metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.238D14, (C4×D7)⋊8D4, C4.35(D4×D7), C28⋊4(C4○D4), C4⋊1D4⋊10D7, D14.7(C2×D4), C28.66(C2×D4), C4⋊2(D4⋊2D7), C28⋊2D4⋊35C2, C28⋊2Q8⋊34C2, (D4×Dic7)⋊34C2, (D7×C42)⋊13C2, (C2×D4).178D14, Dic7.66(C2×D4), C14.94(C22×D4), C28.17D4⋊27C2, (C4×C28).203C22, (C2×C14).260C24, (C2×C28).508C23, C23.66(C22×D7), (D4×C14).161C22, C4⋊Dic7.248C22, (C22×C14).74C23, C7⋊5(C22.26C24), C22.281(C23×D7), C23.D7.72C22, (C2×Dic7).135C23, (C4×Dic7).256C22, (C22×D7).228C23, (C2×Dic14).185C22, (C22×Dic7).157C22, C2.67(C2×D4×D7), (C7×C4⋊1D4)⋊7C2, C14.96(C2×C4○D4), (C2×D4⋊2D7)⋊21C2, C2.60(C2×D4⋊2D7), (C2×C4×D7).251C22, (C2×C4).597(C22×D7), (C2×C7⋊D4).77C22, SmallGroup(448,1169)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.238D14
G = < a,b,c,d | a4=b4=c14=1, d2=b2, ab=ba, cac-1=dad-1=a-1, cbc-1=dbd-1=b-1, dcd-1=b2c-1 >
Subgroups: 1324 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, C23, D7, C14, C14, C14, C42, C42, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×D4, C2×Q8, C4○D4, Dic7, Dic7, C28, D14, D14, C2×C14, C2×C14, C2×C42, C4×D4, C4⋊D4, C4.4D4, C4⋊1D4, C4⋊Q8, C2×C4○D4, Dic14, C4×D7, C4×D7, C2×Dic7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C22.26C24, C4×Dic7, C4×Dic7, C4⋊Dic7, C23.D7, C4×C28, C2×Dic14, C2×C4×D7, C2×C4×D7, D4⋊2D7, C22×Dic7, C2×C7⋊D4, D4×C14, C28⋊2Q8, D7×C42, D4×Dic7, C28.17D4, C28⋊2D4, C7×C4⋊1D4, C2×D4⋊2D7, C42.238D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C22×D4, C2×C4○D4, C22×D7, C22.26C24, D4×D7, D4⋊2D7, C23×D7, C2×D4×D7, C2×D4⋊2D7, C42.238D14
►On 224 points
Generators in S224
(1 203 162 145)(2 146 163 204)(3 205 164 147)(4 148 165 206)(5 207 166 149)(6 150 167 208)(7 209 168 151)(8 152 155 210)(9 197 156 153)(10 154 157 198)(11 199 158 141)(12 142 159 200)(13 201 160 143)(14 144 161 202)(15 137 38 81)(16 82 39 138)(17 139 40 83)(18 84 41 140)(19 127 42 71)(20 72 29 128)(21 129 30 73)(22 74 31 130)(23 131 32 75)(24 76 33 132)(25 133 34 77)(26 78 35 134)(27 135 36 79)(28 80 37 136)(43 106 213 89)(44 90 214 107)(45 108 215 91)(46 92 216 109)(47 110 217 93)(48 94 218 111)(49 112 219 95)(50 96 220 99)(51 100 221 97)(52 98 222 101)(53 102 223 85)(54 86 224 103)(55 104 211 87)(56 88 212 105)(57 118 179 195)(58 196 180 119)(59 120 181 183)(60 184 182 121)(61 122 169 185)(62 186 170 123)(63 124 171 187)(64 188 172 125)(65 126 173 189)(66 190 174 113)(67 114 175 191)(68 192 176 115)(69 116 177 193)(70 194 178 117)
(1 52 184 25)(2 26 185 53)(3 54 186 27)(4 28 187 55)(5 56 188 15)(6 16 189 43)(7 44 190 17)(8 18 191 45)(9 46 192 19)(10 20 193 47)(11 48 194 21)(12 22 195 49)(13 50 196 23)(14 24 183 51)(29 116 217 157)(30 158 218 117)(31 118 219 159)(32 160 220 119)(33 120 221 161)(34 162 222 121)(35 122 223 163)(36 164 224 123)(37 124 211 165)(38 166 212 125)(39 126 213 167)(40 168 214 113)(41 114 215 155)(42 156 216 115)(57 112 142 74)(58 75 143 99)(59 100 144 76)(60 77 145 101)(61 102 146 78)(62 79 147 103)(63 104 148 80)(64 81 149 105)(65 106 150 82)(66 83 151 107)(67 108 152 84)(68 71 153 109)(69 110 154 72)(70 73 141 111)(85 204 134 169)(86 170 135 205)(87 206 136 171)(88 172 137 207)(89 208 138 173)(90 174 139 209)(91 210 140 175)(92 176 127 197)(93 198 128 177)(94 178 129 199)(95 200 130 179)(96 180 131 201)(97 202 132 181)(98 182 133 203)
(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)
(1 161 184 120)(2 119 185 160)(3 159 186 118)(4 117 187 158)(5 157 188 116)(6 115 189 156)(7 155 190 114)(8 113 191 168)(9 167 192 126)(10 125 193 166)(11 165 194 124)(12 123 195 164)(13 163 196 122)(14 121 183 162)(15 29 56 217)(16 216 43 42)(17 41 44 215)(18 214 45 40)(19 39 46 213)(20 212 47 38)(21 37 48 211)(22 224 49 36)(23 35 50 223)(24 222 51 34)(25 33 52 221)(26 220 53 32)(27 31 54 219)(28 218 55 30)(57 205 142 170)(58 169 143 204)(59 203 144 182)(60 181 145 202)(61 201 146 180)(62 179 147 200)(63 199 148 178)(64 177 149 198)(65 197 150 176)(66 175 151 210)(67 209 152 174)(68 173 153 208)(69 207 154 172)(70 171 141 206)(71 138 109 89)(72 88 110 137)(73 136 111 87)(74 86 112 135)(75 134 99 85)(76 98 100 133)(77 132 101 97)(78 96 102 131)(79 130 103 95)(80 94 104 129)(81 128 105 93)(82 92 106 127)(83 140 107 91)(84 90 108 139)
G:=sub<Sym(224)| (1,203,162,145)(2,146,163,204)(3,205,164,147)(4,148,165,206)(5,207,166,149)(6,150,167,208)(7,209,168,151)(8,152,155,210)(9,197,156,153)(10,154,157,198)(11,199,158,141)(12,142,159,200)(13,201,160,143)(14,144,161,202)(15,137,38,81)(16,82,39,138)(17,139,40,83)(18,84,41,140)(19,127,42,71)(20,72,29,128)(21,129,30,73)(22,74,31,130)(23,131,32,75)(24,76,33,132)(25,133,34,77)(26,78,35,134)(27,135,36,79)(28,80,37,136)(43,106,213,89)(44,90,214,107)(45,108,215,91)(46,92,216,109)(47,110,217,93)(48,94,218,111)(49,112,219,95)(50,96,220,99)(51,100,221,97)(52,98,222,101)(53,102,223,85)(54,86,224,103)(55,104,211,87)(56,88,212,105)(57,118,179,195)(58,196,180,119)(59,120,181,183)(60,184,182,121)(61,122,169,185)(62,186,170,123)(63,124,171,187)(64,188,172,125)(65,126,173,189)(66,190,174,113)(67,114,175,191)(68,192,176,115)(69,116,177,193)(70,194,178,117), (1,52,184,25)(2,26,185,53)(3,54,186,27)(4,28,187,55)(5,56,188,15)(6,16,189,43)(7,44,190,17)(8,18,191,45)(9,46,192,19)(10,20,193,47)(11,48,194,21)(12,22,195,49)(13,50,196,23)(14,24,183,51)(29,116,217,157)(30,158,218,117)(31,118,219,159)(32,160,220,119)(33,120,221,161)(34,162,222,121)(35,122,223,163)(36,164,224,123)(37,124,211,165)(38,166,212,125)(39,126,213,167)(40,168,214,113)(41,114,215,155)(42,156,216,115)(57,112,142,74)(58,75,143,99)(59,100,144,76)(60,77,145,101)(61,102,146,78)(62,79,147,103)(63,104,148,80)(64,81,149,105)(65,106,150,82)(66,83,151,107)(67,108,152,84)(68,71,153,109)(69,110,154,72)(70,73,141,111)(85,204,134,169)(86,170,135,205)(87,206,136,171)(88,172,137,207)(89,208,138,173)(90,174,139,209)(91,210,140,175)(92,176,127,197)(93,198,128,177)(94,178,129,199)(95,200,130,179)(96,180,131,201)(97,202,132,181)(98,182,133,203), (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), (1,161,184,120)(2,119,185,160)(3,159,186,118)(4,117,187,158)(5,157,188,116)(6,115,189,156)(7,155,190,114)(8,113,191,168)(9,167,192,126)(10,125,193,166)(11,165,194,124)(12,123,195,164)(13,163,196,122)(14,121,183,162)(15,29,56,217)(16,216,43,42)(17,41,44,215)(18,214,45,40)(19,39,46,213)(20,212,47,38)(21,37,48,211)(22,224,49,36)(23,35,50,223)(24,222,51,34)(25,33,52,221)(26,220,53,32)(27,31,54,219)(28,218,55,30)(57,205,142,170)(58,169,143,204)(59,203,144,182)(60,181,145,202)(61,201,146,180)(62,179,147,200)(63,199,148,178)(64,177,149,198)(65,197,150,176)(66,175,151,210)(67,209,152,174)(68,173,153,208)(69,207,154,172)(70,171,141,206)(71,138,109,89)(72,88,110,137)(73,136,111,87)(74,86,112,135)(75,134,99,85)(76,98,100,133)(77,132,101,97)(78,96,102,131)(79,130,103,95)(80,94,104,129)(81,128,105,93)(82,92,106,127)(83,140,107,91)(84,90,108,139)>;
G:=Group( (1,203,162,145)(2,146,163,204)(3,205,164,147)(4,148,165,206)(5,207,166,149)(6,150,167,208)(7,209,168,151)(8,152,155,210)(9,197,156,153)(10,154,157,198)(11,199,158,141)(12,142,159,200)(13,201,160,143)(14,144,161,202)(15,137,38,81)(16,82,39,138)(17,139,40,83)(18,84,41,140)(19,127,42,71)(20,72,29,128)(21,129,30,73)(22,74,31,130)(23,131,32,75)(24,76,33,132)(25,133,34,77)(26,78,35,134)(27,135,36,79)(28,80,37,136)(43,106,213,89)(44,90,214,107)(45,108,215,91)(46,92,216,109)(47,110,217,93)(48,94,218,111)(49,112,219,95)(50,96,220,99)(51,100,221,97)(52,98,222,101)(53,102,223,85)(54,86,224,103)(55,104,211,87)(56,88,212,105)(57,118,179,195)(58,196,180,119)(59,120,181,183)(60,184,182,121)(61,122,169,185)(62,186,170,123)(63,124,171,187)(64,188,172,125)(65,126,173,189)(66,190,174,113)(67,114,175,191)(68,192,176,115)(69,116,177,193)(70,194,178,117), (1,52,184,25)(2,26,185,53)(3,54,186,27)(4,28,187,55)(5,56,188,15)(6,16,189,43)(7,44,190,17)(8,18,191,45)(9,46,192,19)(10,20,193,47)(11,48,194,21)(12,22,195,49)(13,50,196,23)(14,24,183,51)(29,116,217,157)(30,158,218,117)(31,118,219,159)(32,160,220,119)(33,120,221,161)(34,162,222,121)(35,122,223,163)(36,164,224,123)(37,124,211,165)(38,166,212,125)(39,126,213,167)(40,168,214,113)(41,114,215,155)(42,156,216,115)(57,112,142,74)(58,75,143,99)(59,100,144,76)(60,77,145,101)(61,102,146,78)(62,79,147,103)(63,104,148,80)(64,81,149,105)(65,106,150,82)(66,83,151,107)(67,108,152,84)(68,71,153,109)(69,110,154,72)(70,73,141,111)(85,204,134,169)(86,170,135,205)(87,206,136,171)(88,172,137,207)(89,208,138,173)(90,174,139,209)(91,210,140,175)(92,176,127,197)(93,198,128,177)(94,178,129,199)(95,200,130,179)(96,180,131,201)(97,202,132,181)(98,182,133,203), (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), (1,161,184,120)(2,119,185,160)(3,159,186,118)(4,117,187,158)(5,157,188,116)(6,115,189,156)(7,155,190,114)(8,113,191,168)(9,167,192,126)(10,125,193,166)(11,165,194,124)(12,123,195,164)(13,163,196,122)(14,121,183,162)(15,29,56,217)(16,216,43,42)(17,41,44,215)(18,214,45,40)(19,39,46,213)(20,212,47,38)(21,37,48,211)(22,224,49,36)(23,35,50,223)(24,222,51,34)(25,33,52,221)(26,220,53,32)(27,31,54,219)(28,218,55,30)(57,205,142,170)(58,169,143,204)(59,203,144,182)(60,181,145,202)(61,201,146,180)(62,179,147,200)(63,199,148,178)(64,177,149,198)(65,197,150,176)(66,175,151,210)(67,209,152,174)(68,173,153,208)(69,207,154,172)(70,171,141,206)(71,138,109,89)(72,88,110,137)(73,136,111,87)(74,86,112,135)(75,134,99,85)(76,98,100,133)(77,132,101,97)(78,96,102,131)(79,130,103,95)(80,94,104,129)(81,128,105,93)(82,92,106,127)(83,140,107,91)(84,90,108,139) );
G=PermutationGroup([[(1,203,162,145),(2,146,163,204),(3,205,164,147),(4,148,165,206),(5,207,166,149),(6,150,167,208),(7,209,168,151),(8,152,155,210),(9,197,156,153),(10,154,157,198),(11,199,158,141),(12,142,159,200),(13,201,160,143),(14,144,161,202),(15,137,38,81),(16,82,39,138),(17,139,40,83),(18,84,41,140),(19,127,42,71),(20,72,29,128),(21,129,30,73),(22,74,31,130),(23,131,32,75),(24,76,33,132),(25,133,34,77),(26,78,35,134),(27,135,36,79),(28,80,37,136),(43,106,213,89),(44,90,214,107),(45,108,215,91),(46,92,216,109),(47,110,217,93),(48,94,218,111),(49,112,219,95),(50,96,220,99),(51,100,221,97),(52,98,222,101),(53,102,223,85),(54,86,224,103),(55,104,211,87),(56,88,212,105),(57,118,179,195),(58,196,180,119),(59,120,181,183),(60,184,182,121),(61,122,169,185),(62,186,170,123),(63,124,171,187),(64,188,172,125),(65,126,173,189),(66,190,174,113),(67,114,175,191),(68,192,176,115),(69,116,177,193),(70,194,178,117)], [(1,52,184,25),(2,26,185,53),(3,54,186,27),(4,28,187,55),(5,56,188,15),(6,16,189,43),(7,44,190,17),(8,18,191,45),(9,46,192,19),(10,20,193,47),(11,48,194,21),(12,22,195,49),(13,50,196,23),(14,24,183,51),(29,116,217,157),(30,158,218,117),(31,118,219,159),(32,160,220,119),(33,120,221,161),(34,162,222,121),(35,122,223,163),(36,164,224,123),(37,124,211,165),(38,166,212,125),(39,126,213,167),(40,168,214,113),(41,114,215,155),(42,156,216,115),(57,112,142,74),(58,75,143,99),(59,100,144,76),(60,77,145,101),(61,102,146,78),(62,79,147,103),(63,104,148,80),(64,81,149,105),(65,106,150,82),(66,83,151,107),(67,108,152,84),(68,71,153,109),(69,110,154,72),(70,73,141,111),(85,204,134,169),(86,170,135,205),(87,206,136,171),(88,172,137,207),(89,208,138,173),(90,174,139,209),(91,210,140,175),(92,176,127,197),(93,198,128,177),(94,178,129,199),(95,200,130,179),(96,180,131,201),(97,202,132,181),(98,182,133,203)], [(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)], [(1,161,184,120),(2,119,185,160),(3,159,186,118),(4,117,187,158),(5,157,188,116),(6,115,189,156),(7,155,190,114),(8,113,191,168),(9,167,192,126),(10,125,193,166),(11,165,194,124),(12,123,195,164),(13,163,196,122),(14,121,183,162),(15,29,56,217),(16,216,43,42),(17,41,44,215),(18,214,45,40),(19,39,46,213),(20,212,47,38),(21,37,48,211),(22,224,49,36),(23,35,50,223),(24,222,51,34),(25,33,52,221),(26,220,53,32),(27,31,54,219),(28,218,55,30),(57,205,142,170),(58,169,143,204),(59,203,144,182),(60,181,145,202),(61,201,146,180),(62,179,147,200),(63,199,148,178),(64,177,149,198),(65,197,150,176),(66,175,151,210),(67,209,152,174),(68,173,153,208),(69,207,154,172),(70,171,141,206),(71,138,109,89),(72,88,110,137),(73,136,111,87),(74,86,112,135),(75,134,99,85),(76,98,100,133),(77,132,101,97),(78,96,102,131),(79,130,103,95),(80,94,104,129),(81,128,105,93),(82,92,106,127),(83,140,107,91),(84,90,108,139)]])
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 | 14J | ··· | 14U | 28A | ··· | 28R |
| 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 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 4 | 14 | 14 | 2 | ··· | 2 | 7 | 7 | 7 | 7 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 |
70 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D4×D7 | D4⋊2D7 |
| kernel | C42.238D14 | C28⋊2Q8 | D7×C42 | D4×Dic7 | C28.17D4 | C28⋊2D4 | C7×C4⋊1D4 | C2×D4⋊2D7 | C4×D7 | C4⋊1D4 | C28 | C42 | C2×D4 | C4 | C4 |
| # reps | 1 | 1 | 1 | 4 | 2 | 4 | 1 | 2 | 4 | 3 | 8 | 3 | 18 | 6 | 12 |
Matrix representation of C42.238D14 ►in GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 0 | 21 | 0 | 0 | 0 | 0 |
| 11 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 11 | 21 | 0 | 0 | 0 | 0 |
| 15 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 0 | 0 | 0 | 1 | 0 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,17,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,17,0,0,0,0,0,0,12,0,0,0,0,0,0,17],[0,11,0,0,0,0,21,18,0,0,0,0,0,0,0,28,0,0,0,0,28,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0],[11,15,0,0,0,0,21,18,0,0,0,0,0,0,0,1,0,0,0,0,28,0,0,0,0,0,0,0,0,1,0,0,0,0,28,0] >;
C42.238D14 in GAP, Magma, Sage, TeX
C_4^2._{238}D_{14} % in TeX
G:=Group("C4^2.238D14"); // GroupNames label
G:=SmallGroup(448,1169);
// by ID
G=gap.SmallGroup(448,1169);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,100,675,570,185,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=d*b*d^-1=b^-1,d*c*d^-1=b^2*c^-1>;
// generators/relations