metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.138D14, C14.712+ 1+4, C4.4D4⋊7D7, (C2×Q8).82D14, D14⋊D4⋊38C2, (C2×D4).108D14, C42⋊D7⋊35C2, C22⋊C4.72D14, Dic7⋊Q8⋊21C2, Dic7⋊4D4⋊29C2, Dic7⋊D4⋊33C2, C28.23D4⋊19C2, (C2×C14).214C24, (C2×C28).630C23, (C4×C28).239C22, C2.73(D4⋊6D14), C23.36(C22×D7), D14⋊C4.134C22, Dic7.27(C4○D4), Dic7.D4⋊38C2, (C2×D28).161C22, (D4×C14).208C22, (C22×C14).44C23, (Q8×C14).123C22, (C22×D7).94C23, C22.235(C23×D7), C23.D7.51C22, C23.11D14⋊17C2, Dic7⋊C4.141C22, C7⋊4(C22.49C24), (C2×Dic7).251C23, (C4×Dic7).130C22, (C2×Dic14).175C22, (C22×Dic7).139C22, C2.73(D7×C4○D4), (C7×C4.4D4)⋊8C2, C14.185(C2×C4○D4), (C2×C4×D7).214C22, (C2×C4).73(C22×D7), (C2×C7⋊D4).57C22, (C7×C22⋊C4).61C22, SmallGroup(448,1123)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.138D14
G = < a,b,c,d | a4=b4=c14=1, d2=b2, ab=ba, cac-1=ab2, ad=da, cbc-1=dbd-1=a2b, dcd-1=c-1 >
Subgroups: 1100 in 236 conjugacy classes, 95 normal (27 characteristic)
C1, C2, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, Dic7, Dic7, C28, D14, C2×C14, C2×C14, C42⋊C2, C4×D4, C4⋊D4, C4.4D4, C4.4D4, C4⋊Q8, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C7×Q8, C22×D7, C22×C14, C22.49C24, C4×Dic7, C4×Dic7, Dic7⋊C4, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C22×Dic7, C2×C7⋊D4, D4×C14, Q8×C14, C42⋊D7, C23.11D14, Dic7⋊4D4, D14⋊D4, Dic7.D4, Dic7⋊D4, Dic7⋊Q8, C28.23D4, C7×C4.4D4, C42.138D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.49C24, C23×D7, D4⋊6D14, D7×C4○D4, C42.138D14
►On 224 points
Generators in S224
(1 24 181 168)(2 96 182 55)(3 26 169 156)(4 98 170 43)(5 28 171 158)(6 86 172 45)(7 16 173 160)(8 88 174 47)(9 18 175 162)(10 90 176 49)(11 20 177 164)(12 92 178 51)(13 22 179 166)(14 94 180 53)(15 42 159 185)(17 30 161 187)(19 32 163 189)(21 34 165 191)(23 36 167 193)(25 38 155 195)(27 40 157 183)(29 46 186 87)(31 48 188 89)(33 50 190 91)(35 52 192 93)(37 54 194 95)(39 56 196 97)(41 44 184 85)(57 199 115 110)(58 78 116 139)(59 201 117 112)(60 80 118 127)(61 203 119 100)(62 82 120 129)(63 205 121 102)(64 84 122 131)(65 207 123 104)(66 72 124 133)(67 209 125 106)(68 74 126 135)(69 197 113 108)(70 76 114 137)(71 220 132 145)(73 222 134 147)(75 224 136 149)(77 212 138 151)(79 214 140 153)(81 216 128 141)(83 218 130 143)(99 154 202 215)(101 142 204 217)(103 144 206 219)(105 146 208 221)(107 148 210 223)(109 150 198 211)(111 152 200 213)
(1 71 194 207)(2 133 195 105)(3 73 196 209)(4 135 183 107)(5 75 184 197)(6 137 185 109)(7 77 186 199)(8 139 187 111)(9 79 188 201)(10 127 189 99)(11 81 190 203)(12 129 191 101)(13 83 192 205)(14 131 193 103)(15 150 86 70)(16 212 87 115)(17 152 88 58)(18 214 89 117)(19 154 90 60)(20 216 91 119)(21 142 92 62)(22 218 93 121)(23 144 94 64)(24 220 95 123)(25 146 96 66)(26 222 97 125)(27 148 98 68)(28 224 85 113)(29 110 173 138)(30 200 174 78)(31 112 175 140)(32 202 176 80)(33 100 177 128)(34 204 178 82)(35 102 179 130)(36 206 180 84)(37 104 181 132)(38 208 182 72)(39 106 169 134)(40 210 170 74)(41 108 171 136)(42 198 172 76)(43 126 157 223)(44 69 158 149)(45 114 159 211)(46 57 160 151)(47 116 161 213)(48 59 162 153)(49 118 163 215)(50 61 164 141)(51 120 165 217)(52 63 166 143)(53 122 167 219)(54 65 168 145)(55 124 155 221)(56 67 156 147)
(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 57 194 151)(2 70 195 150)(3 69 196 149)(4 68 183 148)(5 67 184 147)(6 66 185 146)(7 65 186 145)(8 64 187 144)(9 63 188 143)(10 62 189 142)(11 61 190 141)(12 60 191 154)(13 59 192 153)(14 58 193 152)(15 208 86 72)(16 207 87 71)(17 206 88 84)(18 205 89 83)(19 204 90 82)(20 203 91 81)(21 202 92 80)(22 201 93 79)(23 200 94 78)(24 199 95 77)(25 198 96 76)(26 197 97 75)(27 210 98 74)(28 209 85 73)(29 220 173 123)(30 219 174 122)(31 218 175 121)(32 217 176 120)(33 216 177 119)(34 215 178 118)(35 214 179 117)(36 213 180 116)(37 212 181 115)(38 211 182 114)(39 224 169 113)(40 223 170 126)(41 222 171 125)(42 221 172 124)(43 135 157 107)(44 134 158 106)(45 133 159 105)(46 132 160 104)(47 131 161 103)(48 130 162 102)(49 129 163 101)(50 128 164 100)(51 127 165 99)(52 140 166 112)(53 139 167 111)(54 138 168 110)(55 137 155 109)(56 136 156 108)
G:=sub<Sym(224)| (1,24,181,168)(2,96,182,55)(3,26,169,156)(4,98,170,43)(5,28,171,158)(6,86,172,45)(7,16,173,160)(8,88,174,47)(9,18,175,162)(10,90,176,49)(11,20,177,164)(12,92,178,51)(13,22,179,166)(14,94,180,53)(15,42,159,185)(17,30,161,187)(19,32,163,189)(21,34,165,191)(23,36,167,193)(25,38,155,195)(27,40,157,183)(29,46,186,87)(31,48,188,89)(33,50,190,91)(35,52,192,93)(37,54,194,95)(39,56,196,97)(41,44,184,85)(57,199,115,110)(58,78,116,139)(59,201,117,112)(60,80,118,127)(61,203,119,100)(62,82,120,129)(63,205,121,102)(64,84,122,131)(65,207,123,104)(66,72,124,133)(67,209,125,106)(68,74,126,135)(69,197,113,108)(70,76,114,137)(71,220,132,145)(73,222,134,147)(75,224,136,149)(77,212,138,151)(79,214,140,153)(81,216,128,141)(83,218,130,143)(99,154,202,215)(101,142,204,217)(103,144,206,219)(105,146,208,221)(107,148,210,223)(109,150,198,211)(111,152,200,213), (1,71,194,207)(2,133,195,105)(3,73,196,209)(4,135,183,107)(5,75,184,197)(6,137,185,109)(7,77,186,199)(8,139,187,111)(9,79,188,201)(10,127,189,99)(11,81,190,203)(12,129,191,101)(13,83,192,205)(14,131,193,103)(15,150,86,70)(16,212,87,115)(17,152,88,58)(18,214,89,117)(19,154,90,60)(20,216,91,119)(21,142,92,62)(22,218,93,121)(23,144,94,64)(24,220,95,123)(25,146,96,66)(26,222,97,125)(27,148,98,68)(28,224,85,113)(29,110,173,138)(30,200,174,78)(31,112,175,140)(32,202,176,80)(33,100,177,128)(34,204,178,82)(35,102,179,130)(36,206,180,84)(37,104,181,132)(38,208,182,72)(39,106,169,134)(40,210,170,74)(41,108,171,136)(42,198,172,76)(43,126,157,223)(44,69,158,149)(45,114,159,211)(46,57,160,151)(47,116,161,213)(48,59,162,153)(49,118,163,215)(50,61,164,141)(51,120,165,217)(52,63,166,143)(53,122,167,219)(54,65,168,145)(55,124,155,221)(56,67,156,147), (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), (1,57,194,151)(2,70,195,150)(3,69,196,149)(4,68,183,148)(5,67,184,147)(6,66,185,146)(7,65,186,145)(8,64,187,144)(9,63,188,143)(10,62,189,142)(11,61,190,141)(12,60,191,154)(13,59,192,153)(14,58,193,152)(15,208,86,72)(16,207,87,71)(17,206,88,84)(18,205,89,83)(19,204,90,82)(20,203,91,81)(21,202,92,80)(22,201,93,79)(23,200,94,78)(24,199,95,77)(25,198,96,76)(26,197,97,75)(27,210,98,74)(28,209,85,73)(29,220,173,123)(30,219,174,122)(31,218,175,121)(32,217,176,120)(33,216,177,119)(34,215,178,118)(35,214,179,117)(36,213,180,116)(37,212,181,115)(38,211,182,114)(39,224,169,113)(40,223,170,126)(41,222,171,125)(42,221,172,124)(43,135,157,107)(44,134,158,106)(45,133,159,105)(46,132,160,104)(47,131,161,103)(48,130,162,102)(49,129,163,101)(50,128,164,100)(51,127,165,99)(52,140,166,112)(53,139,167,111)(54,138,168,110)(55,137,155,109)(56,136,156,108)>;
G:=Group( (1,24,181,168)(2,96,182,55)(3,26,169,156)(4,98,170,43)(5,28,171,158)(6,86,172,45)(7,16,173,160)(8,88,174,47)(9,18,175,162)(10,90,176,49)(11,20,177,164)(12,92,178,51)(13,22,179,166)(14,94,180,53)(15,42,159,185)(17,30,161,187)(19,32,163,189)(21,34,165,191)(23,36,167,193)(25,38,155,195)(27,40,157,183)(29,46,186,87)(31,48,188,89)(33,50,190,91)(35,52,192,93)(37,54,194,95)(39,56,196,97)(41,44,184,85)(57,199,115,110)(58,78,116,139)(59,201,117,112)(60,80,118,127)(61,203,119,100)(62,82,120,129)(63,205,121,102)(64,84,122,131)(65,207,123,104)(66,72,124,133)(67,209,125,106)(68,74,126,135)(69,197,113,108)(70,76,114,137)(71,220,132,145)(73,222,134,147)(75,224,136,149)(77,212,138,151)(79,214,140,153)(81,216,128,141)(83,218,130,143)(99,154,202,215)(101,142,204,217)(103,144,206,219)(105,146,208,221)(107,148,210,223)(109,150,198,211)(111,152,200,213), (1,71,194,207)(2,133,195,105)(3,73,196,209)(4,135,183,107)(5,75,184,197)(6,137,185,109)(7,77,186,199)(8,139,187,111)(9,79,188,201)(10,127,189,99)(11,81,190,203)(12,129,191,101)(13,83,192,205)(14,131,193,103)(15,150,86,70)(16,212,87,115)(17,152,88,58)(18,214,89,117)(19,154,90,60)(20,216,91,119)(21,142,92,62)(22,218,93,121)(23,144,94,64)(24,220,95,123)(25,146,96,66)(26,222,97,125)(27,148,98,68)(28,224,85,113)(29,110,173,138)(30,200,174,78)(31,112,175,140)(32,202,176,80)(33,100,177,128)(34,204,178,82)(35,102,179,130)(36,206,180,84)(37,104,181,132)(38,208,182,72)(39,106,169,134)(40,210,170,74)(41,108,171,136)(42,198,172,76)(43,126,157,223)(44,69,158,149)(45,114,159,211)(46,57,160,151)(47,116,161,213)(48,59,162,153)(49,118,163,215)(50,61,164,141)(51,120,165,217)(52,63,166,143)(53,122,167,219)(54,65,168,145)(55,124,155,221)(56,67,156,147), (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), (1,57,194,151)(2,70,195,150)(3,69,196,149)(4,68,183,148)(5,67,184,147)(6,66,185,146)(7,65,186,145)(8,64,187,144)(9,63,188,143)(10,62,189,142)(11,61,190,141)(12,60,191,154)(13,59,192,153)(14,58,193,152)(15,208,86,72)(16,207,87,71)(17,206,88,84)(18,205,89,83)(19,204,90,82)(20,203,91,81)(21,202,92,80)(22,201,93,79)(23,200,94,78)(24,199,95,77)(25,198,96,76)(26,197,97,75)(27,210,98,74)(28,209,85,73)(29,220,173,123)(30,219,174,122)(31,218,175,121)(32,217,176,120)(33,216,177,119)(34,215,178,118)(35,214,179,117)(36,213,180,116)(37,212,181,115)(38,211,182,114)(39,224,169,113)(40,223,170,126)(41,222,171,125)(42,221,172,124)(43,135,157,107)(44,134,158,106)(45,133,159,105)(46,132,160,104)(47,131,161,103)(48,130,162,102)(49,129,163,101)(50,128,164,100)(51,127,165,99)(52,140,166,112)(53,139,167,111)(54,138,168,110)(55,137,155,109)(56,136,156,108) );
G=PermutationGroup([[(1,24,181,168),(2,96,182,55),(3,26,169,156),(4,98,170,43),(5,28,171,158),(6,86,172,45),(7,16,173,160),(8,88,174,47),(9,18,175,162),(10,90,176,49),(11,20,177,164),(12,92,178,51),(13,22,179,166),(14,94,180,53),(15,42,159,185),(17,30,161,187),(19,32,163,189),(21,34,165,191),(23,36,167,193),(25,38,155,195),(27,40,157,183),(29,46,186,87),(31,48,188,89),(33,50,190,91),(35,52,192,93),(37,54,194,95),(39,56,196,97),(41,44,184,85),(57,199,115,110),(58,78,116,139),(59,201,117,112),(60,80,118,127),(61,203,119,100),(62,82,120,129),(63,205,121,102),(64,84,122,131),(65,207,123,104),(66,72,124,133),(67,209,125,106),(68,74,126,135),(69,197,113,108),(70,76,114,137),(71,220,132,145),(73,222,134,147),(75,224,136,149),(77,212,138,151),(79,214,140,153),(81,216,128,141),(83,218,130,143),(99,154,202,215),(101,142,204,217),(103,144,206,219),(105,146,208,221),(107,148,210,223),(109,150,198,211),(111,152,200,213)], [(1,71,194,207),(2,133,195,105),(3,73,196,209),(4,135,183,107),(5,75,184,197),(6,137,185,109),(7,77,186,199),(8,139,187,111),(9,79,188,201),(10,127,189,99),(11,81,190,203),(12,129,191,101),(13,83,192,205),(14,131,193,103),(15,150,86,70),(16,212,87,115),(17,152,88,58),(18,214,89,117),(19,154,90,60),(20,216,91,119),(21,142,92,62),(22,218,93,121),(23,144,94,64),(24,220,95,123),(25,146,96,66),(26,222,97,125),(27,148,98,68),(28,224,85,113),(29,110,173,138),(30,200,174,78),(31,112,175,140),(32,202,176,80),(33,100,177,128),(34,204,178,82),(35,102,179,130),(36,206,180,84),(37,104,181,132),(38,208,182,72),(39,106,169,134),(40,210,170,74),(41,108,171,136),(42,198,172,76),(43,126,157,223),(44,69,158,149),(45,114,159,211),(46,57,160,151),(47,116,161,213),(48,59,162,153),(49,118,163,215),(50,61,164,141),(51,120,165,217),(52,63,166,143),(53,122,167,219),(54,65,168,145),(55,124,155,221),(56,67,156,147)], [(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)], [(1,57,194,151),(2,70,195,150),(3,69,196,149),(4,68,183,148),(5,67,184,147),(6,66,185,146),(7,65,186,145),(8,64,187,144),(9,63,188,143),(10,62,189,142),(11,61,190,141),(12,60,191,154),(13,59,192,153),(14,58,193,152),(15,208,86,72),(16,207,87,71),(17,206,88,84),(18,205,89,83),(19,204,90,82),(20,203,91,81),(21,202,92,80),(22,201,93,79),(23,200,94,78),(24,199,95,77),(25,198,96,76),(26,197,97,75),(27,210,98,74),(28,209,85,73),(29,220,173,123),(30,219,174,122),(31,218,175,121),(32,217,176,120),(33,216,177,119),(34,215,178,118),(35,214,179,117),(36,213,180,116),(37,212,181,115),(38,211,182,114),(39,224,169,113),(40,223,170,126),(41,222,171,125),(42,221,172,124),(43,135,157,107),(44,134,158,106),(45,133,159,105),(46,132,160,104),(47,131,161,103),(48,130,162,102),(49,129,163,101),(50,128,164,100),(51,127,165,99),(52,140,166,112),(53,139,167,111),(54,138,168,110),(55,137,155,109),(56,136,156,108)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | ··· | 4O | 4P | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 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 | 4 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | D14 | 2+ 1+4 | D4⋊6D14 | D7×C4○D4 |
| kernel | C42.138D14 | C42⋊D7 | C23.11D14 | Dic7⋊4D4 | D14⋊D4 | Dic7.D4 | Dic7⋊D4 | Dic7⋊Q8 | C28.23D4 | C7×C4.4D4 | C4.4D4 | Dic7 | C42 | C22⋊C4 | C2×D4 | C2×Q8 | C14 | C2 | C2 |
| # reps | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 3 | 8 | 3 | 12 | 3 | 3 | 1 | 6 | 12 |
Matrix representation of C42.138D14 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 19 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 12 | 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 | 23 | 24 |
| 0 | 0 | 0 | 0 | 7 | 6 |
| 26 | 18 | 0 | 0 | 0 | 0 |
| 6 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 8 | 0 | 0 |
| 0 | 0 | 21 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 15 | 27 |
| 0 | 0 | 0 | 0 | 25 | 14 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 8 | 0 | 0 |
| 0 | 0 | 3 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 15 | 27 |
| 0 | 0 | 0 | 0 | 25 | 14 |
G:=sub<GL(6,GF(29))| [28,19,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,23,7,0,0,0,0,24,6],[26,6,0,0,0,0,18,3,0,0,0,0,0,0,8,21,0,0,0,0,8,3,0,0,0,0,0,0,15,25,0,0,0,0,27,14],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,8,3,0,0,0,0,8,21,0,0,0,0,0,0,15,25,0,0,0,0,27,14] >;
C42.138D14 in GAP, Magma, Sage, TeX
C_4^2._{138}D_{14} % in TeX
G:=Group("C4^2.138D14"); // GroupNames label
G:=SmallGroup(448,1123);
// by ID
G=gap.SmallGroup(448,1123);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,758,387,100,346,136,18822]);
// 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=a*b^2,a*d=d*a,c*b*c^-1=d*b*d^-1=a^2*b,d*c*d^-1=c^-1>;
// generators/relations