metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4⋊C4.197D14, (D4×Dic7)⋊27C2, (C2×D4).159D14, Dic7.Q8⋊24C2, (C2×C28).67C23, C22⋊C4.66D14, Dic7⋊4D4⋊17C2, Dic7⋊3Q8⋊30C2, (C2×C14).193C24, D14⋊C4.31C22, Dic7.8(C4○D4), Dic7⋊D4.1C2, (C22×C4).321D14, C22.D4⋊17D7, C23.24(C22×D7), Dic7.D4⋊30C2, C22⋊Dic14⋊28C2, (D4×C14).131C22, C23.D14⋊27C2, Dic7⋊C4.38C22, C4⋊Dic7.224C22, (C22×C14).29C23, (C2×Dic7).98C23, (C22×D7).84C23, C22.214(C23×D7), C23.D7.39C22, C23.11D14⋊11C2, C22.11(D4⋊2D7), C23.23D14⋊19C2, (C22×C28).367C22, C7⋊8(C23.36C23), (C4×Dic7).120C22, (C2×Dic14).166C22, (C22×Dic7).226C22, (C2×C4×Dic7)⋊36C2, C2.57(D7×C4○D4), C4⋊C4⋊D7⋊26C2, C4⋊C4⋊7D7⋊31C2, C14.169(C2×C4○D4), C2.51(C2×D4⋊2D7), (C2×C4×D7).109C22, (C2×C4).58(C22×D7), (C2×C14).45(C4○D4), (C7×C4⋊C4).173C22, (C7×C22.D4)⋊3C2, (C2×C7⋊D4).45C22, (C7×C22⋊C4).48C22, SmallGroup(448,1102)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4⋊C4.197D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2, bab-1=a-1, cac-1=dad-1=ab2, bc=cb, bd=db, dcd-1=c-1 >
Subgroups: 940 in 234 conjugacy classes, 99 normal (91 characteristic)
C1, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, Dic7, Dic7, C28, D14, C2×C14, C2×C14, C2×C14, C2×C42, C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22.D4, 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, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C22×Dic7, C2×C7⋊D4, C22×C28, D4×C14, C23.11D14, C22⋊Dic14, C23.D14, Dic7⋊4D4, Dic7.D4, Dic7⋊3Q8, Dic7.Q8, C4⋊C4⋊7D7, C4⋊C4⋊D7, C2×C4×Dic7, C23.23D14, D4×Dic7, Dic7⋊D4, C7×C22.D4, C4⋊C4.197D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, C22×D7, C23.36C23, D4⋊2D7, C23×D7, C2×D4⋊2D7, D7×C4○D4, C4⋊C4.197D14
►On 224 points
Generators in S224
(1 67 8 155)(2 163 9 61)(3 69 10 157)(4 165 11 63)(5 57 12 159)(6 167 13 65)(7 59 14 161)(15 164 22 62)(16 70 23 158)(17 166 24 64)(18 58 25 160)(19 168 26 66)(20 60 27 162)(21 156 28 68)(29 129 36 214)(30 222 37 137)(31 131 38 216)(32 224 39 139)(33 133 40 218)(34 212 41 127)(35 135 42 220)(43 126 205 119)(44 195 206 188)(45 114 207 121)(46 183 208 190)(47 116 209 123)(48 185 210 192)(49 118 197 125)(50 187 198 194)(51 120 199 113)(52 189 200 196)(53 122 201 115)(54 191 202 184)(55 124 203 117)(56 193 204 186)(71 108 86 101)(72 175 87 182)(73 110 88 103)(74 177 89 170)(75 112 90 105)(76 179 91 172)(77 100 92 107)(78 181 93 174)(79 102 94 109)(80 169 95 176)(81 104 96 111)(82 171 97 178)(83 106 98 99)(84 173 85 180)(128 147 213 154)(130 149 215 142)(132 151 217 144)(134 153 219 146)(136 141 221 148)(138 143 223 150)(140 145 211 152)
(1 126 27 194)(2 113 28 195)(3 114 15 196)(4 115 16 183)(5 116 17 184)(6 117 18 185)(7 118 19 186)(8 119 20 187)(9 120 21 188)(10 121 22 189)(11 122 23 190)(12 123 24 191)(13 124 25 192)(14 125 26 193)(29 102 141 182)(30 103 142 169)(31 104 143 170)(32 105 144 171)(33 106 145 172)(34 107 146 173)(35 108 147 174)(36 109 148 175)(37 110 149 176)(38 111 150 177)(39 112 151 178)(40 99 152 179)(41 100 153 180)(42 101 154 181)(43 162 198 67)(44 163 199 68)(45 164 200 69)(46 165 201 70)(47 166 202 57)(48 167 203 58)(49 168 204 59)(50 155 205 60)(51 156 206 61)(52 157 207 62)(53 158 208 63)(54 159 209 64)(55 160 210 65)(56 161 197 66)(71 213 93 135)(72 214 94 136)(73 215 95 137)(74 216 96 138)(75 217 97 139)(76 218 98 140)(77 219 85 127)(78 220 86 128)(79 221 87 129)(80 222 88 130)(81 223 89 131)(82 224 90 132)(83 211 91 133)(84 212 92 134)
(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 31 8 38)(2 30 9 37)(3 29 10 36)(4 42 11 35)(5 41 12 34)(6 40 13 33)(7 39 14 32)(15 141 22 148)(16 154 23 147)(17 153 24 146)(18 152 25 145)(19 151 26 144)(20 150 27 143)(21 149 28 142)(43 89 205 74)(44 88 206 73)(45 87 207 72)(46 86 208 71)(47 85 209 84)(48 98 210 83)(49 97 197 82)(50 96 198 81)(51 95 199 80)(52 94 200 79)(53 93 201 78)(54 92 202 77)(55 91 203 76)(56 90 204 75)(57 219 159 134)(58 218 160 133)(59 217 161 132)(60 216 162 131)(61 215 163 130)(62 214 164 129)(63 213 165 128)(64 212 166 127)(65 211 167 140)(66 224 168 139)(67 223 155 138)(68 222 156 137)(69 221 157 136)(70 220 158 135)(99 124 106 117)(100 123 107 116)(101 122 108 115)(102 121 109 114)(103 120 110 113)(104 119 111 126)(105 118 112 125)(169 188 176 195)(170 187 177 194)(171 186 178 193)(172 185 179 192)(173 184 180 191)(174 183 181 190)(175 196 182 189)
G:=sub<Sym(224)| (1,67,8,155)(2,163,9,61)(3,69,10,157)(4,165,11,63)(5,57,12,159)(6,167,13,65)(7,59,14,161)(15,164,22,62)(16,70,23,158)(17,166,24,64)(18,58,25,160)(19,168,26,66)(20,60,27,162)(21,156,28,68)(29,129,36,214)(30,222,37,137)(31,131,38,216)(32,224,39,139)(33,133,40,218)(34,212,41,127)(35,135,42,220)(43,126,205,119)(44,195,206,188)(45,114,207,121)(46,183,208,190)(47,116,209,123)(48,185,210,192)(49,118,197,125)(50,187,198,194)(51,120,199,113)(52,189,200,196)(53,122,201,115)(54,191,202,184)(55,124,203,117)(56,193,204,186)(71,108,86,101)(72,175,87,182)(73,110,88,103)(74,177,89,170)(75,112,90,105)(76,179,91,172)(77,100,92,107)(78,181,93,174)(79,102,94,109)(80,169,95,176)(81,104,96,111)(82,171,97,178)(83,106,98,99)(84,173,85,180)(128,147,213,154)(130,149,215,142)(132,151,217,144)(134,153,219,146)(136,141,221,148)(138,143,223,150)(140,145,211,152), (1,126,27,194)(2,113,28,195)(3,114,15,196)(4,115,16,183)(5,116,17,184)(6,117,18,185)(7,118,19,186)(8,119,20,187)(9,120,21,188)(10,121,22,189)(11,122,23,190)(12,123,24,191)(13,124,25,192)(14,125,26,193)(29,102,141,182)(30,103,142,169)(31,104,143,170)(32,105,144,171)(33,106,145,172)(34,107,146,173)(35,108,147,174)(36,109,148,175)(37,110,149,176)(38,111,150,177)(39,112,151,178)(40,99,152,179)(41,100,153,180)(42,101,154,181)(43,162,198,67)(44,163,199,68)(45,164,200,69)(46,165,201,70)(47,166,202,57)(48,167,203,58)(49,168,204,59)(50,155,205,60)(51,156,206,61)(52,157,207,62)(53,158,208,63)(54,159,209,64)(55,160,210,65)(56,161,197,66)(71,213,93,135)(72,214,94,136)(73,215,95,137)(74,216,96,138)(75,217,97,139)(76,218,98,140)(77,219,85,127)(78,220,86,128)(79,221,87,129)(80,222,88,130)(81,223,89,131)(82,224,90,132)(83,211,91,133)(84,212,92,134), (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), (1,31,8,38)(2,30,9,37)(3,29,10,36)(4,42,11,35)(5,41,12,34)(6,40,13,33)(7,39,14,32)(15,141,22,148)(16,154,23,147)(17,153,24,146)(18,152,25,145)(19,151,26,144)(20,150,27,143)(21,149,28,142)(43,89,205,74)(44,88,206,73)(45,87,207,72)(46,86,208,71)(47,85,209,84)(48,98,210,83)(49,97,197,82)(50,96,198,81)(51,95,199,80)(52,94,200,79)(53,93,201,78)(54,92,202,77)(55,91,203,76)(56,90,204,75)(57,219,159,134)(58,218,160,133)(59,217,161,132)(60,216,162,131)(61,215,163,130)(62,214,164,129)(63,213,165,128)(64,212,166,127)(65,211,167,140)(66,224,168,139)(67,223,155,138)(68,222,156,137)(69,221,157,136)(70,220,158,135)(99,124,106,117)(100,123,107,116)(101,122,108,115)(102,121,109,114)(103,120,110,113)(104,119,111,126)(105,118,112,125)(169,188,176,195)(170,187,177,194)(171,186,178,193)(172,185,179,192)(173,184,180,191)(174,183,181,190)(175,196,182,189)>;
G:=Group( (1,67,8,155)(2,163,9,61)(3,69,10,157)(4,165,11,63)(5,57,12,159)(6,167,13,65)(7,59,14,161)(15,164,22,62)(16,70,23,158)(17,166,24,64)(18,58,25,160)(19,168,26,66)(20,60,27,162)(21,156,28,68)(29,129,36,214)(30,222,37,137)(31,131,38,216)(32,224,39,139)(33,133,40,218)(34,212,41,127)(35,135,42,220)(43,126,205,119)(44,195,206,188)(45,114,207,121)(46,183,208,190)(47,116,209,123)(48,185,210,192)(49,118,197,125)(50,187,198,194)(51,120,199,113)(52,189,200,196)(53,122,201,115)(54,191,202,184)(55,124,203,117)(56,193,204,186)(71,108,86,101)(72,175,87,182)(73,110,88,103)(74,177,89,170)(75,112,90,105)(76,179,91,172)(77,100,92,107)(78,181,93,174)(79,102,94,109)(80,169,95,176)(81,104,96,111)(82,171,97,178)(83,106,98,99)(84,173,85,180)(128,147,213,154)(130,149,215,142)(132,151,217,144)(134,153,219,146)(136,141,221,148)(138,143,223,150)(140,145,211,152), (1,126,27,194)(2,113,28,195)(3,114,15,196)(4,115,16,183)(5,116,17,184)(6,117,18,185)(7,118,19,186)(8,119,20,187)(9,120,21,188)(10,121,22,189)(11,122,23,190)(12,123,24,191)(13,124,25,192)(14,125,26,193)(29,102,141,182)(30,103,142,169)(31,104,143,170)(32,105,144,171)(33,106,145,172)(34,107,146,173)(35,108,147,174)(36,109,148,175)(37,110,149,176)(38,111,150,177)(39,112,151,178)(40,99,152,179)(41,100,153,180)(42,101,154,181)(43,162,198,67)(44,163,199,68)(45,164,200,69)(46,165,201,70)(47,166,202,57)(48,167,203,58)(49,168,204,59)(50,155,205,60)(51,156,206,61)(52,157,207,62)(53,158,208,63)(54,159,209,64)(55,160,210,65)(56,161,197,66)(71,213,93,135)(72,214,94,136)(73,215,95,137)(74,216,96,138)(75,217,97,139)(76,218,98,140)(77,219,85,127)(78,220,86,128)(79,221,87,129)(80,222,88,130)(81,223,89,131)(82,224,90,132)(83,211,91,133)(84,212,92,134), (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), (1,31,8,38)(2,30,9,37)(3,29,10,36)(4,42,11,35)(5,41,12,34)(6,40,13,33)(7,39,14,32)(15,141,22,148)(16,154,23,147)(17,153,24,146)(18,152,25,145)(19,151,26,144)(20,150,27,143)(21,149,28,142)(43,89,205,74)(44,88,206,73)(45,87,207,72)(46,86,208,71)(47,85,209,84)(48,98,210,83)(49,97,197,82)(50,96,198,81)(51,95,199,80)(52,94,200,79)(53,93,201,78)(54,92,202,77)(55,91,203,76)(56,90,204,75)(57,219,159,134)(58,218,160,133)(59,217,161,132)(60,216,162,131)(61,215,163,130)(62,214,164,129)(63,213,165,128)(64,212,166,127)(65,211,167,140)(66,224,168,139)(67,223,155,138)(68,222,156,137)(69,221,157,136)(70,220,158,135)(99,124,106,117)(100,123,107,116)(101,122,108,115)(102,121,109,114)(103,120,110,113)(104,119,111,126)(105,118,112,125)(169,188,176,195)(170,187,177,194)(171,186,178,193)(172,185,179,192)(173,184,180,191)(174,183,181,190)(175,196,182,189) );
G=PermutationGroup([[(1,67,8,155),(2,163,9,61),(3,69,10,157),(4,165,11,63),(5,57,12,159),(6,167,13,65),(7,59,14,161),(15,164,22,62),(16,70,23,158),(17,166,24,64),(18,58,25,160),(19,168,26,66),(20,60,27,162),(21,156,28,68),(29,129,36,214),(30,222,37,137),(31,131,38,216),(32,224,39,139),(33,133,40,218),(34,212,41,127),(35,135,42,220),(43,126,205,119),(44,195,206,188),(45,114,207,121),(46,183,208,190),(47,116,209,123),(48,185,210,192),(49,118,197,125),(50,187,198,194),(51,120,199,113),(52,189,200,196),(53,122,201,115),(54,191,202,184),(55,124,203,117),(56,193,204,186),(71,108,86,101),(72,175,87,182),(73,110,88,103),(74,177,89,170),(75,112,90,105),(76,179,91,172),(77,100,92,107),(78,181,93,174),(79,102,94,109),(80,169,95,176),(81,104,96,111),(82,171,97,178),(83,106,98,99),(84,173,85,180),(128,147,213,154),(130,149,215,142),(132,151,217,144),(134,153,219,146),(136,141,221,148),(138,143,223,150),(140,145,211,152)], [(1,126,27,194),(2,113,28,195),(3,114,15,196),(4,115,16,183),(5,116,17,184),(6,117,18,185),(7,118,19,186),(8,119,20,187),(9,120,21,188),(10,121,22,189),(11,122,23,190),(12,123,24,191),(13,124,25,192),(14,125,26,193),(29,102,141,182),(30,103,142,169),(31,104,143,170),(32,105,144,171),(33,106,145,172),(34,107,146,173),(35,108,147,174),(36,109,148,175),(37,110,149,176),(38,111,150,177),(39,112,151,178),(40,99,152,179),(41,100,153,180),(42,101,154,181),(43,162,198,67),(44,163,199,68),(45,164,200,69),(46,165,201,70),(47,166,202,57),(48,167,203,58),(49,168,204,59),(50,155,205,60),(51,156,206,61),(52,157,207,62),(53,158,208,63),(54,159,209,64),(55,160,210,65),(56,161,197,66),(71,213,93,135),(72,214,94,136),(73,215,95,137),(74,216,96,138),(75,217,97,139),(76,218,98,140),(77,219,85,127),(78,220,86,128),(79,221,87,129),(80,222,88,130),(81,223,89,131),(82,224,90,132),(83,211,91,133),(84,212,92,134)], [(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)], [(1,31,8,38),(2,30,9,37),(3,29,10,36),(4,42,11,35),(5,41,12,34),(6,40,13,33),(7,39,14,32),(15,141,22,148),(16,154,23,147),(17,153,24,146),(18,152,25,145),(19,151,26,144),(20,150,27,143),(21,149,28,142),(43,89,205,74),(44,88,206,73),(45,87,207,72),(46,86,208,71),(47,85,209,84),(48,98,210,83),(49,97,197,82),(50,96,198,81),(51,95,199,80),(52,94,200,79),(53,93,201,78),(54,92,202,77),(55,91,203,76),(56,90,204,75),(57,219,159,134),(58,218,160,133),(59,217,161,132),(60,216,162,131),(61,215,163,130),(62,214,164,129),(63,213,165,128),(64,212,166,127),(65,211,167,140),(66,224,168,139),(67,223,155,138),(68,222,156,137),(69,221,157,136),(70,220,158,135),(99,124,106,117),(100,123,107,116),(101,122,108,115),(102,121,109,114),(103,120,110,113),(104,119,111,126),(105,118,112,125),(169,188,176,195),(170,187,177,194),(171,186,178,193),(172,185,179,192),(173,184,180,191),(174,183,181,190),(175,196,182,189)]])
70 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | ··· | 4Q | 4R | 4S | 4T | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 14P | 14Q | 14R | 28A | ··· | 28L | 28M | ··· | 28U |
| 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 | 14 | ··· | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 7 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
70 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 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | D14 | D4⋊2D7 | D7×C4○D4 |
| kernel | C4⋊C4.197D14 | C23.11D14 | C22⋊Dic14 | C23.D14 | Dic7⋊4D4 | Dic7.D4 | Dic7⋊3Q8 | Dic7.Q8 | C4⋊C4⋊7D7 | C4⋊C4⋊D7 | C2×C4×Dic7 | C23.23D14 | D4×Dic7 | Dic7⋊D4 | C7×C22.D4 | C22.D4 | Dic7 | C2×C14 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C22 | C2 |
| # reps | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 8 | 4 | 9 | 6 | 3 | 3 | 6 | 12 |
Matrix representation of C4⋊C4.197D14 ►in GL6(𝔽29)
| 17 | 21 | 0 | 0 | 0 | 0 |
| 7 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 1 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 27 | 12 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 26 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 25 | 0 | 0 |
| 0 | 0 | 4 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 24 | 1 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 3 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 28 | 0 | 0 |
| 0 | 0 | 4 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 27 | 12 |
G:=sub<GL(6,GF(29))| [17,7,0,0,0,0,21,12,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,12,0,0,0,0,0,1,17],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,17,27,0,0,0,0,0,12],[1,26,0,0,0,0,0,28,0,0,0,0,0,0,25,4,0,0,0,0,25,11,0,0,0,0,0,0,28,24,0,0,0,0,0,1],[28,3,0,0,0,0,0,1,0,0,0,0,0,0,18,4,0,0,0,0,28,11,0,0,0,0,0,0,17,27,0,0,0,0,0,12] >;
C4⋊C4.197D14 in GAP, Magma, Sage, TeX
C_4\rtimes C_4._{197}D_{14} % in TeX
G:=Group("C4:C4.197D14"); // GroupNames label
G:=SmallGroup(448,1102);
// by ID
G=gap.SmallGroup(448,1102);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,100,346,297,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2,b*a*b^-1=a^-1,c*a*c^-1=d*a*d^-1=a*b^2,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations