metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.108D14, C14.582- 1+4, C14.162+ 1+4, (C4×D4)⋊8D7, D4⋊10(C4×D7), D4⋊2D7⋊5C4, (D4×C28)⋊10C2, (D4×Dic7)⋊9C2, C4⋊C4.315D14, (C4×Dic14)⋊30C2, Dic14⋊13(C2×C4), (C2×D4).246D14, C42⋊D7⋊12C2, C14.23(C23×C4), (C2×C14).90C24, C28.33(C22×C4), D14.9(C22×C4), (C22×C4).46D14, Dic7⋊3Q8⋊15C2, Dic7⋊4D4⋊46C2, C2.4(D4⋊6D14), (C4×C28).150C22, (C2×C28).491C23, C22⋊C4.131D14, C22.33(C23×D7), D14⋊C4.121C22, (D4×C14).254C22, C4⋊Dic7.362C22, Dic7.19(C22×C4), C23.169(C22×D7), C2.3(D4.10D14), C23.11D14⋊28C2, Dic7⋊C4.134C22, (C22×C28).363C22, (C22×C14).160C23, C7⋊3(C23.33C23), (C2×Dic7).202C23, (C4×Dic7).203C22, (C22×D7).169C23, C23.D7.104C22, (C2×Dic14).287C22, (C22×Dic7).95C22, C4.33(C2×C4×D7), (D7×C4⋊C4)⋊14C2, (C4×D7)⋊4(C2×C4), C7⋊D4⋊4(C2×C4), (C7×D4)⋊13(C2×C4), (C4×C7⋊D4)⋊41C2, C22.3(C2×C4×D7), C2.25(D7×C22×C4), (C2×C4×D7).63C22, (C2×Dic7⋊C4)⋊38C2, (C2×Dic7)⋊11(C2×C4), (C2×D4⋊2D7).7C2, (C2×C14).3(C22×C4), (C7×C4⋊C4).324C22, (C2×C4).283(C22×D7), (C2×C7⋊D4).111C22, (C7×C22⋊C4).143C22, SmallGroup(448,999)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.108D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2, ab=ba, cac-1=dad-1=a-1, bc=cb, dbd-1=a2b, dcd-1=a2c-1 >
Subgroups: 1108 in 294 conjugacy classes, 151 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, 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, C4○D4, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C14, C2×C4⋊C4, C42⋊C2, C4×D4, C4×D4, C4×Q8, C2×C4○D4, Dic14, C4×D7, C4×D7, C2×Dic7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C23.33C23, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×C4×D7, D4⋊2D7, C22×Dic7, C2×C7⋊D4, C22×C28, D4×C14, C4×Dic14, C42⋊D7, C23.11D14, Dic7⋊4D4, Dic7⋊3Q8, D7×C4⋊C4, C2×Dic7⋊C4, C4×C7⋊D4, D4×Dic7, D4×C28, C2×D4⋊2D7, C42.108D14
Quotients: C1, C2, C4, C22, C2×C4, C23, D7, C22×C4, C24, D14, C23×C4, 2+ 1+4, 2- 1+4, C4×D7, C22×D7, C23.33C23, C2×C4×D7, C23×D7, D7×C22×C4, D4⋊6D14, D4.10D14, C42.108D14
►On 224 points
Generators in S224
(1 173 24 96)(2 97 25 174)(3 175 26 98)(4 85 27 176)(5 177 28 86)(6 87 15 178)(7 179 16 88)(8 89 17 180)(9 181 18 90)(10 91 19 182)(11 169 20 92)(12 93 21 170)(13 171 22 94)(14 95 23 172)(29 130 213 100)(30 101 214 131)(31 132 215 102)(32 103 216 133)(33 134 217 104)(34 105 218 135)(35 136 219 106)(36 107 220 137)(37 138 221 108)(38 109 222 139)(39 140 223 110)(40 111 224 127)(41 128 211 112)(42 99 212 129)(43 191 74 120)(44 121 75 192)(45 193 76 122)(46 123 77 194)(47 195 78 124)(48 125 79 196)(49 183 80 126)(50 113 81 184)(51 185 82 114)(52 115 83 186)(53 187 84 116)(54 117 71 188)(55 189 72 118)(56 119 73 190)(57 164 209 146)(58 147 210 165)(59 166 197 148)(60 149 198 167)(61 168 199 150)(62 151 200 155)(63 156 201 152)(64 153 202 157)(65 158 203 154)(66 141 204 159)(67 160 205 142)(68 143 206 161)(69 162 207 144)(70 145 208 163)
(1 104 146 47)(2 105 147 48)(3 106 148 49)(4 107 149 50)(5 108 150 51)(6 109 151 52)(7 110 152 53)(8 111 153 54)(9 112 154 55)(10 99 141 56)(11 100 142 43)(12 101 143 44)(13 102 144 45)(14 103 145 46)(15 139 155 83)(16 140 156 84)(17 127 157 71)(18 128 158 72)(19 129 159 73)(20 130 160 74)(21 131 161 75)(22 132 162 76)(23 133 163 77)(24 134 164 78)(25 135 165 79)(26 136 166 80)(27 137 167 81)(28 138 168 82)(29 67 191 169)(30 68 192 170)(31 69 193 171)(32 70 194 172)(33 57 195 173)(34 58 196 174)(35 59 183 175)(36 60 184 176)(37 61 185 177)(38 62 186 178)(39 63 187 179)(40 64 188 180)(41 65 189 181)(42 66 190 182)(85 220 198 113)(86 221 199 114)(87 222 200 115)(88 223 201 116)(89 224 202 117)(90 211 203 118)(91 212 204 119)(92 213 205 120)(93 214 206 121)(94 215 207 122)(95 216 208 123)(96 217 209 124)(97 218 210 125)(98 219 197 126)
(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)
(1 145 24 163)(2 162 25 144)(3 143 26 161)(4 160 27 142)(5 141 28 159)(6 158 15 154)(7 153 16 157)(8 156 17 152)(9 151 18 155)(10 168 19 150)(11 149 20 167)(12 166 21 148)(13 147 22 165)(14 164 23 146)(29 113 213 184)(30 183 214 126)(31 125 215 196)(32 195 216 124)(33 123 217 194)(34 193 218 122)(35 121 219 192)(36 191 220 120)(37 119 221 190)(38 189 222 118)(39 117 223 188)(40 187 224 116)(41 115 211 186)(42 185 212 114)(43 137 74 107)(44 106 75 136)(45 135 76 105)(46 104 77 134)(47 133 78 103)(48 102 79 132)(49 131 80 101)(50 100 81 130)(51 129 82 99)(52 112 83 128)(53 127 84 111)(54 110 71 140)(55 139 72 109)(56 108 73 138)(57 172 209 95)(58 94 210 171)(59 170 197 93)(60 92 198 169)(61 182 199 91)(62 90 200 181)(63 180 201 89)(64 88 202 179)(65 178 203 87)(66 86 204 177)(67 176 205 85)(68 98 206 175)(69 174 207 97)(70 96 208 173)
G:=sub<Sym(224)| (1,173,24,96)(2,97,25,174)(3,175,26,98)(4,85,27,176)(5,177,28,86)(6,87,15,178)(7,179,16,88)(8,89,17,180)(9,181,18,90)(10,91,19,182)(11,169,20,92)(12,93,21,170)(13,171,22,94)(14,95,23,172)(29,130,213,100)(30,101,214,131)(31,132,215,102)(32,103,216,133)(33,134,217,104)(34,105,218,135)(35,136,219,106)(36,107,220,137)(37,138,221,108)(38,109,222,139)(39,140,223,110)(40,111,224,127)(41,128,211,112)(42,99,212,129)(43,191,74,120)(44,121,75,192)(45,193,76,122)(46,123,77,194)(47,195,78,124)(48,125,79,196)(49,183,80,126)(50,113,81,184)(51,185,82,114)(52,115,83,186)(53,187,84,116)(54,117,71,188)(55,189,72,118)(56,119,73,190)(57,164,209,146)(58,147,210,165)(59,166,197,148)(60,149,198,167)(61,168,199,150)(62,151,200,155)(63,156,201,152)(64,153,202,157)(65,158,203,154)(66,141,204,159)(67,160,205,142)(68,143,206,161)(69,162,207,144)(70,145,208,163), (1,104,146,47)(2,105,147,48)(3,106,148,49)(4,107,149,50)(5,108,150,51)(6,109,151,52)(7,110,152,53)(8,111,153,54)(9,112,154,55)(10,99,141,56)(11,100,142,43)(12,101,143,44)(13,102,144,45)(14,103,145,46)(15,139,155,83)(16,140,156,84)(17,127,157,71)(18,128,158,72)(19,129,159,73)(20,130,160,74)(21,131,161,75)(22,132,162,76)(23,133,163,77)(24,134,164,78)(25,135,165,79)(26,136,166,80)(27,137,167,81)(28,138,168,82)(29,67,191,169)(30,68,192,170)(31,69,193,171)(32,70,194,172)(33,57,195,173)(34,58,196,174)(35,59,183,175)(36,60,184,176)(37,61,185,177)(38,62,186,178)(39,63,187,179)(40,64,188,180)(41,65,189,181)(42,66,190,182)(85,220,198,113)(86,221,199,114)(87,222,200,115)(88,223,201,116)(89,224,202,117)(90,211,203,118)(91,212,204,119)(92,213,205,120)(93,214,206,121)(94,215,207,122)(95,216,208,123)(96,217,209,124)(97,218,210,125)(98,219,197,126), (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), (1,145,24,163)(2,162,25,144)(3,143,26,161)(4,160,27,142)(5,141,28,159)(6,158,15,154)(7,153,16,157)(8,156,17,152)(9,151,18,155)(10,168,19,150)(11,149,20,167)(12,166,21,148)(13,147,22,165)(14,164,23,146)(29,113,213,184)(30,183,214,126)(31,125,215,196)(32,195,216,124)(33,123,217,194)(34,193,218,122)(35,121,219,192)(36,191,220,120)(37,119,221,190)(38,189,222,118)(39,117,223,188)(40,187,224,116)(41,115,211,186)(42,185,212,114)(43,137,74,107)(44,106,75,136)(45,135,76,105)(46,104,77,134)(47,133,78,103)(48,102,79,132)(49,131,80,101)(50,100,81,130)(51,129,82,99)(52,112,83,128)(53,127,84,111)(54,110,71,140)(55,139,72,109)(56,108,73,138)(57,172,209,95)(58,94,210,171)(59,170,197,93)(60,92,198,169)(61,182,199,91)(62,90,200,181)(63,180,201,89)(64,88,202,179)(65,178,203,87)(66,86,204,177)(67,176,205,85)(68,98,206,175)(69,174,207,97)(70,96,208,173)>;
G:=Group( (1,173,24,96)(2,97,25,174)(3,175,26,98)(4,85,27,176)(5,177,28,86)(6,87,15,178)(7,179,16,88)(8,89,17,180)(9,181,18,90)(10,91,19,182)(11,169,20,92)(12,93,21,170)(13,171,22,94)(14,95,23,172)(29,130,213,100)(30,101,214,131)(31,132,215,102)(32,103,216,133)(33,134,217,104)(34,105,218,135)(35,136,219,106)(36,107,220,137)(37,138,221,108)(38,109,222,139)(39,140,223,110)(40,111,224,127)(41,128,211,112)(42,99,212,129)(43,191,74,120)(44,121,75,192)(45,193,76,122)(46,123,77,194)(47,195,78,124)(48,125,79,196)(49,183,80,126)(50,113,81,184)(51,185,82,114)(52,115,83,186)(53,187,84,116)(54,117,71,188)(55,189,72,118)(56,119,73,190)(57,164,209,146)(58,147,210,165)(59,166,197,148)(60,149,198,167)(61,168,199,150)(62,151,200,155)(63,156,201,152)(64,153,202,157)(65,158,203,154)(66,141,204,159)(67,160,205,142)(68,143,206,161)(69,162,207,144)(70,145,208,163), (1,104,146,47)(2,105,147,48)(3,106,148,49)(4,107,149,50)(5,108,150,51)(6,109,151,52)(7,110,152,53)(8,111,153,54)(9,112,154,55)(10,99,141,56)(11,100,142,43)(12,101,143,44)(13,102,144,45)(14,103,145,46)(15,139,155,83)(16,140,156,84)(17,127,157,71)(18,128,158,72)(19,129,159,73)(20,130,160,74)(21,131,161,75)(22,132,162,76)(23,133,163,77)(24,134,164,78)(25,135,165,79)(26,136,166,80)(27,137,167,81)(28,138,168,82)(29,67,191,169)(30,68,192,170)(31,69,193,171)(32,70,194,172)(33,57,195,173)(34,58,196,174)(35,59,183,175)(36,60,184,176)(37,61,185,177)(38,62,186,178)(39,63,187,179)(40,64,188,180)(41,65,189,181)(42,66,190,182)(85,220,198,113)(86,221,199,114)(87,222,200,115)(88,223,201,116)(89,224,202,117)(90,211,203,118)(91,212,204,119)(92,213,205,120)(93,214,206,121)(94,215,207,122)(95,216,208,123)(96,217,209,124)(97,218,210,125)(98,219,197,126), (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), (1,145,24,163)(2,162,25,144)(3,143,26,161)(4,160,27,142)(5,141,28,159)(6,158,15,154)(7,153,16,157)(8,156,17,152)(9,151,18,155)(10,168,19,150)(11,149,20,167)(12,166,21,148)(13,147,22,165)(14,164,23,146)(29,113,213,184)(30,183,214,126)(31,125,215,196)(32,195,216,124)(33,123,217,194)(34,193,218,122)(35,121,219,192)(36,191,220,120)(37,119,221,190)(38,189,222,118)(39,117,223,188)(40,187,224,116)(41,115,211,186)(42,185,212,114)(43,137,74,107)(44,106,75,136)(45,135,76,105)(46,104,77,134)(47,133,78,103)(48,102,79,132)(49,131,80,101)(50,100,81,130)(51,129,82,99)(52,112,83,128)(53,127,84,111)(54,110,71,140)(55,139,72,109)(56,108,73,138)(57,172,209,95)(58,94,210,171)(59,170,197,93)(60,92,198,169)(61,182,199,91)(62,90,200,181)(63,180,201,89)(64,88,202,179)(65,178,203,87)(66,86,204,177)(67,176,205,85)(68,98,206,175)(69,174,207,97)(70,96,208,173) );
G=PermutationGroup([[(1,173,24,96),(2,97,25,174),(3,175,26,98),(4,85,27,176),(5,177,28,86),(6,87,15,178),(7,179,16,88),(8,89,17,180),(9,181,18,90),(10,91,19,182),(11,169,20,92),(12,93,21,170),(13,171,22,94),(14,95,23,172),(29,130,213,100),(30,101,214,131),(31,132,215,102),(32,103,216,133),(33,134,217,104),(34,105,218,135),(35,136,219,106),(36,107,220,137),(37,138,221,108),(38,109,222,139),(39,140,223,110),(40,111,224,127),(41,128,211,112),(42,99,212,129),(43,191,74,120),(44,121,75,192),(45,193,76,122),(46,123,77,194),(47,195,78,124),(48,125,79,196),(49,183,80,126),(50,113,81,184),(51,185,82,114),(52,115,83,186),(53,187,84,116),(54,117,71,188),(55,189,72,118),(56,119,73,190),(57,164,209,146),(58,147,210,165),(59,166,197,148),(60,149,198,167),(61,168,199,150),(62,151,200,155),(63,156,201,152),(64,153,202,157),(65,158,203,154),(66,141,204,159),(67,160,205,142),(68,143,206,161),(69,162,207,144),(70,145,208,163)], [(1,104,146,47),(2,105,147,48),(3,106,148,49),(4,107,149,50),(5,108,150,51),(6,109,151,52),(7,110,152,53),(8,111,153,54),(9,112,154,55),(10,99,141,56),(11,100,142,43),(12,101,143,44),(13,102,144,45),(14,103,145,46),(15,139,155,83),(16,140,156,84),(17,127,157,71),(18,128,158,72),(19,129,159,73),(20,130,160,74),(21,131,161,75),(22,132,162,76),(23,133,163,77),(24,134,164,78),(25,135,165,79),(26,136,166,80),(27,137,167,81),(28,138,168,82),(29,67,191,169),(30,68,192,170),(31,69,193,171),(32,70,194,172),(33,57,195,173),(34,58,196,174),(35,59,183,175),(36,60,184,176),(37,61,185,177),(38,62,186,178),(39,63,187,179),(40,64,188,180),(41,65,189,181),(42,66,190,182),(85,220,198,113),(86,221,199,114),(87,222,200,115),(88,223,201,116),(89,224,202,117),(90,211,203,118),(91,212,204,119),(92,213,205,120),(93,214,206,121),(94,215,207,122),(95,216,208,123),(96,217,209,124),(97,218,210,125),(98,219,197,126)], [(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)], [(1,145,24,163),(2,162,25,144),(3,143,26,161),(4,160,27,142),(5,141,28,159),(6,158,15,154),(7,153,16,157),(8,156,17,152),(9,151,18,155),(10,168,19,150),(11,149,20,167),(12,166,21,148),(13,147,22,165),(14,164,23,146),(29,113,213,184),(30,183,214,126),(31,125,215,196),(32,195,216,124),(33,123,217,194),(34,193,218,122),(35,121,219,192),(36,191,220,120),(37,119,221,190),(38,189,222,118),(39,117,223,188),(40,187,224,116),(41,115,211,186),(42,185,212,114),(43,137,74,107),(44,106,75,136),(45,135,76,105),(46,104,77,134),(47,133,78,103),(48,102,79,132),(49,131,80,101),(50,100,81,130),(51,129,82,99),(52,112,83,128),(53,127,84,111),(54,110,71,140),(55,139,72,109),(56,108,73,138),(57,172,209,95),(58,94,210,171),(59,170,197,93),(60,92,198,169),(61,182,199,91),(62,90,200,181),(63,180,201,89),(64,88,202,179),(65,178,203,87),(66,86,204,177),(67,176,205,85),(68,98,206,175),(69,174,207,97),(70,96,208,173)]])
94 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | ··· | 4J | 4K | ··· | 4X | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 14 | 14 | 2 | ··· | 2 | 14 | ··· | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
94 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 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 | C4 | D7 | D14 | D14 | D14 | D14 | D14 | C4×D7 | 2+ 1+4 | 2- 1+4 | D4⋊6D14 | D4.10D14 |
| kernel | C42.108D14 | C4×Dic14 | C42⋊D7 | C23.11D14 | Dic7⋊4D4 | Dic7⋊3Q8 | D7×C4⋊C4 | C2×Dic7⋊C4 | C4×C7⋊D4 | D4×Dic7 | D4×C28 | C2×D4⋊2D7 | D4⋊2D7 | C4×D4 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | D4 | C14 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 16 | 3 | 3 | 6 | 3 | 6 | 3 | 24 | 1 | 1 | 6 | 6 |
Matrix representation of C42.108D14 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 28 | 21 | 20 |
| 0 | 0 | 27 | 16 | 6 | 26 |
| 0 | 0 | 13 | 23 | 20 | 1 |
| 0 | 0 | 5 | 26 | 0 | 21 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 22 | 5 | 0 | 0 |
| 0 | 0 | 19 | 7 | 0 | 0 |
| 0 | 0 | 26 | 0 | 13 | 5 |
| 0 | 0 | 21 | 3 | 24 | 16 |
| 1 | 4 | 0 | 0 | 0 | 0 |
| 5 | 21 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 12 | 24 | 3 |
| 0 | 0 | 9 | 23 | 6 | 3 |
| 0 | 0 | 21 | 22 | 9 | 17 |
| 0 | 0 | 28 | 12 | 9 | 21 |
| 8 | 28 | 0 | 0 | 0 | 0 |
| 5 | 21 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 6 | 26 | 5 |
| 0 | 0 | 9 | 21 | 26 | 23 |
| 0 | 0 | 21 | 13 | 12 | 20 |
| 0 | 0 | 14 | 23 | 8 | 20 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,27,13,5,0,0,28,16,23,26,0,0,21,6,20,0,0,0,20,26,1,21],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,22,19,26,21,0,0,5,7,0,3,0,0,0,0,13,24,0,0,0,0,5,16],[1,5,0,0,0,0,4,21,0,0,0,0,0,0,5,9,21,28,0,0,12,23,22,12,0,0,24,6,9,9,0,0,3,3,17,21],[8,5,0,0,0,0,28,21,0,0,0,0,0,0,5,9,21,14,0,0,6,21,13,23,0,0,26,26,12,8,0,0,5,23,20,20] >;
C42.108D14 in GAP, Magma, Sage, TeX
C_4^2._{108}D_{14} % in TeX
G:=Group("C4^2.108D14"); // GroupNames label
G:=SmallGroup(448,999);
// by ID
G=gap.SmallGroup(448,999);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,387,570,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^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=a^2*c^-1>;
// generators/relations