metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.100D14, C14.1002+ 1+4, (C4×D28)⋊12C2, C28⋊4D4⋊4C2, D14⋊D4⋊5C2, C28⋊7D4⋊42C2, C4⋊C4.275D14, C28.6Q8⋊5C2, D14.5D4⋊5C2, C42⋊C2⋊19D7, (C2×C14).79C24, (C4×C28).30C22, C28.237(C4○D4), C4.121(C4○D28), (C2×C28).152C23, D14⋊C4.64C22, C22⋊C4.103D14, (C2×D28).25C22, (C22×C4).200D14, Dic7⋊C4.4C22, C2.12(D4⋊8D14), C23.90(C22×D7), C4⋊Dic7.294C22, (C2×Dic7).32C23, (C22×D7).27C23, C22.108(C23×D7), (C22×C14).149C23, (C22×C28).309C22, C7⋊1(C22.34C24), C14.35(C2×C4○D4), C2.38(C2×C4○D28), (C2×C4×D7).196C22, (C7×C42⋊C2)⋊21C2, (C7×C4⋊C4).315C22, (C2×C4).280(C22×D7), (C2×C7⋊D4).12C22, (C7×C22⋊C4).118C22, SmallGroup(448,988)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.100D14
G = < a,b,c,d | a4=b4=1, c14=a2, d2=a2b2, ab=ba, ac=ca, dad-1=a-1, cbc-1=dbd-1=a2b, dcd-1=b2c13 >
Subgroups: 1332 in 240 conjugacy classes, 95 normal (23 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C14, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, Dic7, C28, C28, D14, C2×C14, C2×C14, C42⋊C2, C4×D4, C4⋊D4, C22.D4, C42.C2, C4⋊1D4, C4×D7, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C22×D7, C22×C14, C22.34C24, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×C4×D7, C2×D28, C2×C7⋊D4, C22×C28, C28.6Q8, C4×D28, C28⋊4D4, D14⋊D4, D14.5D4, C28⋊7D4, C7×C42⋊C2, C42.100D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.34C24, C4○D28, C23×D7, C2×C4○D28, D4⋊8D14, C42.100D14
►On 224 points
Generators in S224
(1 198 15 212)(2 199 16 213)(3 200 17 214)(4 201 18 215)(5 202 19 216)(6 203 20 217)(7 204 21 218)(8 205 22 219)(9 206 23 220)(10 207 24 221)(11 208 25 222)(12 209 26 223)(13 210 27 224)(14 211 28 197)(29 185 43 171)(30 186 44 172)(31 187 45 173)(32 188 46 174)(33 189 47 175)(34 190 48 176)(35 191 49 177)(36 192 50 178)(37 193 51 179)(38 194 52 180)(39 195 53 181)(40 196 54 182)(41 169 55 183)(42 170 56 184)(57 90 71 104)(58 91 72 105)(59 92 73 106)(60 93 74 107)(61 94 75 108)(62 95 76 109)(63 96 77 110)(64 97 78 111)(65 98 79 112)(66 99 80 85)(67 100 81 86)(68 101 82 87)(69 102 83 88)(70 103 84 89)(113 167 127 153)(114 168 128 154)(115 141 129 155)(116 142 130 156)(117 143 131 157)(118 144 132 158)(119 145 133 159)(120 146 134 160)(121 147 135 161)(122 148 136 162)(123 149 137 163)(124 150 138 164)(125 151 139 165)(126 152 140 166)
(1 191 82 126)(2 178 83 113)(3 193 84 128)(4 180 57 115)(5 195 58 130)(6 182 59 117)(7 169 60 132)(8 184 61 119)(9 171 62 134)(10 186 63 121)(11 173 64 136)(12 188 65 123)(13 175 66 138)(14 190 67 125)(15 177 68 140)(16 192 69 127)(17 179 70 114)(18 194 71 129)(19 181 72 116)(20 196 73 131)(21 183 74 118)(22 170 75 133)(23 185 76 120)(24 172 77 135)(25 187 78 122)(26 174 79 137)(27 189 80 124)(28 176 81 139)(29 95 160 206)(30 110 161 221)(31 97 162 208)(32 112 163 223)(33 99 164 210)(34 86 165 197)(35 101 166 212)(36 88 167 199)(37 103 168 214)(38 90 141 201)(39 105 142 216)(40 92 143 203)(41 107 144 218)(42 94 145 205)(43 109 146 220)(44 96 147 207)(45 111 148 222)(46 98 149 209)(47 85 150 224)(48 100 151 211)(49 87 152 198)(50 102 153 213)(51 89 154 200)(52 104 155 215)(53 91 156 202)(54 106 157 217)(55 93 158 204)(56 108 159 219)
(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)
(1 132 68 183)(2 182 69 131)(3 130 70 181)(4 180 71 129)(5 128 72 179)(6 178 73 127)(7 126 74 177)(8 176 75 125)(9 124 76 175)(10 174 77 123)(11 122 78 173)(12 172 79 121)(13 120 80 171)(14 170 81 119)(15 118 82 169)(16 196 83 117)(17 116 84 195)(18 194 57 115)(19 114 58 193)(20 192 59 113)(21 140 60 191)(22 190 61 139)(23 138 62 189)(24 188 63 137)(25 136 64 187)(26 186 65 135)(27 134 66 185)(28 184 67 133)(29 224 146 99)(30 98 147 223)(31 222 148 97)(32 96 149 221)(33 220 150 95)(34 94 151 219)(35 218 152 93)(36 92 153 217)(37 216 154 91)(38 90 155 215)(39 214 156 89)(40 88 157 213)(41 212 158 87)(42 86 159 211)(43 210 160 85)(44 112 161 209)(45 208 162 111)(46 110 163 207)(47 206 164 109)(48 108 165 205)(49 204 166 107)(50 106 167 203)(51 202 168 105)(52 104 141 201)(53 200 142 103)(54 102 143 199)(55 198 144 101)(56 100 145 197)
G:=sub<Sym(224)| (1,198,15,212)(2,199,16,213)(3,200,17,214)(4,201,18,215)(5,202,19,216)(6,203,20,217)(7,204,21,218)(8,205,22,219)(9,206,23,220)(10,207,24,221)(11,208,25,222)(12,209,26,223)(13,210,27,224)(14,211,28,197)(29,185,43,171)(30,186,44,172)(31,187,45,173)(32,188,46,174)(33,189,47,175)(34,190,48,176)(35,191,49,177)(36,192,50,178)(37,193,51,179)(38,194,52,180)(39,195,53,181)(40,196,54,182)(41,169,55,183)(42,170,56,184)(57,90,71,104)(58,91,72,105)(59,92,73,106)(60,93,74,107)(61,94,75,108)(62,95,76,109)(63,96,77,110)(64,97,78,111)(65,98,79,112)(66,99,80,85)(67,100,81,86)(68,101,82,87)(69,102,83,88)(70,103,84,89)(113,167,127,153)(114,168,128,154)(115,141,129,155)(116,142,130,156)(117,143,131,157)(118,144,132,158)(119,145,133,159)(120,146,134,160)(121,147,135,161)(122,148,136,162)(123,149,137,163)(124,150,138,164)(125,151,139,165)(126,152,140,166), (1,191,82,126)(2,178,83,113)(3,193,84,128)(4,180,57,115)(5,195,58,130)(6,182,59,117)(7,169,60,132)(8,184,61,119)(9,171,62,134)(10,186,63,121)(11,173,64,136)(12,188,65,123)(13,175,66,138)(14,190,67,125)(15,177,68,140)(16,192,69,127)(17,179,70,114)(18,194,71,129)(19,181,72,116)(20,196,73,131)(21,183,74,118)(22,170,75,133)(23,185,76,120)(24,172,77,135)(25,187,78,122)(26,174,79,137)(27,189,80,124)(28,176,81,139)(29,95,160,206)(30,110,161,221)(31,97,162,208)(32,112,163,223)(33,99,164,210)(34,86,165,197)(35,101,166,212)(36,88,167,199)(37,103,168,214)(38,90,141,201)(39,105,142,216)(40,92,143,203)(41,107,144,218)(42,94,145,205)(43,109,146,220)(44,96,147,207)(45,111,148,222)(46,98,149,209)(47,85,150,224)(48,100,151,211)(49,87,152,198)(50,102,153,213)(51,89,154,200)(52,104,155,215)(53,91,156,202)(54,106,157,217)(55,93,158,204)(56,108,159,219), (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), (1,132,68,183)(2,182,69,131)(3,130,70,181)(4,180,71,129)(5,128,72,179)(6,178,73,127)(7,126,74,177)(8,176,75,125)(9,124,76,175)(10,174,77,123)(11,122,78,173)(12,172,79,121)(13,120,80,171)(14,170,81,119)(15,118,82,169)(16,196,83,117)(17,116,84,195)(18,194,57,115)(19,114,58,193)(20,192,59,113)(21,140,60,191)(22,190,61,139)(23,138,62,189)(24,188,63,137)(25,136,64,187)(26,186,65,135)(27,134,66,185)(28,184,67,133)(29,224,146,99)(30,98,147,223)(31,222,148,97)(32,96,149,221)(33,220,150,95)(34,94,151,219)(35,218,152,93)(36,92,153,217)(37,216,154,91)(38,90,155,215)(39,214,156,89)(40,88,157,213)(41,212,158,87)(42,86,159,211)(43,210,160,85)(44,112,161,209)(45,208,162,111)(46,110,163,207)(47,206,164,109)(48,108,165,205)(49,204,166,107)(50,106,167,203)(51,202,168,105)(52,104,141,201)(53,200,142,103)(54,102,143,199)(55,198,144,101)(56,100,145,197)>;
G:=Group( (1,198,15,212)(2,199,16,213)(3,200,17,214)(4,201,18,215)(5,202,19,216)(6,203,20,217)(7,204,21,218)(8,205,22,219)(9,206,23,220)(10,207,24,221)(11,208,25,222)(12,209,26,223)(13,210,27,224)(14,211,28,197)(29,185,43,171)(30,186,44,172)(31,187,45,173)(32,188,46,174)(33,189,47,175)(34,190,48,176)(35,191,49,177)(36,192,50,178)(37,193,51,179)(38,194,52,180)(39,195,53,181)(40,196,54,182)(41,169,55,183)(42,170,56,184)(57,90,71,104)(58,91,72,105)(59,92,73,106)(60,93,74,107)(61,94,75,108)(62,95,76,109)(63,96,77,110)(64,97,78,111)(65,98,79,112)(66,99,80,85)(67,100,81,86)(68,101,82,87)(69,102,83,88)(70,103,84,89)(113,167,127,153)(114,168,128,154)(115,141,129,155)(116,142,130,156)(117,143,131,157)(118,144,132,158)(119,145,133,159)(120,146,134,160)(121,147,135,161)(122,148,136,162)(123,149,137,163)(124,150,138,164)(125,151,139,165)(126,152,140,166), (1,191,82,126)(2,178,83,113)(3,193,84,128)(4,180,57,115)(5,195,58,130)(6,182,59,117)(7,169,60,132)(8,184,61,119)(9,171,62,134)(10,186,63,121)(11,173,64,136)(12,188,65,123)(13,175,66,138)(14,190,67,125)(15,177,68,140)(16,192,69,127)(17,179,70,114)(18,194,71,129)(19,181,72,116)(20,196,73,131)(21,183,74,118)(22,170,75,133)(23,185,76,120)(24,172,77,135)(25,187,78,122)(26,174,79,137)(27,189,80,124)(28,176,81,139)(29,95,160,206)(30,110,161,221)(31,97,162,208)(32,112,163,223)(33,99,164,210)(34,86,165,197)(35,101,166,212)(36,88,167,199)(37,103,168,214)(38,90,141,201)(39,105,142,216)(40,92,143,203)(41,107,144,218)(42,94,145,205)(43,109,146,220)(44,96,147,207)(45,111,148,222)(46,98,149,209)(47,85,150,224)(48,100,151,211)(49,87,152,198)(50,102,153,213)(51,89,154,200)(52,104,155,215)(53,91,156,202)(54,106,157,217)(55,93,158,204)(56,108,159,219), (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), (1,132,68,183)(2,182,69,131)(3,130,70,181)(4,180,71,129)(5,128,72,179)(6,178,73,127)(7,126,74,177)(8,176,75,125)(9,124,76,175)(10,174,77,123)(11,122,78,173)(12,172,79,121)(13,120,80,171)(14,170,81,119)(15,118,82,169)(16,196,83,117)(17,116,84,195)(18,194,57,115)(19,114,58,193)(20,192,59,113)(21,140,60,191)(22,190,61,139)(23,138,62,189)(24,188,63,137)(25,136,64,187)(26,186,65,135)(27,134,66,185)(28,184,67,133)(29,224,146,99)(30,98,147,223)(31,222,148,97)(32,96,149,221)(33,220,150,95)(34,94,151,219)(35,218,152,93)(36,92,153,217)(37,216,154,91)(38,90,155,215)(39,214,156,89)(40,88,157,213)(41,212,158,87)(42,86,159,211)(43,210,160,85)(44,112,161,209)(45,208,162,111)(46,110,163,207)(47,206,164,109)(48,108,165,205)(49,204,166,107)(50,106,167,203)(51,202,168,105)(52,104,141,201)(53,200,142,103)(54,102,143,199)(55,198,144,101)(56,100,145,197) );
G=PermutationGroup([[(1,198,15,212),(2,199,16,213),(3,200,17,214),(4,201,18,215),(5,202,19,216),(6,203,20,217),(7,204,21,218),(8,205,22,219),(9,206,23,220),(10,207,24,221),(11,208,25,222),(12,209,26,223),(13,210,27,224),(14,211,28,197),(29,185,43,171),(30,186,44,172),(31,187,45,173),(32,188,46,174),(33,189,47,175),(34,190,48,176),(35,191,49,177),(36,192,50,178),(37,193,51,179),(38,194,52,180),(39,195,53,181),(40,196,54,182),(41,169,55,183),(42,170,56,184),(57,90,71,104),(58,91,72,105),(59,92,73,106),(60,93,74,107),(61,94,75,108),(62,95,76,109),(63,96,77,110),(64,97,78,111),(65,98,79,112),(66,99,80,85),(67,100,81,86),(68,101,82,87),(69,102,83,88),(70,103,84,89),(113,167,127,153),(114,168,128,154),(115,141,129,155),(116,142,130,156),(117,143,131,157),(118,144,132,158),(119,145,133,159),(120,146,134,160),(121,147,135,161),(122,148,136,162),(123,149,137,163),(124,150,138,164),(125,151,139,165),(126,152,140,166)], [(1,191,82,126),(2,178,83,113),(3,193,84,128),(4,180,57,115),(5,195,58,130),(6,182,59,117),(7,169,60,132),(8,184,61,119),(9,171,62,134),(10,186,63,121),(11,173,64,136),(12,188,65,123),(13,175,66,138),(14,190,67,125),(15,177,68,140),(16,192,69,127),(17,179,70,114),(18,194,71,129),(19,181,72,116),(20,196,73,131),(21,183,74,118),(22,170,75,133),(23,185,76,120),(24,172,77,135),(25,187,78,122),(26,174,79,137),(27,189,80,124),(28,176,81,139),(29,95,160,206),(30,110,161,221),(31,97,162,208),(32,112,163,223),(33,99,164,210),(34,86,165,197),(35,101,166,212),(36,88,167,199),(37,103,168,214),(38,90,141,201),(39,105,142,216),(40,92,143,203),(41,107,144,218),(42,94,145,205),(43,109,146,220),(44,96,147,207),(45,111,148,222),(46,98,149,209),(47,85,150,224),(48,100,151,211),(49,87,152,198),(50,102,153,213),(51,89,154,200),(52,104,155,215),(53,91,156,202),(54,106,157,217),(55,93,158,204),(56,108,159,219)], [(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)], [(1,132,68,183),(2,182,69,131),(3,130,70,181),(4,180,71,129),(5,128,72,179),(6,178,73,127),(7,126,74,177),(8,176,75,125),(9,124,76,175),(10,174,77,123),(11,122,78,173),(12,172,79,121),(13,120,80,171),(14,170,81,119),(15,118,82,169),(16,196,83,117),(17,116,84,195),(18,194,57,115),(19,114,58,193),(20,192,59,113),(21,140,60,191),(22,190,61,139),(23,138,62,189),(24,188,63,137),(25,136,64,187),(26,186,65,135),(27,134,66,185),(28,184,67,133),(29,224,146,99),(30,98,147,223),(31,222,148,97),(32,96,149,221),(33,220,150,95),(34,94,151,219),(35,218,152,93),(36,92,153,217),(37,216,154,91),(38,90,155,215),(39,214,156,89),(40,88,157,213),(41,212,158,87),(42,86,159,211),(43,210,160,85),(44,112,161,209),(45,208,162,111),(46,110,163,207),(47,206,164,109),(48,108,165,205),(49,204,166,107),(50,106,167,203),(51,202,168,105),(52,104,141,201),(53,200,142,103),(54,102,143,199),(55,198,144,101),(56,100,145,197)]])
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 4 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | 4 | 4 | 28 | 28 | 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 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | D14 | C4○D28 | 2+ 1+4 | D4⋊8D14 |
| kernel | C42.100D14 | C28.6Q8 | C4×D28 | C28⋊4D4 | D14⋊D4 | D14.5D4 | C28⋊7D4 | C7×C42⋊C2 | C42⋊C2 | C28 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C4 | C14 | C2 |
| # reps | 1 | 1 | 2 | 1 | 4 | 4 | 2 | 1 | 3 | 4 | 6 | 6 | 6 | 3 | 24 | 2 | 12 |
Matrix representation of C42.100D14 ►in GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 23 | 0 | 0 |
| 0 | 0 | 6 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 19 | 23 |
| 0 | 0 | 0 | 0 | 12 | 10 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 23 | 0 | 0 |
| 0 | 0 | 6 | 8 | 0 | 0 |
| 0 | 0 | 20 | 14 | 10 | 6 |
| 0 | 0 | 18 | 7 | 17 | 19 |
| 1 | 21 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 19 | 11 | 21 |
| 0 | 0 | 10 | 7 | 10 | 6 |
| 0 | 0 | 16 | 21 | 23 | 10 |
| 0 | 0 | 22 | 11 | 9 | 9 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 3 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 20 | 9 | 0 | 0 |
| 0 | 0 | 4 | 9 | 0 | 0 |
| 0 | 0 | 15 | 2 | 1 | 21 |
| 0 | 0 | 15 | 23 | 0 | 28 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,21,6,0,0,0,0,23,8,0,0,0,0,0,0,19,12,0,0,0,0,23,10],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,21,6,20,18,0,0,23,8,14,7,0,0,0,0,10,17,0,0,0,0,6,19],[1,0,0,0,0,0,21,28,0,0,0,0,0,0,19,10,16,22,0,0,19,7,21,11,0,0,11,10,23,9,0,0,21,6,10,9],[12,3,0,0,0,0,0,17,0,0,0,0,0,0,20,4,15,15,0,0,9,9,2,23,0,0,0,0,1,0,0,0,0,0,21,28] >;
C42.100D14 in GAP, Magma, Sage, TeX
C_4^2._{100}D_{14} % in TeX
G:=Group("C4^2.100D14"); // GroupNames label
G:=SmallGroup(448,988);
// by ID
G=gap.SmallGroup(448,988);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,232,100,675,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=a^2,d^2=a^2*b^2,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,c*b*c^-1=d*b*d^-1=a^2*b,d*c*d^-1=b^2*c^13>;
// generators/relations