metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.153D14, C14.1332+ 1+4, (C4×D28)⋊48C2, C42.C2⋊9D7, C4⋊D28⋊33C2, C4⋊C4.209D14, D28⋊C4⋊37C2, (C2×C28).91C23, D14.32(C4○D4), D14.5D4⋊35C2, C28.130(C4○D4), (C4×C28).198C22, (C2×C14).239C24, D14⋊C4.41C22, C4.39(Q8⋊2D7), C2.58(D4⋊8D14), (C2×D28).268C22, Dic7⋊C4.54C22, C4⋊Dic7.315C22, C22.260(C23×D7), (C2×Dic7).124C23, (C4×Dic7).145C22, (C22×D7).104C23, C7⋊10(C22.47C24), (D7×C4⋊C4)⋊39C2, C2.90(D7×C4○D4), C4⋊C4⋊D7⋊37C2, C4⋊C4⋊7D7⋊38C2, C14.201(C2×C4○D4), C2.24(C2×Q8⋊2D7), (C7×C42.C2)⋊12C2, (C2×C4×D7).129C22, (C2×C4).82(C22×D7), (C7×C4⋊C4).194C22, SmallGroup(448,1148)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.153D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2b2, ab=ba, cac-1=dad-1=a-1, cbc-1=a2b-1, dbd-1=a2b, dcd-1=c13 >
Subgroups: 1244 in 238 conjugacy classes, 97 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, C23, D7, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, Dic7, C28, C28, D14, D14, C2×C14, C2×C4⋊C4, C42⋊C2, C4×D4, C4⋊D4, C22.D4, C42.C2, C42⋊2C2, C4×D7, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22.47C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, D14⋊C4, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×C4×D7, C2×C4×D7, C2×D28, C2×D28, C4×D28, D7×C4⋊C4, C4⋊C4⋊7D7, D28⋊C4, D14.5D4, C4⋊D28, C4⋊D28, C4⋊C4⋊D7, C7×C42.C2, C42.153D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.47C24, Q8⋊2D7, C23×D7, C2×Q8⋊2D7, D7×C4○D4, D4⋊8D14, C42.153D14
►On 224 points
Generators in S224
(1 137 211 192)(2 193 212 138)(3 139 213 194)(4 195 214 140)(5 113 215 196)(6 169 216 114)(7 115 217 170)(8 171 218 116)(9 117 219 172)(10 173 220 118)(11 119 221 174)(12 175 222 120)(13 121 223 176)(14 177 224 122)(15 123 197 178)(16 179 198 124)(17 125 199 180)(18 181 200 126)(19 127 201 182)(20 183 202 128)(21 129 203 184)(22 185 204 130)(23 131 205 186)(24 187 206 132)(25 133 207 188)(26 189 208 134)(27 135 209 190)(28 191 210 136)(29 86 72 141)(30 142 73 87)(31 88 74 143)(32 144 75 89)(33 90 76 145)(34 146 77 91)(35 92 78 147)(36 148 79 93)(37 94 80 149)(38 150 81 95)(39 96 82 151)(40 152 83 97)(41 98 84 153)(42 154 57 99)(43 100 58 155)(44 156 59 101)(45 102 60 157)(46 158 61 103)(47 104 62 159)(48 160 63 105)(49 106 64 161)(50 162 65 107)(51 108 66 163)(52 164 67 109)(53 110 68 165)(54 166 69 111)(55 112 70 167)(56 168 71 85)
(1 78 197 49)(2 65 198 36)(3 80 199 51)(4 67 200 38)(5 82 201 53)(6 69 202 40)(7 84 203 55)(8 71 204 42)(9 58 205 29)(10 73 206 44)(11 60 207 31)(12 75 208 46)(13 62 209 33)(14 77 210 48)(15 64 211 35)(16 79 212 50)(17 66 213 37)(18 81 214 52)(19 68 215 39)(20 83 216 54)(21 70 217 41)(22 57 218 56)(23 72 219 43)(24 59 220 30)(25 74 221 45)(26 61 222 32)(27 76 223 47)(28 63 224 34)(85 130 154 171)(86 117 155 186)(87 132 156 173)(88 119 157 188)(89 134 158 175)(90 121 159 190)(91 136 160 177)(92 123 161 192)(93 138 162 179)(94 125 163 194)(95 140 164 181)(96 127 165 196)(97 114 166 183)(98 129 167 170)(99 116 168 185)(100 131 141 172)(101 118 142 187)(102 133 143 174)(103 120 144 189)(104 135 145 176)(105 122 146 191)(106 137 147 178)(107 124 148 193)(108 139 149 180)(109 126 150 195)(110 113 151 182)(111 128 152 169)(112 115 153 184)
(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)
(1 224 15 210)(2 209 16 223)(3 222 17 208)(4 207 18 221)(5 220 19 206)(6 205 20 219)(7 218 21 204)(8 203 22 217)(9 216 23 202)(10 201 24 215)(11 214 25 200)(12 199 26 213)(13 212 27 198)(14 197 28 211)(29 40 43 54)(30 53 44 39)(31 38 45 52)(32 51 46 37)(33 36 47 50)(34 49 48 35)(41 56 55 42)(57 84 71 70)(58 69 72 83)(59 82 73 68)(60 67 74 81)(61 80 75 66)(62 65 76 79)(63 78 77 64)(85 112 99 98)(86 97 100 111)(87 110 101 96)(88 95 102 109)(89 108 103 94)(90 93 104 107)(91 106 105 92)(113 173 127 187)(114 186 128 172)(115 171 129 185)(116 184 130 170)(117 169 131 183)(118 182 132 196)(119 195 133 181)(120 180 134 194)(121 193 135 179)(122 178 136 192)(123 191 137 177)(124 176 138 190)(125 189 139 175)(126 174 140 188)(141 152 155 166)(142 165 156 151)(143 150 157 164)(144 163 158 149)(145 148 159 162)(146 161 160 147)(153 168 167 154)
G:=sub<Sym(224)| (1,137,211,192)(2,193,212,138)(3,139,213,194)(4,195,214,140)(5,113,215,196)(6,169,216,114)(7,115,217,170)(8,171,218,116)(9,117,219,172)(10,173,220,118)(11,119,221,174)(12,175,222,120)(13,121,223,176)(14,177,224,122)(15,123,197,178)(16,179,198,124)(17,125,199,180)(18,181,200,126)(19,127,201,182)(20,183,202,128)(21,129,203,184)(22,185,204,130)(23,131,205,186)(24,187,206,132)(25,133,207,188)(26,189,208,134)(27,135,209,190)(28,191,210,136)(29,86,72,141)(30,142,73,87)(31,88,74,143)(32,144,75,89)(33,90,76,145)(34,146,77,91)(35,92,78,147)(36,148,79,93)(37,94,80,149)(38,150,81,95)(39,96,82,151)(40,152,83,97)(41,98,84,153)(42,154,57,99)(43,100,58,155)(44,156,59,101)(45,102,60,157)(46,158,61,103)(47,104,62,159)(48,160,63,105)(49,106,64,161)(50,162,65,107)(51,108,66,163)(52,164,67,109)(53,110,68,165)(54,166,69,111)(55,112,70,167)(56,168,71,85), (1,78,197,49)(2,65,198,36)(3,80,199,51)(4,67,200,38)(5,82,201,53)(6,69,202,40)(7,84,203,55)(8,71,204,42)(9,58,205,29)(10,73,206,44)(11,60,207,31)(12,75,208,46)(13,62,209,33)(14,77,210,48)(15,64,211,35)(16,79,212,50)(17,66,213,37)(18,81,214,52)(19,68,215,39)(20,83,216,54)(21,70,217,41)(22,57,218,56)(23,72,219,43)(24,59,220,30)(25,74,221,45)(26,61,222,32)(27,76,223,47)(28,63,224,34)(85,130,154,171)(86,117,155,186)(87,132,156,173)(88,119,157,188)(89,134,158,175)(90,121,159,190)(91,136,160,177)(92,123,161,192)(93,138,162,179)(94,125,163,194)(95,140,164,181)(96,127,165,196)(97,114,166,183)(98,129,167,170)(99,116,168,185)(100,131,141,172)(101,118,142,187)(102,133,143,174)(103,120,144,189)(104,135,145,176)(105,122,146,191)(106,137,147,178)(107,124,148,193)(108,139,149,180)(109,126,150,195)(110,113,151,182)(111,128,152,169)(112,115,153,184), (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), (1,224,15,210)(2,209,16,223)(3,222,17,208)(4,207,18,221)(5,220,19,206)(6,205,20,219)(7,218,21,204)(8,203,22,217)(9,216,23,202)(10,201,24,215)(11,214,25,200)(12,199,26,213)(13,212,27,198)(14,197,28,211)(29,40,43,54)(30,53,44,39)(31,38,45,52)(32,51,46,37)(33,36,47,50)(34,49,48,35)(41,56,55,42)(57,84,71,70)(58,69,72,83)(59,82,73,68)(60,67,74,81)(61,80,75,66)(62,65,76,79)(63,78,77,64)(85,112,99,98)(86,97,100,111)(87,110,101,96)(88,95,102,109)(89,108,103,94)(90,93,104,107)(91,106,105,92)(113,173,127,187)(114,186,128,172)(115,171,129,185)(116,184,130,170)(117,169,131,183)(118,182,132,196)(119,195,133,181)(120,180,134,194)(121,193,135,179)(122,178,136,192)(123,191,137,177)(124,176,138,190)(125,189,139,175)(126,174,140,188)(141,152,155,166)(142,165,156,151)(143,150,157,164)(144,163,158,149)(145,148,159,162)(146,161,160,147)(153,168,167,154)>;
G:=Group( (1,137,211,192)(2,193,212,138)(3,139,213,194)(4,195,214,140)(5,113,215,196)(6,169,216,114)(7,115,217,170)(8,171,218,116)(9,117,219,172)(10,173,220,118)(11,119,221,174)(12,175,222,120)(13,121,223,176)(14,177,224,122)(15,123,197,178)(16,179,198,124)(17,125,199,180)(18,181,200,126)(19,127,201,182)(20,183,202,128)(21,129,203,184)(22,185,204,130)(23,131,205,186)(24,187,206,132)(25,133,207,188)(26,189,208,134)(27,135,209,190)(28,191,210,136)(29,86,72,141)(30,142,73,87)(31,88,74,143)(32,144,75,89)(33,90,76,145)(34,146,77,91)(35,92,78,147)(36,148,79,93)(37,94,80,149)(38,150,81,95)(39,96,82,151)(40,152,83,97)(41,98,84,153)(42,154,57,99)(43,100,58,155)(44,156,59,101)(45,102,60,157)(46,158,61,103)(47,104,62,159)(48,160,63,105)(49,106,64,161)(50,162,65,107)(51,108,66,163)(52,164,67,109)(53,110,68,165)(54,166,69,111)(55,112,70,167)(56,168,71,85), (1,78,197,49)(2,65,198,36)(3,80,199,51)(4,67,200,38)(5,82,201,53)(6,69,202,40)(7,84,203,55)(8,71,204,42)(9,58,205,29)(10,73,206,44)(11,60,207,31)(12,75,208,46)(13,62,209,33)(14,77,210,48)(15,64,211,35)(16,79,212,50)(17,66,213,37)(18,81,214,52)(19,68,215,39)(20,83,216,54)(21,70,217,41)(22,57,218,56)(23,72,219,43)(24,59,220,30)(25,74,221,45)(26,61,222,32)(27,76,223,47)(28,63,224,34)(85,130,154,171)(86,117,155,186)(87,132,156,173)(88,119,157,188)(89,134,158,175)(90,121,159,190)(91,136,160,177)(92,123,161,192)(93,138,162,179)(94,125,163,194)(95,140,164,181)(96,127,165,196)(97,114,166,183)(98,129,167,170)(99,116,168,185)(100,131,141,172)(101,118,142,187)(102,133,143,174)(103,120,144,189)(104,135,145,176)(105,122,146,191)(106,137,147,178)(107,124,148,193)(108,139,149,180)(109,126,150,195)(110,113,151,182)(111,128,152,169)(112,115,153,184), (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), (1,224,15,210)(2,209,16,223)(3,222,17,208)(4,207,18,221)(5,220,19,206)(6,205,20,219)(7,218,21,204)(8,203,22,217)(9,216,23,202)(10,201,24,215)(11,214,25,200)(12,199,26,213)(13,212,27,198)(14,197,28,211)(29,40,43,54)(30,53,44,39)(31,38,45,52)(32,51,46,37)(33,36,47,50)(34,49,48,35)(41,56,55,42)(57,84,71,70)(58,69,72,83)(59,82,73,68)(60,67,74,81)(61,80,75,66)(62,65,76,79)(63,78,77,64)(85,112,99,98)(86,97,100,111)(87,110,101,96)(88,95,102,109)(89,108,103,94)(90,93,104,107)(91,106,105,92)(113,173,127,187)(114,186,128,172)(115,171,129,185)(116,184,130,170)(117,169,131,183)(118,182,132,196)(119,195,133,181)(120,180,134,194)(121,193,135,179)(122,178,136,192)(123,191,137,177)(124,176,138,190)(125,189,139,175)(126,174,140,188)(141,152,155,166)(142,165,156,151)(143,150,157,164)(144,163,158,149)(145,148,159,162)(146,161,160,147)(153,168,167,154) );
G=PermutationGroup([[(1,137,211,192),(2,193,212,138),(3,139,213,194),(4,195,214,140),(5,113,215,196),(6,169,216,114),(7,115,217,170),(8,171,218,116),(9,117,219,172),(10,173,220,118),(11,119,221,174),(12,175,222,120),(13,121,223,176),(14,177,224,122),(15,123,197,178),(16,179,198,124),(17,125,199,180),(18,181,200,126),(19,127,201,182),(20,183,202,128),(21,129,203,184),(22,185,204,130),(23,131,205,186),(24,187,206,132),(25,133,207,188),(26,189,208,134),(27,135,209,190),(28,191,210,136),(29,86,72,141),(30,142,73,87),(31,88,74,143),(32,144,75,89),(33,90,76,145),(34,146,77,91),(35,92,78,147),(36,148,79,93),(37,94,80,149),(38,150,81,95),(39,96,82,151),(40,152,83,97),(41,98,84,153),(42,154,57,99),(43,100,58,155),(44,156,59,101),(45,102,60,157),(46,158,61,103),(47,104,62,159),(48,160,63,105),(49,106,64,161),(50,162,65,107),(51,108,66,163),(52,164,67,109),(53,110,68,165),(54,166,69,111),(55,112,70,167),(56,168,71,85)], [(1,78,197,49),(2,65,198,36),(3,80,199,51),(4,67,200,38),(5,82,201,53),(6,69,202,40),(7,84,203,55),(8,71,204,42),(9,58,205,29),(10,73,206,44),(11,60,207,31),(12,75,208,46),(13,62,209,33),(14,77,210,48),(15,64,211,35),(16,79,212,50),(17,66,213,37),(18,81,214,52),(19,68,215,39),(20,83,216,54),(21,70,217,41),(22,57,218,56),(23,72,219,43),(24,59,220,30),(25,74,221,45),(26,61,222,32),(27,76,223,47),(28,63,224,34),(85,130,154,171),(86,117,155,186),(87,132,156,173),(88,119,157,188),(89,134,158,175),(90,121,159,190),(91,136,160,177),(92,123,161,192),(93,138,162,179),(94,125,163,194),(95,140,164,181),(96,127,165,196),(97,114,166,183),(98,129,167,170),(99,116,168,185),(100,131,141,172),(101,118,142,187),(102,133,143,174),(103,120,144,189),(104,135,145,176),(105,122,146,191),(106,137,147,178),(107,124,148,193),(108,139,149,180),(109,126,150,195),(110,113,151,182),(111,128,152,169),(112,115,153,184)], [(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)], [(1,224,15,210),(2,209,16,223),(3,222,17,208),(4,207,18,221),(5,220,19,206),(6,205,20,219),(7,218,21,204),(8,203,22,217),(9,216,23,202),(10,201,24,215),(11,214,25,200),(12,199,26,213),(13,212,27,198),(14,197,28,211),(29,40,43,54),(30,53,44,39),(31,38,45,52),(32,51,46,37),(33,36,47,50),(34,49,48,35),(41,56,55,42),(57,84,71,70),(58,69,72,83),(59,82,73,68),(60,67,74,81),(61,80,75,66),(62,65,76,79),(63,78,77,64),(85,112,99,98),(86,97,100,111),(87,110,101,96),(88,95,102,109),(89,108,103,94),(90,93,104,107),(91,106,105,92),(113,173,127,187),(114,186,128,172),(115,171,129,185),(116,184,130,170),(117,169,131,183),(118,182,132,196),(119,195,133,181),(120,180,134,194),(121,193,135,179),(122,178,136,192),(123,191,137,177),(124,176,138,190),(125,189,139,175),(126,174,140,188),(141,152,155,166),(142,165,156,151),(143,150,157,164),(144,163,158,149),(145,148,159,162),(146,161,160,147),(153,168,167,154)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | 4B | 4C | 4D | 4E | ··· | 4I | 4J | ··· | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 14 | ··· | 14 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | 2+ 1+4 | Q8⋊2D7 | D7×C4○D4 | D4⋊8D14 |
| kernel | C42.153D14 | C4×D28 | D7×C4⋊C4 | C4⋊C4⋊7D7 | D28⋊C4 | D14.5D4 | C4⋊D28 | C4⋊C4⋊D7 | C7×C42.C2 | C42.C2 | C28 | D14 | C42 | C4⋊C4 | C14 | C4 | C2 | C2 |
| # reps | 1 | 2 | 1 | 1 | 2 | 2 | 4 | 2 | 1 | 3 | 4 | 4 | 3 | 18 | 1 | 6 | 6 | 6 |
Matrix representation of C42.153D14 ►in GL6(𝔽29)
| 0 | 12 | 0 | 0 | 0 | 0 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 9 | 16 | 0 | 0 | 0 | 0 |
| 13 | 20 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 8 | 0 | 0 |
| 0 | 0 | 13 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 20 | 13 | 0 | 0 | 0 | 0 |
| 16 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 1 | 0 | 0 |
| 0 | 0 | 24 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
G:=sub<GL(6,GF(29))| [0,12,0,0,0,0,12,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,1,0],[9,13,0,0,0,0,16,20,0,0,0,0,0,0,2,13,0,0,0,0,8,9,0,0,0,0,0,0,17,0,0,0,0,0,0,12],[20,16,0,0,0,0,13,9,0,0,0,0,0,0,21,24,0,0,0,0,1,8,0,0,0,0,0,0,17,0,0,0,0,0,0,17] >;
C42.153D14 in GAP, Magma, Sage, TeX
C_4^2._{153}D_{14} % in TeX
G:=Group("C4^2.153D14"); // GroupNames label
G:=SmallGroup(448,1148);
// by ID
G=gap.SmallGroup(448,1148);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,387,100,1571,185,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^2*b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=a^2*b^-1,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations