metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.179D14, C14.852+ 1+4, C4⋊Q8⋊17D7, (C4×D28)⋊52C2, C4⋊D28⋊41C2, C4⋊C4.222D14, (C2×Q8).89D14, C28.141(C4○D4), C28.23D4⋊28C2, (C4×C28).219C22, (C2×C28).640C23, (C2×C14).278C24, D14⋊C4.53C22, C4.42(Q8⋊2D7), C2.89(D4⋊6D14), (C2×D28).275C22, C4⋊Dic7.387C22, (Q8×C14).145C22, C22.299(C23×D7), C7⋊5(C22.49C24), (C4×Dic7).167C22, (C2×Dic7).275C23, (C22×D7).123C23, (C7×C4⋊Q8)⋊20C2, C4⋊C4⋊7D7⋊44C2, C14.125(C2×C4○D4), C2.33(C2×Q8⋊2D7), (C2×C4×D7).151C22, (C7×C4⋊C4).221C22, (C2×C4).603(C22×D7), SmallGroup(448,1187)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.179D14
G = < a,b,c,d | a4=b4=1, c14=b2, d2=a2b2, ab=ba, cac-1=dad-1=a-1, cbc-1=b-1, dbd-1=a2b, dcd-1=a2c13 >
Subgroups: 1196 in 236 conjugacy classes, 99 normal (13 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, C4⋊C4, C22×C4, C2×D4, C2×Q8, Dic7, C28, C28, D14, C2×C14, C42⋊C2, C4×D4, C4⋊D4, C4.4D4, C4⋊Q8, C4×D7, D28, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C22.49C24, C4×Dic7, C4⋊Dic7, D14⋊C4, C4×C28, C7×C4⋊C4, C2×C4×D7, C2×D28, Q8×C14, C4×D28, C4⋊C4⋊7D7, C4⋊D28, C28.23D4, C7×C4⋊Q8, C42.179D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.49C24, Q8⋊2D7, C23×D7, D4⋊6D14, C2×Q8⋊2D7, C42.179D14
►On 224 points
Generators in S224
(1 180 76 117)(2 118 77 181)(3 182 78 119)(4 120 79 183)(5 184 80 121)(6 122 81 185)(7 186 82 123)(8 124 83 187)(9 188 84 125)(10 126 57 189)(11 190 58 127)(12 128 59 191)(13 192 60 129)(14 130 61 193)(15 194 62 131)(16 132 63 195)(17 196 64 133)(18 134 65 169)(19 170 66 135)(20 136 67 171)(21 172 68 137)(22 138 69 173)(23 174 70 139)(24 140 71 175)(25 176 72 113)(26 114 73 177)(27 178 74 115)(28 116 75 179)(29 98 163 201)(30 202 164 99)(31 100 165 203)(32 204 166 101)(33 102 167 205)(34 206 168 103)(35 104 141 207)(36 208 142 105)(37 106 143 209)(38 210 144 107)(39 108 145 211)(40 212 146 109)(41 110 147 213)(42 214 148 111)(43 112 149 215)(44 216 150 85)(45 86 151 217)(46 218 152 87)(47 88 153 219)(48 220 154 89)(49 90 155 221)(50 222 156 91)(51 92 157 223)(52 224 158 93)(53 94 159 197)(54 198 160 95)(55 96 161 199)(56 200 162 97)
(1 51 15 37)(2 38 16 52)(3 53 17 39)(4 40 18 54)(5 55 19 41)(6 42 20 56)(7 29 21 43)(8 44 22 30)(9 31 23 45)(10 46 24 32)(11 33 25 47)(12 48 26 34)(13 35 27 49)(14 50 28 36)(57 152 71 166)(58 167 72 153)(59 154 73 168)(60 141 74 155)(61 156 75 142)(62 143 76 157)(63 158 77 144)(64 145 78 159)(65 160 79 146)(66 147 80 161)(67 162 81 148)(68 149 82 163)(69 164 83 150)(70 151 84 165)(85 173 99 187)(86 188 100 174)(87 175 101 189)(88 190 102 176)(89 177 103 191)(90 192 104 178)(91 179 105 193)(92 194 106 180)(93 181 107 195)(94 196 108 182)(95 183 109 169)(96 170 110 184)(97 185 111 171)(98 172 112 186)(113 219 127 205)(114 206 128 220)(115 221 129 207)(116 208 130 222)(117 223 131 209)(118 210 132 224)(119 197 133 211)(120 212 134 198)(121 199 135 213)(122 214 136 200)(123 201 137 215)(124 216 138 202)(125 203 139 217)(126 218 140 204)
(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)
(1 222 62 105)(2 104 63 221)(3 220 64 103)(4 102 65 219)(5 218 66 101)(6 100 67 217)(7 216 68 99)(8 98 69 215)(9 214 70 97)(10 96 71 213)(11 212 72 95)(12 94 73 211)(13 210 74 93)(14 92 75 209)(15 208 76 91)(16 90 77 207)(17 206 78 89)(18 88 79 205)(19 204 80 87)(20 86 81 203)(21 202 82 85)(22 112 83 201)(23 200 84 111)(24 110 57 199)(25 198 58 109)(26 108 59 197)(27 224 60 107)(28 106 61 223)(29 173 149 124)(30 123 150 172)(31 171 151 122)(32 121 152 170)(33 169 153 120)(34 119 154 196)(35 195 155 118)(36 117 156 194)(37 193 157 116)(38 115 158 192)(39 191 159 114)(40 113 160 190)(41 189 161 140)(42 139 162 188)(43 187 163 138)(44 137 164 186)(45 185 165 136)(46 135 166 184)(47 183 167 134)(48 133 168 182)(49 181 141 132)(50 131 142 180)(51 179 143 130)(52 129 144 178)(53 177 145 128)(54 127 146 176)(55 175 147 126)(56 125 148 174)
G:=sub<Sym(224)| (1,180,76,117)(2,118,77,181)(3,182,78,119)(4,120,79,183)(5,184,80,121)(6,122,81,185)(7,186,82,123)(8,124,83,187)(9,188,84,125)(10,126,57,189)(11,190,58,127)(12,128,59,191)(13,192,60,129)(14,130,61,193)(15,194,62,131)(16,132,63,195)(17,196,64,133)(18,134,65,169)(19,170,66,135)(20,136,67,171)(21,172,68,137)(22,138,69,173)(23,174,70,139)(24,140,71,175)(25,176,72,113)(26,114,73,177)(27,178,74,115)(28,116,75,179)(29,98,163,201)(30,202,164,99)(31,100,165,203)(32,204,166,101)(33,102,167,205)(34,206,168,103)(35,104,141,207)(36,208,142,105)(37,106,143,209)(38,210,144,107)(39,108,145,211)(40,212,146,109)(41,110,147,213)(42,214,148,111)(43,112,149,215)(44,216,150,85)(45,86,151,217)(46,218,152,87)(47,88,153,219)(48,220,154,89)(49,90,155,221)(50,222,156,91)(51,92,157,223)(52,224,158,93)(53,94,159,197)(54,198,160,95)(55,96,161,199)(56,200,162,97), (1,51,15,37)(2,38,16,52)(3,53,17,39)(4,40,18,54)(5,55,19,41)(6,42,20,56)(7,29,21,43)(8,44,22,30)(9,31,23,45)(10,46,24,32)(11,33,25,47)(12,48,26,34)(13,35,27,49)(14,50,28,36)(57,152,71,166)(58,167,72,153)(59,154,73,168)(60,141,74,155)(61,156,75,142)(62,143,76,157)(63,158,77,144)(64,145,78,159)(65,160,79,146)(66,147,80,161)(67,162,81,148)(68,149,82,163)(69,164,83,150)(70,151,84,165)(85,173,99,187)(86,188,100,174)(87,175,101,189)(88,190,102,176)(89,177,103,191)(90,192,104,178)(91,179,105,193)(92,194,106,180)(93,181,107,195)(94,196,108,182)(95,183,109,169)(96,170,110,184)(97,185,111,171)(98,172,112,186)(113,219,127,205)(114,206,128,220)(115,221,129,207)(116,208,130,222)(117,223,131,209)(118,210,132,224)(119,197,133,211)(120,212,134,198)(121,199,135,213)(122,214,136,200)(123,201,137,215)(124,216,138,202)(125,203,139,217)(126,218,140,204), (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), (1,222,62,105)(2,104,63,221)(3,220,64,103)(4,102,65,219)(5,218,66,101)(6,100,67,217)(7,216,68,99)(8,98,69,215)(9,214,70,97)(10,96,71,213)(11,212,72,95)(12,94,73,211)(13,210,74,93)(14,92,75,209)(15,208,76,91)(16,90,77,207)(17,206,78,89)(18,88,79,205)(19,204,80,87)(20,86,81,203)(21,202,82,85)(22,112,83,201)(23,200,84,111)(24,110,57,199)(25,198,58,109)(26,108,59,197)(27,224,60,107)(28,106,61,223)(29,173,149,124)(30,123,150,172)(31,171,151,122)(32,121,152,170)(33,169,153,120)(34,119,154,196)(35,195,155,118)(36,117,156,194)(37,193,157,116)(38,115,158,192)(39,191,159,114)(40,113,160,190)(41,189,161,140)(42,139,162,188)(43,187,163,138)(44,137,164,186)(45,185,165,136)(46,135,166,184)(47,183,167,134)(48,133,168,182)(49,181,141,132)(50,131,142,180)(51,179,143,130)(52,129,144,178)(53,177,145,128)(54,127,146,176)(55,175,147,126)(56,125,148,174)>;
G:=Group( (1,180,76,117)(2,118,77,181)(3,182,78,119)(4,120,79,183)(5,184,80,121)(6,122,81,185)(7,186,82,123)(8,124,83,187)(9,188,84,125)(10,126,57,189)(11,190,58,127)(12,128,59,191)(13,192,60,129)(14,130,61,193)(15,194,62,131)(16,132,63,195)(17,196,64,133)(18,134,65,169)(19,170,66,135)(20,136,67,171)(21,172,68,137)(22,138,69,173)(23,174,70,139)(24,140,71,175)(25,176,72,113)(26,114,73,177)(27,178,74,115)(28,116,75,179)(29,98,163,201)(30,202,164,99)(31,100,165,203)(32,204,166,101)(33,102,167,205)(34,206,168,103)(35,104,141,207)(36,208,142,105)(37,106,143,209)(38,210,144,107)(39,108,145,211)(40,212,146,109)(41,110,147,213)(42,214,148,111)(43,112,149,215)(44,216,150,85)(45,86,151,217)(46,218,152,87)(47,88,153,219)(48,220,154,89)(49,90,155,221)(50,222,156,91)(51,92,157,223)(52,224,158,93)(53,94,159,197)(54,198,160,95)(55,96,161,199)(56,200,162,97), (1,51,15,37)(2,38,16,52)(3,53,17,39)(4,40,18,54)(5,55,19,41)(6,42,20,56)(7,29,21,43)(8,44,22,30)(9,31,23,45)(10,46,24,32)(11,33,25,47)(12,48,26,34)(13,35,27,49)(14,50,28,36)(57,152,71,166)(58,167,72,153)(59,154,73,168)(60,141,74,155)(61,156,75,142)(62,143,76,157)(63,158,77,144)(64,145,78,159)(65,160,79,146)(66,147,80,161)(67,162,81,148)(68,149,82,163)(69,164,83,150)(70,151,84,165)(85,173,99,187)(86,188,100,174)(87,175,101,189)(88,190,102,176)(89,177,103,191)(90,192,104,178)(91,179,105,193)(92,194,106,180)(93,181,107,195)(94,196,108,182)(95,183,109,169)(96,170,110,184)(97,185,111,171)(98,172,112,186)(113,219,127,205)(114,206,128,220)(115,221,129,207)(116,208,130,222)(117,223,131,209)(118,210,132,224)(119,197,133,211)(120,212,134,198)(121,199,135,213)(122,214,136,200)(123,201,137,215)(124,216,138,202)(125,203,139,217)(126,218,140,204), (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), (1,222,62,105)(2,104,63,221)(3,220,64,103)(4,102,65,219)(5,218,66,101)(6,100,67,217)(7,216,68,99)(8,98,69,215)(9,214,70,97)(10,96,71,213)(11,212,72,95)(12,94,73,211)(13,210,74,93)(14,92,75,209)(15,208,76,91)(16,90,77,207)(17,206,78,89)(18,88,79,205)(19,204,80,87)(20,86,81,203)(21,202,82,85)(22,112,83,201)(23,200,84,111)(24,110,57,199)(25,198,58,109)(26,108,59,197)(27,224,60,107)(28,106,61,223)(29,173,149,124)(30,123,150,172)(31,171,151,122)(32,121,152,170)(33,169,153,120)(34,119,154,196)(35,195,155,118)(36,117,156,194)(37,193,157,116)(38,115,158,192)(39,191,159,114)(40,113,160,190)(41,189,161,140)(42,139,162,188)(43,187,163,138)(44,137,164,186)(45,185,165,136)(46,135,166,184)(47,183,167,134)(48,133,168,182)(49,181,141,132)(50,131,142,180)(51,179,143,130)(52,129,144,178)(53,177,145,128)(54,127,146,176)(55,175,147,126)(56,125,148,174) );
G=PermutationGroup([[(1,180,76,117),(2,118,77,181),(3,182,78,119),(4,120,79,183),(5,184,80,121),(6,122,81,185),(7,186,82,123),(8,124,83,187),(9,188,84,125),(10,126,57,189),(11,190,58,127),(12,128,59,191),(13,192,60,129),(14,130,61,193),(15,194,62,131),(16,132,63,195),(17,196,64,133),(18,134,65,169),(19,170,66,135),(20,136,67,171),(21,172,68,137),(22,138,69,173),(23,174,70,139),(24,140,71,175),(25,176,72,113),(26,114,73,177),(27,178,74,115),(28,116,75,179),(29,98,163,201),(30,202,164,99),(31,100,165,203),(32,204,166,101),(33,102,167,205),(34,206,168,103),(35,104,141,207),(36,208,142,105),(37,106,143,209),(38,210,144,107),(39,108,145,211),(40,212,146,109),(41,110,147,213),(42,214,148,111),(43,112,149,215),(44,216,150,85),(45,86,151,217),(46,218,152,87),(47,88,153,219),(48,220,154,89),(49,90,155,221),(50,222,156,91),(51,92,157,223),(52,224,158,93),(53,94,159,197),(54,198,160,95),(55,96,161,199),(56,200,162,97)], [(1,51,15,37),(2,38,16,52),(3,53,17,39),(4,40,18,54),(5,55,19,41),(6,42,20,56),(7,29,21,43),(8,44,22,30),(9,31,23,45),(10,46,24,32),(11,33,25,47),(12,48,26,34),(13,35,27,49),(14,50,28,36),(57,152,71,166),(58,167,72,153),(59,154,73,168),(60,141,74,155),(61,156,75,142),(62,143,76,157),(63,158,77,144),(64,145,78,159),(65,160,79,146),(66,147,80,161),(67,162,81,148),(68,149,82,163),(69,164,83,150),(70,151,84,165),(85,173,99,187),(86,188,100,174),(87,175,101,189),(88,190,102,176),(89,177,103,191),(90,192,104,178),(91,179,105,193),(92,194,106,180),(93,181,107,195),(94,196,108,182),(95,183,109,169),(96,170,110,184),(97,185,111,171),(98,172,112,186),(113,219,127,205),(114,206,128,220),(115,221,129,207),(116,208,130,222),(117,223,131,209),(118,210,132,224),(119,197,133,211),(120,212,134,198),(121,199,135,213),(122,214,136,200),(123,201,137,215),(124,216,138,202),(125,203,139,217),(126,218,140,204)], [(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)], [(1,222,62,105),(2,104,63,221),(3,220,64,103),(4,102,65,219),(5,218,66,101),(6,100,67,217),(7,216,68,99),(8,98,69,215),(9,214,70,97),(10,96,71,213),(11,212,72,95),(12,94,73,211),(13,210,74,93),(14,92,75,209),(15,208,76,91),(16,90,77,207),(17,206,78,89),(18,88,79,205),(19,204,80,87),(20,86,81,203),(21,202,82,85),(22,112,83,201),(23,200,84,111),(24,110,57,199),(25,198,58,109),(26,108,59,197),(27,224,60,107),(28,106,61,223),(29,173,149,124),(30,123,150,172),(31,171,151,122),(32,121,152,170),(33,169,153,120),(34,119,154,196),(35,195,155,118),(36,117,156,194),(37,193,157,116),(38,115,158,192),(39,191,159,114),(40,113,160,190),(41,189,161,140),(42,139,162,188),(43,187,163,138),(44,137,164,186),(45,185,165,136),(46,135,166,184),(47,183,167,134),(48,133,168,182),(49,181,141,132),(50,131,142,180),(51,179,143,130),(52,129,144,178),(53,177,145,128),(54,127,146,176),(55,175,147,126),(56,125,148,174)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | ··· | 4I | 4J | ··· | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 14 | ··· | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | 2+ 1+4 | Q8⋊2D7 | D4⋊6D14 |
| kernel | C42.179D14 | C4×D28 | C4⋊C4⋊7D7 | C4⋊D28 | C28.23D4 | C7×C4⋊Q8 | C4⋊Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | C14 | C4 | C2 |
| # reps | 1 | 2 | 4 | 4 | 4 | 1 | 3 | 8 | 3 | 12 | 6 | 1 | 12 | 6 |
Matrix representation of C42.179D14 ►in GL6(𝔽29)
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 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 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 5 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 19 | 0 | 0 |
| 0 | 0 | 10 | 19 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 27 |
| 0 | 0 | 0 | 0 | 1 | 28 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,0,17,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[12,0,0,0,0,0,0,17,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,12,0,0,0,0,0,5,17],[0,12,0,0,0,0,12,0,0,0,0,0,0,0,7,10,0,0,0,0,19,19,0,0,0,0,0,0,1,1,0,0,0,0,27,28],[0,17,0,0,0,0,12,0,0,0,0,0,0,0,0,28,0,0,0,0,28,0,0,0,0,0,0,0,12,0,0,0,0,0,0,12] >;
C42.179D14 in GAP, Magma, Sage, TeX
C_4^2._{179}D_{14} % in TeX
G:=Group("C4^2.179D14"); // GroupNames label
G:=SmallGroup(448,1187);
// by ID
G=gap.SmallGroup(448,1187);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,387,100,675,570,185,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=b^2,d^2=a^2*b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=b^-1,d*b*d^-1=a^2*b,d*c*d^-1=a^2*c^13>;
// generators/relations