metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.176D14, C14.382- 1+4, C4⋊Q8⋊14D7, C4⋊C4.125D14, (Q8×Dic7)⋊23C2, Dic7.Q8⋊42C2, (C2×Q8).148D14, C28.6Q8⋊25C2, C42⋊D7.9C2, C28.138(C4○D4), C4.42(D4⋊2D7), (C2×C14).275C24, (C2×C28).108C23, (C4×C28).216C22, D14⋊3Q8.13C2, D14⋊C4.154C22, Dic7⋊C4.63C22, C4⋊Dic7.254C22, (Q8×C14).142C22, C22.296(C23×D7), C7⋊7(C22.35C24), (C4×Dic7).164C22, (C2×Dic7).273C23, (C22×D7).120C23, C2.39(Q8.10D14), (C7×C4⋊Q8)⋊17C2, C4⋊C4⋊D7.4C2, C14.101(C2×C4○D4), C2.65(C2×D4⋊2D7), (C2×C4×D7).148C22, (C7×C4⋊C4).218C22, (C2×C4).221(C22×D7), SmallGroup(448,1184)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.176D14
G = < a,b,c,d | a4=b4=1, c14=a2, d2=a2b2, ab=ba, cac-1=dad-1=a-1, cbc-1=b-1, dbd-1=a2b-1, dcd-1=b2c13 >
Subgroups: 716 in 192 conjugacy classes, 95 normal (19 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, Q8, C23, D7, C14, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×Q8, Dic7, C28, C28, D14, C2×C14, C42⋊C2, C4×Q8, C22⋊Q8, C42.C2, C42⋊2C2, C4⋊Q8, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C22.35C24, C4×Dic7, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C4×C28, C7×C4⋊C4, C2×C4×D7, Q8×C14, C28.6Q8, C42⋊D7, Dic7.Q8, C4⋊C4⋊D7, Q8×Dic7, D14⋊3Q8, C7×C4⋊Q8, C42.176D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2- 1+4, C22×D7, C22.35C24, D4⋊2D7, C23×D7, C2×D4⋊2D7, Q8.10D14, C42.176D14
►On 224 points
Generators in S224
(1 219 15 205)(2 206 16 220)(3 221 17 207)(4 208 18 222)(5 223 19 209)(6 210 20 224)(7 197 21 211)(8 212 22 198)(9 199 23 213)(10 214 24 200)(11 201 25 215)(12 216 26 202)(13 203 27 217)(14 218 28 204)(29 133 43 119)(30 120 44 134)(31 135 45 121)(32 122 46 136)(33 137 47 123)(34 124 48 138)(35 139 49 125)(36 126 50 140)(37 113 51 127)(38 128 52 114)(39 115 53 129)(40 130 54 116)(41 117 55 131)(42 132 56 118)(57 156 71 142)(58 143 72 157)(59 158 73 144)(60 145 74 159)(61 160 75 146)(62 147 76 161)(63 162 77 148)(64 149 78 163)(65 164 79 150)(66 151 80 165)(67 166 81 152)(68 153 82 167)(69 168 83 154)(70 155 84 141)(85 185 99 171)(86 172 100 186)(87 187 101 173)(88 174 102 188)(89 189 103 175)(90 176 104 190)(91 191 105 177)(92 178 106 192)(93 193 107 179)(94 180 108 194)(95 195 109 181)(96 182 110 196)(97 169 111 183)(98 184 112 170)
(1 178 127 165)(2 166 128 179)(3 180 129 167)(4 168 130 181)(5 182 131 141)(6 142 132 183)(7 184 133 143)(8 144 134 185)(9 186 135 145)(10 146 136 187)(11 188 137 147)(12 148 138 189)(13 190 139 149)(14 150 140 191)(15 192 113 151)(16 152 114 193)(17 194 115 153)(18 154 116 195)(19 196 117 155)(20 156 118 169)(21 170 119 157)(22 158 120 171)(23 172 121 159)(24 160 122 173)(25 174 123 161)(26 162 124 175)(27 176 125 163)(28 164 126 177)(29 58 211 98)(30 99 212 59)(31 60 213 100)(32 101 214 61)(33 62 215 102)(34 103 216 63)(35 64 217 104)(36 105 218 65)(37 66 219 106)(38 107 220 67)(39 68 221 108)(40 109 222 69)(41 70 223 110)(42 111 224 71)(43 72 197 112)(44 85 198 73)(45 74 199 86)(46 87 200 75)(47 76 201 88)(48 89 202 77)(49 78 203 90)(50 91 204 79)(51 80 205 92)(52 93 206 81)(53 82 207 94)(54 95 208 83)(55 84 209 96)(56 97 210 57)
(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 14 113 126)(2 125 114 13)(3 12 115 124)(4 123 116 11)(5 10 117 122)(6 121 118 9)(7 8 119 120)(15 28 127 140)(16 139 128 27)(17 26 129 138)(18 137 130 25)(19 24 131 136)(20 135 132 23)(21 22 133 134)(29 30 197 198)(31 56 199 224)(32 223 200 55)(33 54 201 222)(34 221 202 53)(35 52 203 220)(36 219 204 51)(37 50 205 218)(38 217 206 49)(39 48 207 216)(40 215 208 47)(41 46 209 214)(42 213 210 45)(43 44 211 212)(57 100 111 74)(58 73 112 99)(59 98 85 72)(60 71 86 97)(61 96 87 70)(62 69 88 95)(63 94 89 68)(64 67 90 93)(65 92 91 66)(75 110 101 84)(76 83 102 109)(77 108 103 82)(78 81 104 107)(79 106 105 80)(141 160 196 187)(142 186 169 159)(143 158 170 185)(144 184 171 157)(145 156 172 183)(146 182 173 155)(147 154 174 181)(148 180 175 153)(149 152 176 179)(150 178 177 151)(161 168 188 195)(162 194 189 167)(163 166 190 193)(164 192 191 165)
G:=sub<Sym(224)| (1,219,15,205)(2,206,16,220)(3,221,17,207)(4,208,18,222)(5,223,19,209)(6,210,20,224)(7,197,21,211)(8,212,22,198)(9,199,23,213)(10,214,24,200)(11,201,25,215)(12,216,26,202)(13,203,27,217)(14,218,28,204)(29,133,43,119)(30,120,44,134)(31,135,45,121)(32,122,46,136)(33,137,47,123)(34,124,48,138)(35,139,49,125)(36,126,50,140)(37,113,51,127)(38,128,52,114)(39,115,53,129)(40,130,54,116)(41,117,55,131)(42,132,56,118)(57,156,71,142)(58,143,72,157)(59,158,73,144)(60,145,74,159)(61,160,75,146)(62,147,76,161)(63,162,77,148)(64,149,78,163)(65,164,79,150)(66,151,80,165)(67,166,81,152)(68,153,82,167)(69,168,83,154)(70,155,84,141)(85,185,99,171)(86,172,100,186)(87,187,101,173)(88,174,102,188)(89,189,103,175)(90,176,104,190)(91,191,105,177)(92,178,106,192)(93,193,107,179)(94,180,108,194)(95,195,109,181)(96,182,110,196)(97,169,111,183)(98,184,112,170), (1,178,127,165)(2,166,128,179)(3,180,129,167)(4,168,130,181)(5,182,131,141)(6,142,132,183)(7,184,133,143)(8,144,134,185)(9,186,135,145)(10,146,136,187)(11,188,137,147)(12,148,138,189)(13,190,139,149)(14,150,140,191)(15,192,113,151)(16,152,114,193)(17,194,115,153)(18,154,116,195)(19,196,117,155)(20,156,118,169)(21,170,119,157)(22,158,120,171)(23,172,121,159)(24,160,122,173)(25,174,123,161)(26,162,124,175)(27,176,125,163)(28,164,126,177)(29,58,211,98)(30,99,212,59)(31,60,213,100)(32,101,214,61)(33,62,215,102)(34,103,216,63)(35,64,217,104)(36,105,218,65)(37,66,219,106)(38,107,220,67)(39,68,221,108)(40,109,222,69)(41,70,223,110)(42,111,224,71)(43,72,197,112)(44,85,198,73)(45,74,199,86)(46,87,200,75)(47,76,201,88)(48,89,202,77)(49,78,203,90)(50,91,204,79)(51,80,205,92)(52,93,206,81)(53,82,207,94)(54,95,208,83)(55,84,209,96)(56,97,210,57), (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), (1,14,113,126)(2,125,114,13)(3,12,115,124)(4,123,116,11)(5,10,117,122)(6,121,118,9)(7,8,119,120)(15,28,127,140)(16,139,128,27)(17,26,129,138)(18,137,130,25)(19,24,131,136)(20,135,132,23)(21,22,133,134)(29,30,197,198)(31,56,199,224)(32,223,200,55)(33,54,201,222)(34,221,202,53)(35,52,203,220)(36,219,204,51)(37,50,205,218)(38,217,206,49)(39,48,207,216)(40,215,208,47)(41,46,209,214)(42,213,210,45)(43,44,211,212)(57,100,111,74)(58,73,112,99)(59,98,85,72)(60,71,86,97)(61,96,87,70)(62,69,88,95)(63,94,89,68)(64,67,90,93)(65,92,91,66)(75,110,101,84)(76,83,102,109)(77,108,103,82)(78,81,104,107)(79,106,105,80)(141,160,196,187)(142,186,169,159)(143,158,170,185)(144,184,171,157)(145,156,172,183)(146,182,173,155)(147,154,174,181)(148,180,175,153)(149,152,176,179)(150,178,177,151)(161,168,188,195)(162,194,189,167)(163,166,190,193)(164,192,191,165)>;
G:=Group( (1,219,15,205)(2,206,16,220)(3,221,17,207)(4,208,18,222)(5,223,19,209)(6,210,20,224)(7,197,21,211)(8,212,22,198)(9,199,23,213)(10,214,24,200)(11,201,25,215)(12,216,26,202)(13,203,27,217)(14,218,28,204)(29,133,43,119)(30,120,44,134)(31,135,45,121)(32,122,46,136)(33,137,47,123)(34,124,48,138)(35,139,49,125)(36,126,50,140)(37,113,51,127)(38,128,52,114)(39,115,53,129)(40,130,54,116)(41,117,55,131)(42,132,56,118)(57,156,71,142)(58,143,72,157)(59,158,73,144)(60,145,74,159)(61,160,75,146)(62,147,76,161)(63,162,77,148)(64,149,78,163)(65,164,79,150)(66,151,80,165)(67,166,81,152)(68,153,82,167)(69,168,83,154)(70,155,84,141)(85,185,99,171)(86,172,100,186)(87,187,101,173)(88,174,102,188)(89,189,103,175)(90,176,104,190)(91,191,105,177)(92,178,106,192)(93,193,107,179)(94,180,108,194)(95,195,109,181)(96,182,110,196)(97,169,111,183)(98,184,112,170), (1,178,127,165)(2,166,128,179)(3,180,129,167)(4,168,130,181)(5,182,131,141)(6,142,132,183)(7,184,133,143)(8,144,134,185)(9,186,135,145)(10,146,136,187)(11,188,137,147)(12,148,138,189)(13,190,139,149)(14,150,140,191)(15,192,113,151)(16,152,114,193)(17,194,115,153)(18,154,116,195)(19,196,117,155)(20,156,118,169)(21,170,119,157)(22,158,120,171)(23,172,121,159)(24,160,122,173)(25,174,123,161)(26,162,124,175)(27,176,125,163)(28,164,126,177)(29,58,211,98)(30,99,212,59)(31,60,213,100)(32,101,214,61)(33,62,215,102)(34,103,216,63)(35,64,217,104)(36,105,218,65)(37,66,219,106)(38,107,220,67)(39,68,221,108)(40,109,222,69)(41,70,223,110)(42,111,224,71)(43,72,197,112)(44,85,198,73)(45,74,199,86)(46,87,200,75)(47,76,201,88)(48,89,202,77)(49,78,203,90)(50,91,204,79)(51,80,205,92)(52,93,206,81)(53,82,207,94)(54,95,208,83)(55,84,209,96)(56,97,210,57), (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), (1,14,113,126)(2,125,114,13)(3,12,115,124)(4,123,116,11)(5,10,117,122)(6,121,118,9)(7,8,119,120)(15,28,127,140)(16,139,128,27)(17,26,129,138)(18,137,130,25)(19,24,131,136)(20,135,132,23)(21,22,133,134)(29,30,197,198)(31,56,199,224)(32,223,200,55)(33,54,201,222)(34,221,202,53)(35,52,203,220)(36,219,204,51)(37,50,205,218)(38,217,206,49)(39,48,207,216)(40,215,208,47)(41,46,209,214)(42,213,210,45)(43,44,211,212)(57,100,111,74)(58,73,112,99)(59,98,85,72)(60,71,86,97)(61,96,87,70)(62,69,88,95)(63,94,89,68)(64,67,90,93)(65,92,91,66)(75,110,101,84)(76,83,102,109)(77,108,103,82)(78,81,104,107)(79,106,105,80)(141,160,196,187)(142,186,169,159)(143,158,170,185)(144,184,171,157)(145,156,172,183)(146,182,173,155)(147,154,174,181)(148,180,175,153)(149,152,176,179)(150,178,177,151)(161,168,188,195)(162,194,189,167)(163,166,190,193)(164,192,191,165) );
G=PermutationGroup([[(1,219,15,205),(2,206,16,220),(3,221,17,207),(4,208,18,222),(5,223,19,209),(6,210,20,224),(7,197,21,211),(8,212,22,198),(9,199,23,213),(10,214,24,200),(11,201,25,215),(12,216,26,202),(13,203,27,217),(14,218,28,204),(29,133,43,119),(30,120,44,134),(31,135,45,121),(32,122,46,136),(33,137,47,123),(34,124,48,138),(35,139,49,125),(36,126,50,140),(37,113,51,127),(38,128,52,114),(39,115,53,129),(40,130,54,116),(41,117,55,131),(42,132,56,118),(57,156,71,142),(58,143,72,157),(59,158,73,144),(60,145,74,159),(61,160,75,146),(62,147,76,161),(63,162,77,148),(64,149,78,163),(65,164,79,150),(66,151,80,165),(67,166,81,152),(68,153,82,167),(69,168,83,154),(70,155,84,141),(85,185,99,171),(86,172,100,186),(87,187,101,173),(88,174,102,188),(89,189,103,175),(90,176,104,190),(91,191,105,177),(92,178,106,192),(93,193,107,179),(94,180,108,194),(95,195,109,181),(96,182,110,196),(97,169,111,183),(98,184,112,170)], [(1,178,127,165),(2,166,128,179),(3,180,129,167),(4,168,130,181),(5,182,131,141),(6,142,132,183),(7,184,133,143),(8,144,134,185),(9,186,135,145),(10,146,136,187),(11,188,137,147),(12,148,138,189),(13,190,139,149),(14,150,140,191),(15,192,113,151),(16,152,114,193),(17,194,115,153),(18,154,116,195),(19,196,117,155),(20,156,118,169),(21,170,119,157),(22,158,120,171),(23,172,121,159),(24,160,122,173),(25,174,123,161),(26,162,124,175),(27,176,125,163),(28,164,126,177),(29,58,211,98),(30,99,212,59),(31,60,213,100),(32,101,214,61),(33,62,215,102),(34,103,216,63),(35,64,217,104),(36,105,218,65),(37,66,219,106),(38,107,220,67),(39,68,221,108),(40,109,222,69),(41,70,223,110),(42,111,224,71),(43,72,197,112),(44,85,198,73),(45,74,199,86),(46,87,200,75),(47,76,201,88),(48,89,202,77),(49,78,203,90),(50,91,204,79),(51,80,205,92),(52,93,206,81),(53,82,207,94),(54,95,208,83),(55,84,209,96),(56,97,210,57)], [(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)], [(1,14,113,126),(2,125,114,13),(3,12,115,124),(4,123,116,11),(5,10,117,122),(6,121,118,9),(7,8,119,120),(15,28,127,140),(16,139,128,27),(17,26,129,138),(18,137,130,25),(19,24,131,136),(20,135,132,23),(21,22,133,134),(29,30,197,198),(31,56,199,224),(32,223,200,55),(33,54,201,222),(34,221,202,53),(35,52,203,220),(36,219,204,51),(37,50,205,218),(38,217,206,49),(39,48,207,216),(40,215,208,47),(41,46,209,214),(42,213,210,45),(43,44,211,212),(57,100,111,74),(58,73,112,99),(59,98,85,72),(60,71,86,97),(61,96,87,70),(62,69,88,95),(63,94,89,68),(64,67,90,93),(65,92,91,66),(75,110,101,84),(76,83,102,109),(77,108,103,82),(78,81,104,107),(79,106,105,80),(141,160,196,187),(142,186,169,159),(143,158,170,185),(144,184,171,157),(145,156,172,183),(146,182,173,155),(147,154,174,181),(148,180,175,153),(149,152,176,179),(150,178,177,151),(161,168,188,195),(162,194,189,167),(163,166,190,193),(164,192,191,165)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | ··· | 4H | 4I | 4J | 4K | 4L | 4M | ··· | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | 2- 1+4 | D4⋊2D7 | Q8.10D14 |
| kernel | C42.176D14 | C28.6Q8 | C42⋊D7 | Dic7.Q8 | C4⋊C4⋊D7 | Q8×Dic7 | D14⋊3Q8 | C7×C4⋊Q8 | C4⋊Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 4 | 4 | 2 | 2 | 1 | 3 | 4 | 3 | 12 | 6 | 2 | 6 | 12 |
Matrix representation of C42.176D14 ►in GL8(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 12 | 17 | 0 |
| 0 | 0 | 0 | 0 | 25 | 16 | 0 | 17 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 18 | 16 | 18 |
| 0 | 0 | 0 | 0 | 0 | 5 | 26 | 13 |
| 26 | 13 | 13 | 21 | 0 | 0 | 0 | 0 |
| 16 | 16 | 8 | 8 | 0 | 0 | 0 | 0 |
| 13 | 21 | 3 | 16 | 0 | 0 | 0 | 0 |
| 8 | 8 | 13 | 13 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 15 | 27 | 0 | 3 |
| 0 | 0 | 0 | 0 | 26 | 10 | 14 | 18 |
| 0 | 0 | 0 | 0 | 7 | 8 | 7 | 2 |
| 0 | 0 | 0 | 0 | 22 | 26 | 19 | 26 |
| 24 | 7 | 12 | 18 | 0 | 0 | 0 | 0 |
| 22 | 5 | 11 | 17 | 0 | 0 | 0 | 0 |
| 12 | 18 | 5 | 22 | 0 | 0 | 0 | 0 |
| 11 | 17 | 7 | 24 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 1 | 13 | 25 |
| 0 | 0 | 0 | 0 | 5 | 9 | 0 | 1 |
| 0 | 0 | 0 | 0 | 18 | 14 | 18 | 5 |
| 0 | 0 | 0 | 0 | 0 | 2 | 22 | 11 |
G:=sub<GL(8,GF(29))| [28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,12,0,2,25,0,0,0,0,0,12,12,16,0,0,0,0,0,0,17,0,0,0,0,0,0,0,0,17],[0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,8,2,13,0,0,0,0,0,11,21,18,5,0,0,0,0,0,0,16,26,0,0,0,0,0,0,18,13],[26,16,13,8,0,0,0,0,13,16,21,8,0,0,0,0,13,8,3,13,0,0,0,0,21,8,16,13,0,0,0,0,0,0,0,0,15,26,7,22,0,0,0,0,27,10,8,26,0,0,0,0,0,14,7,19,0,0,0,0,3,18,2,26],[24,22,12,11,0,0,0,0,7,5,18,17,0,0,0,0,12,11,5,7,0,0,0,0,18,17,22,24,0,0,0,0,0,0,0,0,20,5,18,0,0,0,0,0,1,9,14,2,0,0,0,0,13,0,18,22,0,0,0,0,25,1,5,11] >;
C42.176D14 in GAP, Magma, Sage, TeX
C_4^2._{176}D_{14} % in TeX
G:=Group("C4^2.176D14"); // GroupNames label
G:=SmallGroup(448,1184);
// by ID
G=gap.SmallGroup(448,1184);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,758,219,100,675,297,136,18822]);
// 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,c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=b^-1,d*b*d^-1=a^2*b^-1,d*c*d^-1=b^2*c^13>;
// generators/relations