28).104C22, (C22×C14).152C23, C7⋊3(C23.36C23), (C4×Dic7).292C22, (C2×Dic7).200C23, C23.D7.101C22, (C2×Dic14).235C22, (C22×Dic7).219C22, (C4×C7⋊D4)⋊3C2, (C2×C4×Dic7)⋊35C2, C2.17(D7×C4○D4), C4⋊C4⋊D7⋊50C2, C2.39(C2×C4○D28), C14.136(C2×C4○D4), C2.18(C2×D4⋊2D7), (C2×C4×D7).197C22, (C2×C14).13(C4○D4), (C7×C4⋊C4).318C22, (C2×C4).153(C22×D7), (C2×C7⋊D4).108C22, (C7×C22⋊C4).119C22, SmallGroup(448,991)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.102D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2b2, ab=ba, cac-1=a-1, dad-1=ab2, bc=cb, bd=db, dcd-1=c-1 >
Subgroups: 916 in 234 conjugacy classes, 101 normal (91 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, 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, C2×C14, C2×C42, C42⋊C2, C4×D4, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22.D4, C4.4D4, C42.C2, C42⋊2C2, Dic14, C4×D7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C23.36C23, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C22×Dic7, C2×C7⋊D4, C22×C28, D4×C14, C4×Dic14, C42⋊D7, C22⋊Dic14, C23.D14, Dic7.D4, C22.D28, Dic7.Q8, C4⋊C4⋊D7, C2×C4×Dic7, C23.21D14, C4×C7⋊D4, C23.18D14, Dic7⋊D4, D4×C28, C42.102D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, C22×D7, C23.36C23, C4○D28, D4⋊2D7, C23×D7, C2×C4○D28, C2×D4⋊2D7, D7×C4○D4, C42.102D14
►On 224 points
Generators in S224
(1 35 26 177)(2 178 27 36)(3 37 28 179)(4 180 15 38)(5 39 16 181)(6 182 17 40)(7 41 18 169)(8 170 19 42)(9 29 20 171)(10 172 21 30)(11 31 22 173)(12 174 23 32)(13 33 24 175)(14 176 25 34)(43 109 95 201)(44 202 96 110)(45 111 97 203)(46 204 98 112)(47 99 85 205)(48 206 86 100)(49 101 87 207)(50 208 88 102)(51 103 89 209)(52 210 90 104)(53 105 91 197)(54 198 92 106)(55 107 93 199)(56 200 94 108)(57 124 72 219)(58 220 73 125)(59 126 74 221)(60 222 75 113)(61 114 76 223)(62 224 77 115)(63 116 78 211)(64 212 79 117)(65 118 80 213)(66 214 81 119)(67 120 82 215)(68 216 83 121)(69 122 84 217)(70 218 71 123)(127 149 187 168)(128 155 188 150)(129 151 189 156)(130 157 190 152)(131 153 191 158)(132 159 192 154)(133 141 193 160)(134 161 194 142)(135 143 195 162)(136 163 196 144)(137 145 183 164)(138 165 184 146)(139 147 185 166)(140 167 186 148)
(1 55 19 86)(2 56 20 87)(3 43 21 88)(4 44 22 89)(5 45 23 90)(6 46 24 91)(7 47 25 92)(8 48 26 93)(9 49 27 94)(10 50 28 95)(11 51 15 96)(12 52 16 97)(13 53 17 98)(14 54 18 85)(29 101 36 108)(30 102 37 109)(31 103 38 110)(32 104 39 111)(33 105 40 112)(34 106 41 99)(35 107 42 100)(57 186 79 133)(58 187 80 134)(59 188 81 135)(60 189 82 136)(61 190 83 137)(62 191 84 138)(63 192 71 139)(64 193 72 140)(65 194 73 127)(66 195 74 128)(67 196 75 129)(68 183 76 130)(69 184 77 131)(70 185 78 132)(113 151 120 144)(114 152 121 145)(115 153 122 146)(116 154 123 147)(117 141 124 148)(118 142 125 149)(119 143 126 150)(155 214 162 221)(156 215 163 222)(157 216 164 223)(158 217 165 224)(159 218 166 211)(160 219 167 212)(161 220 168 213)(169 205 176 198)(170 206 177 199)(171 207 178 200)(172 208 179 201)(173 209 180 202)(174 210 181 203)(175 197 182 204)
(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)
(1 183 8 190)(2 196 9 189)(3 195 10 188)(4 194 11 187)(5 193 12 186)(6 192 13 185)(7 191 14 184)(15 134 22 127)(16 133 23 140)(17 132 24 139)(18 131 25 138)(19 130 26 137)(20 129 27 136)(21 128 28 135)(29 163 178 151)(30 162 179 150)(31 161 180 149)(32 160 181 148)(33 159 182 147)(34 158 169 146)(35 157 170 145)(36 156 171 144)(37 155 172 143)(38 168 173 142)(39 167 174 141)(40 166 175 154)(41 165 176 153)(42 164 177 152)(43 74 50 81)(44 73 51 80)(45 72 52 79)(46 71 53 78)(47 84 54 77)(48 83 55 76)(49 82 56 75)(57 90 64 97)(58 89 65 96)(59 88 66 95)(60 87 67 94)(61 86 68 93)(62 85 69 92)(63 98 70 91)(99 224 198 122)(100 223 199 121)(101 222 200 120)(102 221 201 119)(103 220 202 118)(104 219 203 117)(105 218 204 116)(106 217 205 115)(107 216 206 114)(108 215 207 113)(109 214 208 126)(110 213 209 125)(111 212 210 124)(112 211 197 123)
G:=sub<Sym(224)| (1,35,26,177)(2,178,27,36)(3,37,28,179)(4,180,15,38)(5,39,16,181)(6,182,17,40)(7,41,18,169)(8,170,19,42)(9,29,20,171)(10,172,21,30)(11,31,22,173)(12,174,23,32)(13,33,24,175)(14,176,25,34)(43,109,95,201)(44,202,96,110)(45,111,97,203)(46,204,98,112)(47,99,85,205)(48,206,86,100)(49,101,87,207)(50,208,88,102)(51,103,89,209)(52,210,90,104)(53,105,91,197)(54,198,92,106)(55,107,93,199)(56,200,94,108)(57,124,72,219)(58,220,73,125)(59,126,74,221)(60,222,75,113)(61,114,76,223)(62,224,77,115)(63,116,78,211)(64,212,79,117)(65,118,80,213)(66,214,81,119)(67,120,82,215)(68,216,83,121)(69,122,84,217)(70,218,71,123)(127,149,187,168)(128,155,188,150)(129,151,189,156)(130,157,190,152)(131,153,191,158)(132,159,192,154)(133,141,193,160)(134,161,194,142)(135,143,195,162)(136,163,196,144)(137,145,183,164)(138,165,184,146)(139,147,185,166)(140,167,186,148), (1,55,19,86)(2,56,20,87)(3,43,21,88)(4,44,22,89)(5,45,23,90)(6,46,24,91)(7,47,25,92)(8,48,26,93)(9,49,27,94)(10,50,28,95)(11,51,15,96)(12,52,16,97)(13,53,17,98)(14,54,18,85)(29,101,36,108)(30,102,37,109)(31,103,38,110)(32,104,39,111)(33,105,40,112)(34,106,41,99)(35,107,42,100)(57,186,79,133)(58,187,80,134)(59,188,81,135)(60,189,82,136)(61,190,83,137)(62,191,84,138)(63,192,71,139)(64,193,72,140)(65,194,73,127)(66,195,74,128)(67,196,75,129)(68,183,76,130)(69,184,77,131)(70,185,78,132)(113,151,120,144)(114,152,121,145)(115,153,122,146)(116,154,123,147)(117,141,124,148)(118,142,125,149)(119,143,126,150)(155,214,162,221)(156,215,163,222)(157,216,164,223)(158,217,165,224)(159,218,166,211)(160,219,167,212)(161,220,168,213)(169,205,176,198)(170,206,177,199)(171,207,178,200)(172,208,179,201)(173,209,180,202)(174,210,181,203)(175,197,182,204), (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), (1,183,8,190)(2,196,9,189)(3,195,10,188)(4,194,11,187)(5,193,12,186)(6,192,13,185)(7,191,14,184)(15,134,22,127)(16,133,23,140)(17,132,24,139)(18,131,25,138)(19,130,26,137)(20,129,27,136)(21,128,28,135)(29,163,178,151)(30,162,179,150)(31,161,180,149)(32,160,181,148)(33,159,182,147)(34,158,169,146)(35,157,170,145)(36,156,171,144)(37,155,172,143)(38,168,173,142)(39,167,174,141)(40,166,175,154)(41,165,176,153)(42,164,177,152)(43,74,50,81)(44,73,51,80)(45,72,52,79)(46,71,53,78)(47,84,54,77)(48,83,55,76)(49,82,56,75)(57,90,64,97)(58,89,65,96)(59,88,66,95)(60,87,67,94)(61,86,68,93)(62,85,69,92)(63,98,70,91)(99,224,198,122)(100,223,199,121)(101,222,200,120)(102,221,201,119)(103,220,202,118)(104,219,203,117)(105,218,204,116)(106,217,205,115)(107,216,206,114)(108,215,207,113)(109,214,208,126)(110,213,209,125)(111,212,210,124)(112,211,197,123)>;
G:=Group( (1,35,26,177)(2,178,27,36)(3,37,28,179)(4,180,15,38)(5,39,16,181)(6,182,17,40)(7,41,18,169)(8,170,19,42)(9,29,20,171)(10,172,21,30)(11,31,22,173)(12,174,23,32)(13,33,24,175)(14,176,25,34)(43,109,95,201)(44,202,96,110)(45,111,97,203)(46,204,98,112)(47,99,85,205)(48,206,86,100)(49,101,87,207)(50,208,88,102)(51,103,89,209)(52,210,90,104)(53,105,91,197)(54,198,92,106)(55,107,93,199)(56,200,94,108)(57,124,72,219)(58,220,73,125)(59,126,74,221)(60,222,75,113)(61,114,76,223)(62,224,77,115)(63,116,78,211)(64,212,79,117)(65,118,80,213)(66,214,81,119)(67,120,82,215)(68,216,83,121)(69,122,84,217)(70,218,71,123)(127,149,187,168)(128,155,188,150)(129,151,189,156)(130,157,190,152)(131,153,191,158)(132,159,192,154)(133,141,193,160)(134,161,194,142)(135,143,195,162)(136,163,196,144)(137,145,183,164)(138,165,184,146)(139,147,185,166)(140,167,186,148), (1,55,19,86)(2,56,20,87)(3,43,21,88)(4,44,22,89)(5,45,23,90)(6,46,24,91)(7,47,25,92)(8,48,26,93)(9,49,27,94)(10,50,28,95)(11,51,15,96)(12,52,16,97)(13,53,17,98)(14,54,18,85)(29,101,36,108)(30,102,37,109)(31,103,38,110)(32,104,39,111)(33,105,40,112)(34,106,41,99)(35,107,42,100)(57,186,79,133)(58,187,80,134)(59,188,81,135)(60,189,82,136)(61,190,83,137)(62,191,84,138)(63,192,71,139)(64,193,72,140)(65,194,73,127)(66,195,74,128)(67,196,75,129)(68,183,76,130)(69,184,77,131)(70,185,78,132)(113,151,120,144)(114,152,121,145)(115,153,122,146)(116,154,123,147)(117,141,124,148)(118,142,125,149)(119,143,126,150)(155,214,162,221)(156,215,163,222)(157,216,164,223)(158,217,165,224)(159,218,166,211)(160,219,167,212)(161,220,168,213)(169,205,176,198)(170,206,177,199)(171,207,178,200)(172,208,179,201)(173,209,180,202)(174,210,181,203)(175,197,182,204), (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), (1,183,8,190)(2,196,9,189)(3,195,10,188)(4,194,11,187)(5,193,12,186)(6,192,13,185)(7,191,14,184)(15,134,22,127)(16,133,23,140)(17,132,24,139)(18,131,25,138)(19,130,26,137)(20,129,27,136)(21,128,28,135)(29,163,178,151)(30,162,179,150)(31,161,180,149)(32,160,181,148)(33,159,182,147)(34,158,169,146)(35,157,170,145)(36,156,171,144)(37,155,172,143)(38,168,173,142)(39,167,174,141)(40,166,175,154)(41,165,176,153)(42,164,177,152)(43,74,50,81)(44,73,51,80)(45,72,52,79)(46,71,53,78)(47,84,54,77)(48,83,55,76)(49,82,56,75)(57,90,64,97)(58,89,65,96)(59,88,66,95)(60,87,67,94)(61,86,68,93)(62,85,69,92)(63,98,70,91)(99,224,198,122)(100,223,199,121)(101,222,200,120)(102,221,201,119)(103,220,202,118)(104,219,203,117)(105,218,204,116)(106,217,205,115)(107,216,206,114)(108,215,207,113)(109,214,208,126)(110,213,209,125)(111,212,210,124)(112,211,197,123) );
G=PermutationGroup([[(1,35,26,177),(2,178,27,36),(3,37,28,179),(4,180,15,38),(5,39,16,181),(6,182,17,40),(7,41,18,169),(8,170,19,42),(9,29,20,171),(10,172,21,30),(11,31,22,173),(12,174,23,32),(13,33,24,175),(14,176,25,34),(43,109,95,201),(44,202,96,110),(45,111,97,203),(46,204,98,112),(47,99,85,205),(48,206,86,100),(49,101,87,207),(50,208,88,102),(51,103,89,209),(52,210,90,104),(53,105,91,197),(54,198,92,106),(55,107,93,199),(56,200,94,108),(57,124,72,219),(58,220,73,125),(59,126,74,221),(60,222,75,113),(61,114,76,223),(62,224,77,115),(63,116,78,211),(64,212,79,117),(65,118,80,213),(66,214,81,119),(67,120,82,215),(68,216,83,121),(69,122,84,217),(70,218,71,123),(127,149,187,168),(128,155,188,150),(129,151,189,156),(130,157,190,152),(131,153,191,158),(132,159,192,154),(133,141,193,160),(134,161,194,142),(135,143,195,162),(136,163,196,144),(137,145,183,164),(138,165,184,146),(139,147,185,166),(140,167,186,148)], [(1,55,19,86),(2,56,20,87),(3,43,21,88),(4,44,22,89),(5,45,23,90),(6,46,24,91),(7,47,25,92),(8,48,26,93),(9,49,27,94),(10,50,28,95),(11,51,15,96),(12,52,16,97),(13,53,17,98),(14,54,18,85),(29,101,36,108),(30,102,37,109),(31,103,38,110),(32,104,39,111),(33,105,40,112),(34,106,41,99),(35,107,42,100),(57,186,79,133),(58,187,80,134),(59,188,81,135),(60,189,82,136),(61,190,83,137),(62,191,84,138),(63,192,71,139),(64,193,72,140),(65,194,73,127),(66,195,74,128),(67,196,75,129),(68,183,76,130),(69,184,77,131),(70,185,78,132),(113,151,120,144),(114,152,121,145),(115,153,122,146),(116,154,123,147),(117,141,124,148),(118,142,125,149),(119,143,126,150),(155,214,162,221),(156,215,163,222),(157,216,164,223),(158,217,165,224),(159,218,166,211),(160,219,167,212),(161,220,168,213),(169,205,176,198),(170,206,177,199),(171,207,178,200),(172,208,179,201),(173,209,180,202),(174,210,181,203),(175,197,182,204)], [(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)], [(1,183,8,190),(2,196,9,189),(3,195,10,188),(4,194,11,187),(5,193,12,186),(6,192,13,185),(7,191,14,184),(15,134,22,127),(16,133,23,140),(17,132,24,139),(18,131,25,138),(19,130,26,137),(20,129,27,136),(21,128,28,135),(29,163,178,151),(30,162,179,150),(31,161,180,149),(32,160,181,148),(33,159,182,147),(34,158,169,146),(35,157,170,145),(36,156,171,144),(37,155,172,143),(38,168,173,142),(39,167,174,141),(40,166,175,154),(41,165,176,153),(42,164,177,152),(43,74,50,81),(44,73,51,80),(45,72,52,79),(46,71,53,78),(47,84,54,77),(48,83,55,76),(49,82,56,75),(57,90,64,97),(58,89,65,96),(59,88,66,95),(60,87,67,94),(61,86,68,93),(62,85,69,92),(63,98,70,91),(99,224,198,122),(100,223,199,121),(101,222,200,120),(102,221,201,119),(103,220,202,118),(104,219,203,117),(105,218,204,116),(106,217,205,115),(107,216,206,114),(108,215,207,113),(109,214,208,126),(110,213,209,125),(111,212,210,124),(112,211,197,123)]])
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | ··· | 4Q | 4R | 4S | 4T | 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 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 28 | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | C4○D4 | D14 | D14 | D14 | D14 | D14 | C4○D28 | D4⋊2D7 | D7×C4○D4 |
| kernel | C42.102D14 | C4×Dic14 | C42⋊D7 | C22⋊Dic14 | C23.D14 | Dic7.D4 | C22.D28 | Dic7.Q8 | C4⋊C4⋊D7 | C2×C4×Dic7 | C23.21D14 | C4×C7⋊D4 | C23.18D14 | Dic7⋊D4 | D4×C28 | C4×D4 | Dic7 | C28 | C2×C14 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C22 | C4 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 3 | 4 | 4 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 6 | 6 |
Matrix representation of C42.102D14 ►in GL4(𝔽29) generated by
| 0 | 28 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 11 | 2 |
| 0 | 0 | 27 | 18 |
| 17 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 |
| 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 17 |
| 1 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 4 | 4 |
| 0 | 0 | 25 | 18 |
| 1 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 19 | 19 |
| 0 | 0 | 13 | 10 |
G:=sub<GL(4,GF(29))| [0,1,0,0,28,0,0,0,0,0,11,27,0,0,2,18],[17,0,0,0,0,17,0,0,0,0,17,0,0,0,0,17],[1,0,0,0,0,28,0,0,0,0,4,25,0,0,4,18],[1,0,0,0,0,28,0,0,0,0,19,13,0,0,19,10] >;
C42.102D14 in GAP, Magma, Sage, TeX
C_4^2._{102}D_{14} % in TeX
G:=Group("C4^2.102D14"); // GroupNames label
G:=SmallGroup(448,991);
// by ID
G=gap.SmallGroup(448,991);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,100,1123,794,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2*b^2,a*b=b*a,c*a*c^-1=a^-1,d*a*d^-1=a*b^2,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations