metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.104D14, C14.142+ 1+4, (C4×D4)⋊6D7, (D4×C28)⋊7C2, C28⋊7D4⋊6C2, D14⋊D4⋊6C2, C4⋊C4.279D14, Dic7.Q8⋊6C2, (C2×D4).208D14, D14.5D4⋊6C2, C42⋊2D7⋊15C2, C42⋊D7⋊31C2, (C2×C14).84C24, Dic7⋊4D4⋊44C2, Dic7⋊D4⋊25C2, (C2×C28).620C23, (C4×C28).237C22, D14⋊C4.65C22, C22⋊C4.129D14, (C2×D28).26C22, C22.1(C4○D28), (C22×C4).203D14, C23.D14⋊5C2, C4⋊Dic7.38C22, C2.17(D4⋊6D14), Dic7.20(C4○D4), (D4×C14).302C22, Dic7⋊C4.64C22, (C22×C28).78C22, (C2×Dic7).34C23, (C22×D7).29C23, C22.112(C23×D7), C23.164(C22×D7), C23.23D14⋊15C2, (C22×C14).154C23, C7⋊3(C22.47C24), (C4×Dic7).201C22, C23.D7.102C22, (C22×Dic7).92C22, (C4×C7⋊D4)⋊38C2, C2.19(D7×C4○D4), C2.40(C2×C4○D28), C14.36(C2×C4○D4), (C2×Dic7⋊C4)⋊25C2, (C2×C4×D7).198C22, (C2×C14).14(C4○D4), (C7×C4⋊C4).320C22, (C2×C4).652(C22×D7), (C2×C7⋊D4).13C22, (C7×C22⋊C4).141C22, SmallGroup(448,993)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.104D14
G = < a,b,c,d | a4=b4=c14=1, d2=b2, ab=ba, ac=ca, dad-1=ab2, cbc-1=dbd-1=a2b-1, dcd-1=c-1 >
Subgroups: 1076 in 238 conjugacy classes, 97 normal (91 characteristic)
C1, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, Dic7, Dic7, C28, D14, C2×C14, C2×C14, C2×C14, C2×C4⋊C4, C42⋊C2, C4×D4, C4×D4, C4⋊D4, C22.D4, C42.C2, C42⋊2C2, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C22.47C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×C4×D7, C2×D28, C22×Dic7, C2×C7⋊D4, C22×C28, D4×C14, C42⋊D7, C42⋊2D7, C23.D14, Dic7⋊4D4, D14⋊D4, Dic7.Q8, D14.5D4, C2×Dic7⋊C4, C4×C7⋊D4, C23.23D14, C28⋊7D4, Dic7⋊D4, D4×C28, C42.104D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.47C24, C4○D28, C23×D7, C2×C4○D28, D4⋊6D14, D7×C4○D4, C42.104D14
►On 224 points
Generators in S224
(1 23 37 106)(2 24 38 107)(3 25 39 108)(4 26 40 109)(5 27 41 110)(6 28 42 111)(7 15 29 112)(8 16 30 99)(9 17 31 100)(10 18 32 101)(11 19 33 102)(12 20 34 103)(13 21 35 104)(14 22 36 105)(43 182 50 175)(44 169 51 176)(45 170 52 177)(46 171 53 178)(47 172 54 179)(48 173 55 180)(49 174 56 181)(57 201 162 183)(58 202 163 184)(59 203 164 185)(60 204 165 186)(61 205 166 187)(62 206 167 188)(63 207 168 189)(64 208 155 190)(65 209 156 191)(66 210 157 192)(67 197 158 193)(68 198 159 194)(69 199 160 195)(70 200 161 196)(71 147 78 154)(72 148 79 141)(73 149 80 142)(74 150 81 143)(75 151 82 144)(76 152 83 145)(77 153 84 146)(85 125 92 118)(86 126 93 119)(87 113 94 120)(88 114 95 121)(89 115 96 122)(90 116 97 123)(91 117 98 124)(127 213 134 220)(128 214 135 221)(129 215 136 222)(130 216 137 223)(131 217 138 224)(132 218 139 211)(133 219 140 212)
(1 93 8 172)(2 180 9 87)(3 95 10 174)(4 182 11 89)(5 97 12 176)(6 170 13 91)(7 85 14 178)(15 125 22 46)(16 54 23 119)(17 113 24 48)(18 56 25 121)(19 115 26 50)(20 44 27 123)(21 117 28 52)(29 92 36 171)(30 179 37 86)(31 94 38 173)(32 181 39 88)(33 96 40 175)(34 169 41 90)(35 98 42 177)(43 102 122 109)(45 104 124 111)(47 106 126 99)(49 108 114 101)(51 110 116 103)(53 112 118 105)(55 100 120 107)(57 212 64 143)(58 151 65 220)(59 214 66 145)(60 153 67 222)(61 216 68 147)(62 141 69 224)(63 218 70 149)(71 187 130 194)(72 199 131 206)(73 189 132 196)(74 201 133 208)(75 191 134 184)(76 203 135 210)(77 193 136 186)(78 205 137 198)(79 195 138 188)(80 207 139 200)(81 183 140 190)(82 209 127 202)(83 185 128 192)(84 197 129 204)(142 168 211 161)(144 156 213 163)(146 158 215 165)(148 160 217 167)(150 162 219 155)(152 164 221 157)(154 166 223 159)
(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 58 8 65)(2 57 9 64)(3 70 10 63)(4 69 11 62)(5 68 12 61)(6 67 13 60)(7 66 14 59)(15 203 22 210)(16 202 23 209)(17 201 24 208)(18 200 25 207)(19 199 26 206)(20 198 27 205)(21 197 28 204)(29 157 36 164)(30 156 37 163)(31 155 38 162)(32 168 39 161)(33 167 40 160)(34 166 41 159)(35 165 42 158)(43 131 122 72)(44 130 123 71)(45 129 124 84)(46 128 125 83)(47 127 126 82)(48 140 113 81)(49 139 114 80)(50 138 115 79)(51 137 116 78)(52 136 117 77)(53 135 118 76)(54 134 119 75)(55 133 120 74)(56 132 121 73)(85 221 178 152)(86 220 179 151)(87 219 180 150)(88 218 181 149)(89 217 182 148)(90 216 169 147)(91 215 170 146)(92 214 171 145)(93 213 172 144)(94 212 173 143)(95 211 174 142)(96 224 175 141)(97 223 176 154)(98 222 177 153)(99 184 106 191)(100 183 107 190)(101 196 108 189)(102 195 109 188)(103 194 110 187)(104 193 111 186)(105 192 112 185)
G:=sub<Sym(224)| (1,23,37,106)(2,24,38,107)(3,25,39,108)(4,26,40,109)(5,27,41,110)(6,28,42,111)(7,15,29,112)(8,16,30,99)(9,17,31,100)(10,18,32,101)(11,19,33,102)(12,20,34,103)(13,21,35,104)(14,22,36,105)(43,182,50,175)(44,169,51,176)(45,170,52,177)(46,171,53,178)(47,172,54,179)(48,173,55,180)(49,174,56,181)(57,201,162,183)(58,202,163,184)(59,203,164,185)(60,204,165,186)(61,205,166,187)(62,206,167,188)(63,207,168,189)(64,208,155,190)(65,209,156,191)(66,210,157,192)(67,197,158,193)(68,198,159,194)(69,199,160,195)(70,200,161,196)(71,147,78,154)(72,148,79,141)(73,149,80,142)(74,150,81,143)(75,151,82,144)(76,152,83,145)(77,153,84,146)(85,125,92,118)(86,126,93,119)(87,113,94,120)(88,114,95,121)(89,115,96,122)(90,116,97,123)(91,117,98,124)(127,213,134,220)(128,214,135,221)(129,215,136,222)(130,216,137,223)(131,217,138,224)(132,218,139,211)(133,219,140,212), (1,93,8,172)(2,180,9,87)(3,95,10,174)(4,182,11,89)(5,97,12,176)(6,170,13,91)(7,85,14,178)(15,125,22,46)(16,54,23,119)(17,113,24,48)(18,56,25,121)(19,115,26,50)(20,44,27,123)(21,117,28,52)(29,92,36,171)(30,179,37,86)(31,94,38,173)(32,181,39,88)(33,96,40,175)(34,169,41,90)(35,98,42,177)(43,102,122,109)(45,104,124,111)(47,106,126,99)(49,108,114,101)(51,110,116,103)(53,112,118,105)(55,100,120,107)(57,212,64,143)(58,151,65,220)(59,214,66,145)(60,153,67,222)(61,216,68,147)(62,141,69,224)(63,218,70,149)(71,187,130,194)(72,199,131,206)(73,189,132,196)(74,201,133,208)(75,191,134,184)(76,203,135,210)(77,193,136,186)(78,205,137,198)(79,195,138,188)(80,207,139,200)(81,183,140,190)(82,209,127,202)(83,185,128,192)(84,197,129,204)(142,168,211,161)(144,156,213,163)(146,158,215,165)(148,160,217,167)(150,162,219,155)(152,164,221,157)(154,166,223,159), (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), (1,58,8,65)(2,57,9,64)(3,70,10,63)(4,69,11,62)(5,68,12,61)(6,67,13,60)(7,66,14,59)(15,203,22,210)(16,202,23,209)(17,201,24,208)(18,200,25,207)(19,199,26,206)(20,198,27,205)(21,197,28,204)(29,157,36,164)(30,156,37,163)(31,155,38,162)(32,168,39,161)(33,167,40,160)(34,166,41,159)(35,165,42,158)(43,131,122,72)(44,130,123,71)(45,129,124,84)(46,128,125,83)(47,127,126,82)(48,140,113,81)(49,139,114,80)(50,138,115,79)(51,137,116,78)(52,136,117,77)(53,135,118,76)(54,134,119,75)(55,133,120,74)(56,132,121,73)(85,221,178,152)(86,220,179,151)(87,219,180,150)(88,218,181,149)(89,217,182,148)(90,216,169,147)(91,215,170,146)(92,214,171,145)(93,213,172,144)(94,212,173,143)(95,211,174,142)(96,224,175,141)(97,223,176,154)(98,222,177,153)(99,184,106,191)(100,183,107,190)(101,196,108,189)(102,195,109,188)(103,194,110,187)(104,193,111,186)(105,192,112,185)>;
G:=Group( (1,23,37,106)(2,24,38,107)(3,25,39,108)(4,26,40,109)(5,27,41,110)(6,28,42,111)(7,15,29,112)(8,16,30,99)(9,17,31,100)(10,18,32,101)(11,19,33,102)(12,20,34,103)(13,21,35,104)(14,22,36,105)(43,182,50,175)(44,169,51,176)(45,170,52,177)(46,171,53,178)(47,172,54,179)(48,173,55,180)(49,174,56,181)(57,201,162,183)(58,202,163,184)(59,203,164,185)(60,204,165,186)(61,205,166,187)(62,206,167,188)(63,207,168,189)(64,208,155,190)(65,209,156,191)(66,210,157,192)(67,197,158,193)(68,198,159,194)(69,199,160,195)(70,200,161,196)(71,147,78,154)(72,148,79,141)(73,149,80,142)(74,150,81,143)(75,151,82,144)(76,152,83,145)(77,153,84,146)(85,125,92,118)(86,126,93,119)(87,113,94,120)(88,114,95,121)(89,115,96,122)(90,116,97,123)(91,117,98,124)(127,213,134,220)(128,214,135,221)(129,215,136,222)(130,216,137,223)(131,217,138,224)(132,218,139,211)(133,219,140,212), (1,93,8,172)(2,180,9,87)(3,95,10,174)(4,182,11,89)(5,97,12,176)(6,170,13,91)(7,85,14,178)(15,125,22,46)(16,54,23,119)(17,113,24,48)(18,56,25,121)(19,115,26,50)(20,44,27,123)(21,117,28,52)(29,92,36,171)(30,179,37,86)(31,94,38,173)(32,181,39,88)(33,96,40,175)(34,169,41,90)(35,98,42,177)(43,102,122,109)(45,104,124,111)(47,106,126,99)(49,108,114,101)(51,110,116,103)(53,112,118,105)(55,100,120,107)(57,212,64,143)(58,151,65,220)(59,214,66,145)(60,153,67,222)(61,216,68,147)(62,141,69,224)(63,218,70,149)(71,187,130,194)(72,199,131,206)(73,189,132,196)(74,201,133,208)(75,191,134,184)(76,203,135,210)(77,193,136,186)(78,205,137,198)(79,195,138,188)(80,207,139,200)(81,183,140,190)(82,209,127,202)(83,185,128,192)(84,197,129,204)(142,168,211,161)(144,156,213,163)(146,158,215,165)(148,160,217,167)(150,162,219,155)(152,164,221,157)(154,166,223,159), (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), (1,58,8,65)(2,57,9,64)(3,70,10,63)(4,69,11,62)(5,68,12,61)(6,67,13,60)(7,66,14,59)(15,203,22,210)(16,202,23,209)(17,201,24,208)(18,200,25,207)(19,199,26,206)(20,198,27,205)(21,197,28,204)(29,157,36,164)(30,156,37,163)(31,155,38,162)(32,168,39,161)(33,167,40,160)(34,166,41,159)(35,165,42,158)(43,131,122,72)(44,130,123,71)(45,129,124,84)(46,128,125,83)(47,127,126,82)(48,140,113,81)(49,139,114,80)(50,138,115,79)(51,137,116,78)(52,136,117,77)(53,135,118,76)(54,134,119,75)(55,133,120,74)(56,132,121,73)(85,221,178,152)(86,220,179,151)(87,219,180,150)(88,218,181,149)(89,217,182,148)(90,216,169,147)(91,215,170,146)(92,214,171,145)(93,213,172,144)(94,212,173,143)(95,211,174,142)(96,224,175,141)(97,223,176,154)(98,222,177,153)(99,184,106,191)(100,183,107,190)(101,196,108,189)(102,195,109,188)(103,194,110,187)(104,193,111,186)(105,192,112,185) );
G=PermutationGroup([[(1,23,37,106),(2,24,38,107),(3,25,39,108),(4,26,40,109),(5,27,41,110),(6,28,42,111),(7,15,29,112),(8,16,30,99),(9,17,31,100),(10,18,32,101),(11,19,33,102),(12,20,34,103),(13,21,35,104),(14,22,36,105),(43,182,50,175),(44,169,51,176),(45,170,52,177),(46,171,53,178),(47,172,54,179),(48,173,55,180),(49,174,56,181),(57,201,162,183),(58,202,163,184),(59,203,164,185),(60,204,165,186),(61,205,166,187),(62,206,167,188),(63,207,168,189),(64,208,155,190),(65,209,156,191),(66,210,157,192),(67,197,158,193),(68,198,159,194),(69,199,160,195),(70,200,161,196),(71,147,78,154),(72,148,79,141),(73,149,80,142),(74,150,81,143),(75,151,82,144),(76,152,83,145),(77,153,84,146),(85,125,92,118),(86,126,93,119),(87,113,94,120),(88,114,95,121),(89,115,96,122),(90,116,97,123),(91,117,98,124),(127,213,134,220),(128,214,135,221),(129,215,136,222),(130,216,137,223),(131,217,138,224),(132,218,139,211),(133,219,140,212)], [(1,93,8,172),(2,180,9,87),(3,95,10,174),(4,182,11,89),(5,97,12,176),(6,170,13,91),(7,85,14,178),(15,125,22,46),(16,54,23,119),(17,113,24,48),(18,56,25,121),(19,115,26,50),(20,44,27,123),(21,117,28,52),(29,92,36,171),(30,179,37,86),(31,94,38,173),(32,181,39,88),(33,96,40,175),(34,169,41,90),(35,98,42,177),(43,102,122,109),(45,104,124,111),(47,106,126,99),(49,108,114,101),(51,110,116,103),(53,112,118,105),(55,100,120,107),(57,212,64,143),(58,151,65,220),(59,214,66,145),(60,153,67,222),(61,216,68,147),(62,141,69,224),(63,218,70,149),(71,187,130,194),(72,199,131,206),(73,189,132,196),(74,201,133,208),(75,191,134,184),(76,203,135,210),(77,193,136,186),(78,205,137,198),(79,195,138,188),(80,207,139,200),(81,183,140,190),(82,209,127,202),(83,185,128,192),(84,197,129,204),(142,168,211,161),(144,156,213,163),(146,158,215,165),(148,160,217,167),(150,162,219,155),(152,164,221,157),(154,166,223,159)], [(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)], [(1,58,8,65),(2,57,9,64),(3,70,10,63),(4,69,11,62),(5,68,12,61),(6,67,13,60),(7,66,14,59),(15,203,22,210),(16,202,23,209),(17,201,24,208),(18,200,25,207),(19,199,26,206),(20,198,27,205),(21,197,28,204),(29,157,36,164),(30,156,37,163),(31,155,38,162),(32,168,39,161),(33,167,40,160),(34,166,41,159),(35,165,42,158),(43,131,122,72),(44,130,123,71),(45,129,124,84),(46,128,125,83),(47,127,126,82),(48,140,113,81),(49,139,114,80),(50,138,115,79),(51,137,116,78),(52,136,117,77),(53,135,118,76),(54,134,119,75),(55,133,120,74),(56,132,121,73),(85,221,178,152),(86,220,179,151),(87,219,180,150),(88,218,181,149),(89,217,182,148),(90,216,169,147),(91,215,170,146),(92,214,171,145),(93,213,172,144),(94,212,173,143),(95,211,174,142),(96,224,175,141),(97,223,176,154),(98,222,177,153),(99,184,106,191),(100,183,107,190),(101,196,108,189),(102,195,109,188),(103,194,110,187),(104,193,111,186),(105,192,112,185)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 28 | 2 | ··· | 2 | 4 | 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 | 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 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | D14 | D14 | C4○D28 | 2+ 1+4 | D4⋊6D14 | D7×C4○D4 |
| kernel | C42.104D14 | C42⋊D7 | C42⋊2D7 | C23.D14 | Dic7⋊4D4 | D14⋊D4 | Dic7.Q8 | D14.5D4 | C2×Dic7⋊C4 | C4×C7⋊D4 | C23.23D14 | C28⋊7D4 | Dic7⋊D4 | D4×C28 | C4×D4 | Dic7 | C2×C14 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C22 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 3 | 4 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of C42.104D14 ►in GL4(𝔽29) generated by
| 17 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 |
| 0 | 0 | 27 | 25 |
| 0 | 0 | 23 | 2 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 17 |
| 1 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 26 | 26 |
| 0 | 0 | 10 | 0 |
| 28 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 28 | 26 |
| 0 | 0 | 20 | 1 |
G:=sub<GL(4,GF(29))| [17,0,0,0,0,17,0,0,0,0,27,23,0,0,25,2],[0,1,0,0,1,0,0,0,0,0,17,0,0,0,0,17],[1,0,0,0,0,28,0,0,0,0,26,10,0,0,26,0],[28,0,0,0,0,1,0,0,0,0,28,20,0,0,26,1] >;
C42.104D14 in GAP, Magma, Sage, TeX
C_4^2._{104}D_{14} % in TeX
G:=Group("C4^2.104D14"); // GroupNames label
G:=SmallGroup(448,993);
// by ID
G=gap.SmallGroup(448,993);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,758,100,794,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=b^2,a*b=b*a,a*c=c*a,d*a*d^-1=a*b^2,c*b*c^-1=d*b*d^-1=a^2*b^-1,d*c*d^-1=c^-1>;
// generators/relations