metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.240D14, (C4×D7)⋊9D4, C4⋊Q8⋊19D7, C4.38(D4×D7), C28⋊6(C4○D4), D14.8(C2×D4), C28.70(C2×D4), C28⋊4D4⋊17C2, C4⋊D28⋊39C2, C4⋊C4.217D14, C4⋊1(Q8⋊2D7), (D7×C42)⋊14C2, D28⋊C4⋊43C2, (C2×Q8).144D14, Dic7.67(C2×D4), C14.99(C22×D4), C28.23D4⋊26C2, (C4×C28).210C22, (C2×C28).102C23, (C2×C14).269C24, D14⋊C4.50C22, (C2×D28).172C22, (Q8×C14).136C22, C7⋊6(C22.26C24), C22.290(C23×D7), (C2×Dic7).272C23, (C4×Dic7).258C22, (C22×D7).119C23, C2.72(C2×D4×D7), (C7×C4⋊Q8)⋊11C2, (C2×Q8⋊2D7)⋊12C2, C14.120(C2×C4○D4), C2.27(C2×Q8⋊2D7), (C2×C4×D7).143C22, (C7×C4⋊C4).212C22, (C2×C4).599(C22×D7), SmallGroup(448,1178)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.240D14
G = < a,b,c,d | a4=b4=d2=1, c14=b2, ab=ba, cac-1=dad=a-1, cbc-1=dbd=b-1, dcd=b2c13 >
Subgroups: 1612 in 310 conjugacy classes, 111 normal (19 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C14, C42, C42, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C42, C4×D4, C4⋊D4, C4.4D4, C4⋊1D4, C4⋊Q8, C2×C4○D4, C4×D7, C4×D7, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C22×D7, C22.26C24, C4×Dic7, C4×Dic7, D14⋊C4, C4×C28, C7×C4⋊C4, C2×C4×D7, C2×C4×D7, C2×D28, Q8⋊2D7, Q8×C14, D7×C42, C28⋊4D4, D28⋊C4, C4⋊D28, C28.23D4, C7×C4⋊Q8, C2×Q8⋊2D7, C42.240D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C22×D4, C2×C4○D4, C22×D7, C22.26C24, D4×D7, Q8⋊2D7, C23×D7, C2×D4×D7, C2×Q8⋊2D7, C42.240D14
►On 224 points
Generators in S224
(1 44 95 196)(2 169 96 45)(3 46 97 170)(4 171 98 47)(5 48 99 172)(6 173 100 49)(7 50 101 174)(8 175 102 51)(9 52 103 176)(10 177 104 53)(11 54 105 178)(12 179 106 55)(13 56 107 180)(14 181 108 29)(15 30 109 182)(16 183 110 31)(17 32 111 184)(18 185 112 33)(19 34 85 186)(20 187 86 35)(21 36 87 188)(22 189 88 37)(23 38 89 190)(24 191 90 39)(25 40 91 192)(26 193 92 41)(27 42 93 194)(28 195 94 43)(57 130 147 217)(58 218 148 131)(59 132 149 219)(60 220 150 133)(61 134 151 221)(62 222 152 135)(63 136 153 223)(64 224 154 137)(65 138 155 197)(66 198 156 139)(67 140 157 199)(68 200 158 113)(69 114 159 201)(70 202 160 115)(71 116 161 203)(72 204 162 117)(73 118 163 205)(74 206 164 119)(75 120 165 207)(76 208 166 121)(77 122 167 209)(78 210 168 123)(79 124 141 211)(80 212 142 125)(81 126 143 213)(82 214 144 127)(83 128 145 215)(84 216 146 129)
(1 203 15 217)(2 218 16 204)(3 205 17 219)(4 220 18 206)(5 207 19 221)(6 222 20 208)(7 209 21 223)(8 224 22 210)(9 211 23 197)(10 198 24 212)(11 213 25 199)(12 200 26 214)(13 215 27 201)(14 202 28 216)(29 70 43 84)(30 57 44 71)(31 72 45 58)(32 59 46 73)(33 74 47 60)(34 61 48 75)(35 76 49 62)(36 63 50 77)(37 78 51 64)(38 65 52 79)(39 80 53 66)(40 67 54 81)(41 82 55 68)(42 69 56 83)(85 134 99 120)(86 121 100 135)(87 136 101 122)(88 123 102 137)(89 138 103 124)(90 125 104 139)(91 140 105 126)(92 127 106 113)(93 114 107 128)(94 129 108 115)(95 116 109 130)(96 131 110 117)(97 118 111 132)(98 133 112 119)(141 190 155 176)(142 177 156 191)(143 192 157 178)(144 179 158 193)(145 194 159 180)(146 181 160 195)(147 196 161 182)(148 183 162 169)(149 170 163 184)(150 185 164 171)(151 172 165 186)(152 187 166 173)(153 174 167 188)(154 189 168 175)
(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)
(1 108)(2 107)(3 106)(4 105)(5 104)(6 103)(7 102)(8 101)(9 100)(10 99)(11 98)(12 97)(13 96)(14 95)(15 94)(16 93)(17 92)(18 91)(19 90)(20 89)(21 88)(22 87)(23 86)(24 85)(25 112)(26 111)(27 110)(28 109)(29 196)(30 195)(31 194)(32 193)(33 192)(34 191)(35 190)(36 189)(37 188)(38 187)(39 186)(40 185)(41 184)(42 183)(43 182)(44 181)(45 180)(46 179)(47 178)(48 177)(49 176)(50 175)(51 174)(52 173)(53 172)(54 171)(55 170)(56 169)(57 160)(58 159)(59 158)(60 157)(61 156)(62 155)(63 154)(64 153)(65 152)(66 151)(67 150)(68 149)(69 148)(70 147)(71 146)(72 145)(73 144)(74 143)(75 142)(76 141)(77 168)(78 167)(79 166)(80 165)(81 164)(82 163)(83 162)(84 161)(113 219)(114 218)(115 217)(116 216)(117 215)(118 214)(119 213)(120 212)(121 211)(122 210)(123 209)(124 208)(125 207)(126 206)(127 205)(128 204)(129 203)(130 202)(131 201)(132 200)(133 199)(134 198)(135 197)(136 224)(137 223)(138 222)(139 221)(140 220)
G:=sub<Sym(224)| (1,44,95,196)(2,169,96,45)(3,46,97,170)(4,171,98,47)(5,48,99,172)(6,173,100,49)(7,50,101,174)(8,175,102,51)(9,52,103,176)(10,177,104,53)(11,54,105,178)(12,179,106,55)(13,56,107,180)(14,181,108,29)(15,30,109,182)(16,183,110,31)(17,32,111,184)(18,185,112,33)(19,34,85,186)(20,187,86,35)(21,36,87,188)(22,189,88,37)(23,38,89,190)(24,191,90,39)(25,40,91,192)(26,193,92,41)(27,42,93,194)(28,195,94,43)(57,130,147,217)(58,218,148,131)(59,132,149,219)(60,220,150,133)(61,134,151,221)(62,222,152,135)(63,136,153,223)(64,224,154,137)(65,138,155,197)(66,198,156,139)(67,140,157,199)(68,200,158,113)(69,114,159,201)(70,202,160,115)(71,116,161,203)(72,204,162,117)(73,118,163,205)(74,206,164,119)(75,120,165,207)(76,208,166,121)(77,122,167,209)(78,210,168,123)(79,124,141,211)(80,212,142,125)(81,126,143,213)(82,214,144,127)(83,128,145,215)(84,216,146,129), (1,203,15,217)(2,218,16,204)(3,205,17,219)(4,220,18,206)(5,207,19,221)(6,222,20,208)(7,209,21,223)(8,224,22,210)(9,211,23,197)(10,198,24,212)(11,213,25,199)(12,200,26,214)(13,215,27,201)(14,202,28,216)(29,70,43,84)(30,57,44,71)(31,72,45,58)(32,59,46,73)(33,74,47,60)(34,61,48,75)(35,76,49,62)(36,63,50,77)(37,78,51,64)(38,65,52,79)(39,80,53,66)(40,67,54,81)(41,82,55,68)(42,69,56,83)(85,134,99,120)(86,121,100,135)(87,136,101,122)(88,123,102,137)(89,138,103,124)(90,125,104,139)(91,140,105,126)(92,127,106,113)(93,114,107,128)(94,129,108,115)(95,116,109,130)(96,131,110,117)(97,118,111,132)(98,133,112,119)(141,190,155,176)(142,177,156,191)(143,192,157,178)(144,179,158,193)(145,194,159,180)(146,181,160,195)(147,196,161,182)(148,183,162,169)(149,170,163,184)(150,185,164,171)(151,172,165,186)(152,187,166,173)(153,174,167,188)(154,189,168,175), (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), (1,108)(2,107)(3,106)(4,105)(5,104)(6,103)(7,102)(8,101)(9,100)(10,99)(11,98)(12,97)(13,96)(14,95)(15,94)(16,93)(17,92)(18,91)(19,90)(20,89)(21,88)(22,87)(23,86)(24,85)(25,112)(26,111)(27,110)(28,109)(29,196)(30,195)(31,194)(32,193)(33,192)(34,191)(35,190)(36,189)(37,188)(38,187)(39,186)(40,185)(41,184)(42,183)(43,182)(44,181)(45,180)(46,179)(47,178)(48,177)(49,176)(50,175)(51,174)(52,173)(53,172)(54,171)(55,170)(56,169)(57,160)(58,159)(59,158)(60,157)(61,156)(62,155)(63,154)(64,153)(65,152)(66,151)(67,150)(68,149)(69,148)(70,147)(71,146)(72,145)(73,144)(74,143)(75,142)(76,141)(77,168)(78,167)(79,166)(80,165)(81,164)(82,163)(83,162)(84,161)(113,219)(114,218)(115,217)(116,216)(117,215)(118,214)(119,213)(120,212)(121,211)(122,210)(123,209)(124,208)(125,207)(126,206)(127,205)(128,204)(129,203)(130,202)(131,201)(132,200)(133,199)(134,198)(135,197)(136,224)(137,223)(138,222)(139,221)(140,220)>;
G:=Group( (1,44,95,196)(2,169,96,45)(3,46,97,170)(4,171,98,47)(5,48,99,172)(6,173,100,49)(7,50,101,174)(8,175,102,51)(9,52,103,176)(10,177,104,53)(11,54,105,178)(12,179,106,55)(13,56,107,180)(14,181,108,29)(15,30,109,182)(16,183,110,31)(17,32,111,184)(18,185,112,33)(19,34,85,186)(20,187,86,35)(21,36,87,188)(22,189,88,37)(23,38,89,190)(24,191,90,39)(25,40,91,192)(26,193,92,41)(27,42,93,194)(28,195,94,43)(57,130,147,217)(58,218,148,131)(59,132,149,219)(60,220,150,133)(61,134,151,221)(62,222,152,135)(63,136,153,223)(64,224,154,137)(65,138,155,197)(66,198,156,139)(67,140,157,199)(68,200,158,113)(69,114,159,201)(70,202,160,115)(71,116,161,203)(72,204,162,117)(73,118,163,205)(74,206,164,119)(75,120,165,207)(76,208,166,121)(77,122,167,209)(78,210,168,123)(79,124,141,211)(80,212,142,125)(81,126,143,213)(82,214,144,127)(83,128,145,215)(84,216,146,129), (1,203,15,217)(2,218,16,204)(3,205,17,219)(4,220,18,206)(5,207,19,221)(6,222,20,208)(7,209,21,223)(8,224,22,210)(9,211,23,197)(10,198,24,212)(11,213,25,199)(12,200,26,214)(13,215,27,201)(14,202,28,216)(29,70,43,84)(30,57,44,71)(31,72,45,58)(32,59,46,73)(33,74,47,60)(34,61,48,75)(35,76,49,62)(36,63,50,77)(37,78,51,64)(38,65,52,79)(39,80,53,66)(40,67,54,81)(41,82,55,68)(42,69,56,83)(85,134,99,120)(86,121,100,135)(87,136,101,122)(88,123,102,137)(89,138,103,124)(90,125,104,139)(91,140,105,126)(92,127,106,113)(93,114,107,128)(94,129,108,115)(95,116,109,130)(96,131,110,117)(97,118,111,132)(98,133,112,119)(141,190,155,176)(142,177,156,191)(143,192,157,178)(144,179,158,193)(145,194,159,180)(146,181,160,195)(147,196,161,182)(148,183,162,169)(149,170,163,184)(150,185,164,171)(151,172,165,186)(152,187,166,173)(153,174,167,188)(154,189,168,175), (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), (1,108)(2,107)(3,106)(4,105)(5,104)(6,103)(7,102)(8,101)(9,100)(10,99)(11,98)(12,97)(13,96)(14,95)(15,94)(16,93)(17,92)(18,91)(19,90)(20,89)(21,88)(22,87)(23,86)(24,85)(25,112)(26,111)(27,110)(28,109)(29,196)(30,195)(31,194)(32,193)(33,192)(34,191)(35,190)(36,189)(37,188)(38,187)(39,186)(40,185)(41,184)(42,183)(43,182)(44,181)(45,180)(46,179)(47,178)(48,177)(49,176)(50,175)(51,174)(52,173)(53,172)(54,171)(55,170)(56,169)(57,160)(58,159)(59,158)(60,157)(61,156)(62,155)(63,154)(64,153)(65,152)(66,151)(67,150)(68,149)(69,148)(70,147)(71,146)(72,145)(73,144)(74,143)(75,142)(76,141)(77,168)(78,167)(79,166)(80,165)(81,164)(82,163)(83,162)(84,161)(113,219)(114,218)(115,217)(116,216)(117,215)(118,214)(119,213)(120,212)(121,211)(122,210)(123,209)(124,208)(125,207)(126,206)(127,205)(128,204)(129,203)(130,202)(131,201)(132,200)(133,199)(134,198)(135,197)(136,224)(137,223)(138,222)(139,221)(140,220) );
G=PermutationGroup([[(1,44,95,196),(2,169,96,45),(3,46,97,170),(4,171,98,47),(5,48,99,172),(6,173,100,49),(7,50,101,174),(8,175,102,51),(9,52,103,176),(10,177,104,53),(11,54,105,178),(12,179,106,55),(13,56,107,180),(14,181,108,29),(15,30,109,182),(16,183,110,31),(17,32,111,184),(18,185,112,33),(19,34,85,186),(20,187,86,35),(21,36,87,188),(22,189,88,37),(23,38,89,190),(24,191,90,39),(25,40,91,192),(26,193,92,41),(27,42,93,194),(28,195,94,43),(57,130,147,217),(58,218,148,131),(59,132,149,219),(60,220,150,133),(61,134,151,221),(62,222,152,135),(63,136,153,223),(64,224,154,137),(65,138,155,197),(66,198,156,139),(67,140,157,199),(68,200,158,113),(69,114,159,201),(70,202,160,115),(71,116,161,203),(72,204,162,117),(73,118,163,205),(74,206,164,119),(75,120,165,207),(76,208,166,121),(77,122,167,209),(78,210,168,123),(79,124,141,211),(80,212,142,125),(81,126,143,213),(82,214,144,127),(83,128,145,215),(84,216,146,129)], [(1,203,15,217),(2,218,16,204),(3,205,17,219),(4,220,18,206),(5,207,19,221),(6,222,20,208),(7,209,21,223),(8,224,22,210),(9,211,23,197),(10,198,24,212),(11,213,25,199),(12,200,26,214),(13,215,27,201),(14,202,28,216),(29,70,43,84),(30,57,44,71),(31,72,45,58),(32,59,46,73),(33,74,47,60),(34,61,48,75),(35,76,49,62),(36,63,50,77),(37,78,51,64),(38,65,52,79),(39,80,53,66),(40,67,54,81),(41,82,55,68),(42,69,56,83),(85,134,99,120),(86,121,100,135),(87,136,101,122),(88,123,102,137),(89,138,103,124),(90,125,104,139),(91,140,105,126),(92,127,106,113),(93,114,107,128),(94,129,108,115),(95,116,109,130),(96,131,110,117),(97,118,111,132),(98,133,112,119),(141,190,155,176),(142,177,156,191),(143,192,157,178),(144,179,158,193),(145,194,159,180),(146,181,160,195),(147,196,161,182),(148,183,162,169),(149,170,163,184),(150,185,164,171),(151,172,165,186),(152,187,166,173),(153,174,167,188),(154,189,168,175)], [(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)], [(1,108),(2,107),(3,106),(4,105),(5,104),(6,103),(7,102),(8,101),(9,100),(10,99),(11,98),(12,97),(13,96),(14,95),(15,94),(16,93),(17,92),(18,91),(19,90),(20,89),(21,88),(22,87),(23,86),(24,85),(25,112),(26,111),(27,110),(28,109),(29,196),(30,195),(31,194),(32,193),(33,192),(34,191),(35,190),(36,189),(37,188),(38,187),(39,186),(40,185),(41,184),(42,183),(43,182),(44,181),(45,180),(46,179),(47,178),(48,177),(49,176),(50,175),(51,174),(52,173),(53,172),(54,171),(55,170),(56,169),(57,160),(58,159),(59,158),(60,157),(61,156),(62,155),(63,154),(64,153),(65,152),(66,151),(67,150),(68,149),(69,148),(70,147),(71,146),(72,145),(73,144),(74,143),(75,142),(76,141),(77,168),(78,167),(79,166),(80,165),(81,164),(82,163),(83,162),(84,161),(113,219),(114,218),(115,217),(116,216),(117,215),(118,214),(119,213),(120,212),(121,211),(122,210),(123,209),(124,208),(125,207),(126,206),(127,205),(128,204),(129,203),(130,202),(131,201),(132,200),(133,199),(134,198),(135,197),(136,224),(137,223),(138,222),(139,221),(140,220)]])
70 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 4Q | 4R | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 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 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 7 | 14 | 14 | 14 | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
70 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | D4×D7 | Q8⋊2D7 |
| kernel | C42.240D14 | D7×C42 | C28⋊4D4 | D28⋊C4 | C4⋊D28 | C28.23D4 | C7×C4⋊Q8 | C2×Q8⋊2D7 | C4×D7 | C4⋊Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | C4 | C4 |
| # reps | 1 | 1 | 1 | 4 | 4 | 2 | 1 | 2 | 4 | 3 | 8 | 3 | 12 | 6 | 6 | 12 |
Matrix representation of C42.240D14 ►in GL6(𝔽29)
| 12 | 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 | 9 | 16 |
| 0 | 0 | 0 | 0 | 13 | 20 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 8 | 0 | 0 |
| 0 | 0 | 12 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 22 | 26 | 0 | 0 |
| 0 | 0 | 16 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 0 | 0 | 0 | 28 | 0 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,0,17,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,9,13,0,0,0,0,16,20],[17,0,0,0,0,0,0,12,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[0,28,0,0,0,0,1,0,0,0,0,0,0,0,10,12,0,0,0,0,8,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,22,16,0,0,0,0,26,7,0,0,0,0,0,0,0,28,0,0,0,0,28,0] >;
C42.240D14 in GAP, Magma, Sage, TeX
C_4^2._{240}D_{14} % in TeX
G:=Group("C4^2.240D14"); // GroupNames label
G:=SmallGroup(448,1178);
// by ID
G=gap.SmallGroup(448,1178);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,100,675,570,185,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=d^2=1,c^14=b^2,a*b=b*a,c*a*c^-1=d*a*d=a^-1,c*b*c^-1=d*b*d=b^-1,d*c*d=b^2*c^13>;
// generators/relations