metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.240D14, (C4×D7)⋊9D4, C4⋊Q8⋊19D7, C4.38(D4×D7), C28⋊6(C4○D4), D14.8(C2×D4), C28.70(C2×D4), C4⋊D28⋊17C2, C28⋊1D4⋊39C2, C4⋊C4.217D14, C4⋊1(Q8⋊2D7), (D7×C42)⋊14C2, D28⋊C4⋊43C2, (C2×Q8).144D14, Dic7.67(C2×D4), C14.99(C22×D4), C28.23D4⋊26C2, (C2×C14).269C24, (C2×C28).102C23, (C4×C28).210C22, D14⋊C4.50C22, (C2×D28).172C22, (Q8×C14).136C22, C7⋊6(C22.26C24), C22.290(C23×D7), (C4×Dic7).258C22, (C2×Dic7).272C23, (C22×D7).119C23, C2.72(C2×D4×D7), (C7×C4⋊Q8)⋊11C2, (C2×Q8⋊2D7)⋊12C2, C14.120(C2×C4○D4), C2.27(C2×Q8⋊2D7), (C2×C4×D7).143C22, (C7×C4⋊C4).212C22, (C2×C4).599(C22×D7), SmallGroup(448,1178)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1612 in 310 conjugacy classes, 111 normal (19 characteristic)
C1, C2, C2 [×2], C2 [×6], C4 [×6], C4 [×8], C22, C22 [×16], C7, C2×C4, C2×C4 [×6], C2×C4 [×19], D4 [×20], Q8 [×4], C23 [×5], D7 [×6], C14, C14 [×2], C42, C42 [×3], C22⋊C4 [×8], C4⋊C4 [×4], C22×C4 [×7], C2×D4 [×10], C2×Q8 [×2], C4○D4 [×8], Dic7 [×2], Dic7 [×2], C28 [×6], C28 [×4], D14 [×2], D14 [×14], C2×C14, C2×C42, C4×D4 [×4], C4⋊D4 [×4], C4.4D4 [×2], C4⋊1D4, C4⋊Q8, C2×C4○D4 [×2], C4×D7 [×4], C4×D7 [×12], D28 [×20], C2×Dic7, C2×Dic7 [×2], C2×C28, C2×C28 [×6], C7×Q8 [×4], C22×D7, C22×D7 [×4], C22.26C24, C4×Dic7, C4×Dic7 [×2], D14⋊C4 [×8], C4×C28, C7×C4⋊C4 [×4], C2×C4×D7, C2×C4×D7 [×6], C2×D28 [×10], Q8⋊2D7 [×8], Q8×C14 [×2], D7×C42, C4⋊D28, D28⋊C4 [×4], C28⋊1D4 [×4], C28.23D4 [×2], C7×C4⋊Q8, C2×Q8⋊2D7 [×2], C42.240D14
Quotients:
C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D7, C2×D4 [×6], C4○D4 [×4], C24, D14 [×7], C22×D4, C2×C4○D4 [×2], C22×D7 [×7], C22.26C24, D4×D7 [×2], Q8⋊2D7 [×4], C23×D7, C2×D4×D7, C2×Q8⋊2D7 [×2], C42.240D14
Generators and relations
G = < a,b,c,d | a4=b4=d2=1, c14=b2, ab=ba, cac-1=dad=a-1, cbc-1=dbd=b-1, dcd=b2c13 >
►On 224 points
Generators in S224
(1 205 175 151)(2 152 176 206)(3 207 177 153)(4 154 178 208)(5 209 179 155)(6 156 180 210)(7 211 181 157)(8 158 182 212)(9 213 183 159)(10 160 184 214)(11 215 185 161)(12 162 186 216)(13 217 187 163)(14 164 188 218)(15 219 189 165)(16 166 190 220)(17 221 191 167)(18 168 192 222)(19 223 193 141)(20 142 194 224)(21 197 195 143)(22 144 196 198)(23 199 169 145)(24 146 170 200)(25 201 171 147)(26 148 172 202)(27 203 173 149)(28 150 174 204)(29 93 76 130)(30 131 77 94)(31 95 78 132)(32 133 79 96)(33 97 80 134)(34 135 81 98)(35 99 82 136)(36 137 83 100)(37 101 84 138)(38 139 57 102)(39 103 58 140)(40 113 59 104)(41 105 60 114)(42 115 61 106)(43 107 62 116)(44 117 63 108)(45 109 64 118)(46 119 65 110)(47 111 66 120)(48 121 67 112)(49 85 68 122)(50 123 69 86)(51 87 70 124)(52 125 71 88)(53 89 72 126)(54 127 73 90)(55 91 74 128)(56 129 75 92)
(1 82 15 68)(2 69 16 83)(3 84 17 70)(4 71 18 57)(5 58 19 72)(6 73 20 59)(7 60 21 74)(8 75 22 61)(9 62 23 76)(10 77 24 63)(11 64 25 78)(12 79 26 65)(13 66 27 80)(14 81 28 67)(29 183 43 169)(30 170 44 184)(31 185 45 171)(32 172 46 186)(33 187 47 173)(34 174 48 188)(35 189 49 175)(36 176 50 190)(37 191 51 177)(38 178 52 192)(39 193 53 179)(40 180 54 194)(41 195 55 181)(42 182 56 196)(85 151 99 165)(86 166 100 152)(87 153 101 167)(88 168 102 154)(89 155 103 141)(90 142 104 156)(91 157 105 143)(92 144 106 158)(93 159 107 145)(94 146 108 160)(95 161 109 147)(96 148 110 162)(97 163 111 149)(98 150 112 164)(113 210 127 224)(114 197 128 211)(115 212 129 198)(116 199 130 213)(117 214 131 200)(118 201 132 215)(119 216 133 202)(120 203 134 217)(121 218 135 204)(122 205 136 219)(123 220 137 206)(124 207 138 221)(125 222 139 208)(126 209 140 223)
(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)
(1 188)(2 187)(3 186)(4 185)(5 184)(6 183)(7 182)(8 181)(9 180)(10 179)(11 178)(12 177)(13 176)(14 175)(15 174)(16 173)(17 172)(18 171)(19 170)(20 169)(21 196)(22 195)(23 194)(24 193)(25 192)(26 191)(27 190)(28 189)(29 73)(30 72)(31 71)(32 70)(33 69)(34 68)(35 67)(36 66)(37 65)(38 64)(39 63)(40 62)(41 61)(42 60)(43 59)(44 58)(45 57)(46 84)(47 83)(48 82)(49 81)(50 80)(51 79)(52 78)(53 77)(54 76)(55 75)(56 74)(85 135)(86 134)(87 133)(88 132)(89 131)(90 130)(91 129)(92 128)(93 127)(94 126)(95 125)(96 124)(97 123)(98 122)(99 121)(100 120)(101 119)(102 118)(103 117)(104 116)(105 115)(106 114)(107 113)(108 140)(109 139)(110 138)(111 137)(112 136)(141 200)(142 199)(143 198)(144 197)(145 224)(146 223)(147 222)(148 221)(149 220)(150 219)(151 218)(152 217)(153 216)(154 215)(155 214)(156 213)(157 212)(158 211)(159 210)(160 209)(161 208)(162 207)(163 206)(164 205)(165 204)(166 203)(167 202)(168 201)
G:=sub<Sym(224)| (1,205,175,151)(2,152,176,206)(3,207,177,153)(4,154,178,208)(5,209,179,155)(6,156,180,210)(7,211,181,157)(8,158,182,212)(9,213,183,159)(10,160,184,214)(11,215,185,161)(12,162,186,216)(13,217,187,163)(14,164,188,218)(15,219,189,165)(16,166,190,220)(17,221,191,167)(18,168,192,222)(19,223,193,141)(20,142,194,224)(21,197,195,143)(22,144,196,198)(23,199,169,145)(24,146,170,200)(25,201,171,147)(26,148,172,202)(27,203,173,149)(28,150,174,204)(29,93,76,130)(30,131,77,94)(31,95,78,132)(32,133,79,96)(33,97,80,134)(34,135,81,98)(35,99,82,136)(36,137,83,100)(37,101,84,138)(38,139,57,102)(39,103,58,140)(40,113,59,104)(41,105,60,114)(42,115,61,106)(43,107,62,116)(44,117,63,108)(45,109,64,118)(46,119,65,110)(47,111,66,120)(48,121,67,112)(49,85,68,122)(50,123,69,86)(51,87,70,124)(52,125,71,88)(53,89,72,126)(54,127,73,90)(55,91,74,128)(56,129,75,92), (1,82,15,68)(2,69,16,83)(3,84,17,70)(4,71,18,57)(5,58,19,72)(6,73,20,59)(7,60,21,74)(8,75,22,61)(9,62,23,76)(10,77,24,63)(11,64,25,78)(12,79,26,65)(13,66,27,80)(14,81,28,67)(29,183,43,169)(30,170,44,184)(31,185,45,171)(32,172,46,186)(33,187,47,173)(34,174,48,188)(35,189,49,175)(36,176,50,190)(37,191,51,177)(38,178,52,192)(39,193,53,179)(40,180,54,194)(41,195,55,181)(42,182,56,196)(85,151,99,165)(86,166,100,152)(87,153,101,167)(88,168,102,154)(89,155,103,141)(90,142,104,156)(91,157,105,143)(92,144,106,158)(93,159,107,145)(94,146,108,160)(95,161,109,147)(96,148,110,162)(97,163,111,149)(98,150,112,164)(113,210,127,224)(114,197,128,211)(115,212,129,198)(116,199,130,213)(117,214,131,200)(118,201,132,215)(119,216,133,202)(120,203,134,217)(121,218,135,204)(122,205,136,219)(123,220,137,206)(124,207,138,221)(125,222,139,208)(126,209,140,223), (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), (1,188)(2,187)(3,186)(4,185)(5,184)(6,183)(7,182)(8,181)(9,180)(10,179)(11,178)(12,177)(13,176)(14,175)(15,174)(16,173)(17,172)(18,171)(19,170)(20,169)(21,196)(22,195)(23,194)(24,193)(25,192)(26,191)(27,190)(28,189)(29,73)(30,72)(31,71)(32,70)(33,69)(34,68)(35,67)(36,66)(37,65)(38,64)(39,63)(40,62)(41,61)(42,60)(43,59)(44,58)(45,57)(46,84)(47,83)(48,82)(49,81)(50,80)(51,79)(52,78)(53,77)(54,76)(55,75)(56,74)(85,135)(86,134)(87,133)(88,132)(89,131)(90,130)(91,129)(92,128)(93,127)(94,126)(95,125)(96,124)(97,123)(98,122)(99,121)(100,120)(101,119)(102,118)(103,117)(104,116)(105,115)(106,114)(107,113)(108,140)(109,139)(110,138)(111,137)(112,136)(141,200)(142,199)(143,198)(144,197)(145,224)(146,223)(147,222)(148,221)(149,220)(150,219)(151,218)(152,217)(153,216)(154,215)(155,214)(156,213)(157,212)(158,211)(159,210)(160,209)(161,208)(162,207)(163,206)(164,205)(165,204)(166,203)(167,202)(168,201)>;
G:=Group( (1,205,175,151)(2,152,176,206)(3,207,177,153)(4,154,178,208)(5,209,179,155)(6,156,180,210)(7,211,181,157)(8,158,182,212)(9,213,183,159)(10,160,184,214)(11,215,185,161)(12,162,186,216)(13,217,187,163)(14,164,188,218)(15,219,189,165)(16,166,190,220)(17,221,191,167)(18,168,192,222)(19,223,193,141)(20,142,194,224)(21,197,195,143)(22,144,196,198)(23,199,169,145)(24,146,170,200)(25,201,171,147)(26,148,172,202)(27,203,173,149)(28,150,174,204)(29,93,76,130)(30,131,77,94)(31,95,78,132)(32,133,79,96)(33,97,80,134)(34,135,81,98)(35,99,82,136)(36,137,83,100)(37,101,84,138)(38,139,57,102)(39,103,58,140)(40,113,59,104)(41,105,60,114)(42,115,61,106)(43,107,62,116)(44,117,63,108)(45,109,64,118)(46,119,65,110)(47,111,66,120)(48,121,67,112)(49,85,68,122)(50,123,69,86)(51,87,70,124)(52,125,71,88)(53,89,72,126)(54,127,73,90)(55,91,74,128)(56,129,75,92), (1,82,15,68)(2,69,16,83)(3,84,17,70)(4,71,18,57)(5,58,19,72)(6,73,20,59)(7,60,21,74)(8,75,22,61)(9,62,23,76)(10,77,24,63)(11,64,25,78)(12,79,26,65)(13,66,27,80)(14,81,28,67)(29,183,43,169)(30,170,44,184)(31,185,45,171)(32,172,46,186)(33,187,47,173)(34,174,48,188)(35,189,49,175)(36,176,50,190)(37,191,51,177)(38,178,52,192)(39,193,53,179)(40,180,54,194)(41,195,55,181)(42,182,56,196)(85,151,99,165)(86,166,100,152)(87,153,101,167)(88,168,102,154)(89,155,103,141)(90,142,104,156)(91,157,105,143)(92,144,106,158)(93,159,107,145)(94,146,108,160)(95,161,109,147)(96,148,110,162)(97,163,111,149)(98,150,112,164)(113,210,127,224)(114,197,128,211)(115,212,129,198)(116,199,130,213)(117,214,131,200)(118,201,132,215)(119,216,133,202)(120,203,134,217)(121,218,135,204)(122,205,136,219)(123,220,137,206)(124,207,138,221)(125,222,139,208)(126,209,140,223), (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), (1,188)(2,187)(3,186)(4,185)(5,184)(6,183)(7,182)(8,181)(9,180)(10,179)(11,178)(12,177)(13,176)(14,175)(15,174)(16,173)(17,172)(18,171)(19,170)(20,169)(21,196)(22,195)(23,194)(24,193)(25,192)(26,191)(27,190)(28,189)(29,73)(30,72)(31,71)(32,70)(33,69)(34,68)(35,67)(36,66)(37,65)(38,64)(39,63)(40,62)(41,61)(42,60)(43,59)(44,58)(45,57)(46,84)(47,83)(48,82)(49,81)(50,80)(51,79)(52,78)(53,77)(54,76)(55,75)(56,74)(85,135)(86,134)(87,133)(88,132)(89,131)(90,130)(91,129)(92,128)(93,127)(94,126)(95,125)(96,124)(97,123)(98,122)(99,121)(100,120)(101,119)(102,118)(103,117)(104,116)(105,115)(106,114)(107,113)(108,140)(109,139)(110,138)(111,137)(112,136)(141,200)(142,199)(143,198)(144,197)(145,224)(146,223)(147,222)(148,221)(149,220)(150,219)(151,218)(152,217)(153,216)(154,215)(155,214)(156,213)(157,212)(158,211)(159,210)(160,209)(161,208)(162,207)(163,206)(164,205)(165,204)(166,203)(167,202)(168,201) );
G=PermutationGroup([(1,205,175,151),(2,152,176,206),(3,207,177,153),(4,154,178,208),(5,209,179,155),(6,156,180,210),(7,211,181,157),(8,158,182,212),(9,213,183,159),(10,160,184,214),(11,215,185,161),(12,162,186,216),(13,217,187,163),(14,164,188,218),(15,219,189,165),(16,166,190,220),(17,221,191,167),(18,168,192,222),(19,223,193,141),(20,142,194,224),(21,197,195,143),(22,144,196,198),(23,199,169,145),(24,146,170,200),(25,201,171,147),(26,148,172,202),(27,203,173,149),(28,150,174,204),(29,93,76,130),(30,131,77,94),(31,95,78,132),(32,133,79,96),(33,97,80,134),(34,135,81,98),(35,99,82,136),(36,137,83,100),(37,101,84,138),(38,139,57,102),(39,103,58,140),(40,113,59,104),(41,105,60,114),(42,115,61,106),(43,107,62,116),(44,117,63,108),(45,109,64,118),(46,119,65,110),(47,111,66,120),(48,121,67,112),(49,85,68,122),(50,123,69,86),(51,87,70,124),(52,125,71,88),(53,89,72,126),(54,127,73,90),(55,91,74,128),(56,129,75,92)], [(1,82,15,68),(2,69,16,83),(3,84,17,70),(4,71,18,57),(5,58,19,72),(6,73,20,59),(7,60,21,74),(8,75,22,61),(9,62,23,76),(10,77,24,63),(11,64,25,78),(12,79,26,65),(13,66,27,80),(14,81,28,67),(29,183,43,169),(30,170,44,184),(31,185,45,171),(32,172,46,186),(33,187,47,173),(34,174,48,188),(35,189,49,175),(36,176,50,190),(37,191,51,177),(38,178,52,192),(39,193,53,179),(40,180,54,194),(41,195,55,181),(42,182,56,196),(85,151,99,165),(86,166,100,152),(87,153,101,167),(88,168,102,154),(89,155,103,141),(90,142,104,156),(91,157,105,143),(92,144,106,158),(93,159,107,145),(94,146,108,160),(95,161,109,147),(96,148,110,162),(97,163,111,149),(98,150,112,164),(113,210,127,224),(114,197,128,211),(115,212,129,198),(116,199,130,213),(117,214,131,200),(118,201,132,215),(119,216,133,202),(120,203,134,217),(121,218,135,204),(122,205,136,219),(123,220,137,206),(124,207,138,221),(125,222,139,208),(126,209,140,223)], [(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)], [(1,188),(2,187),(3,186),(4,185),(5,184),(6,183),(7,182),(8,181),(9,180),(10,179),(11,178),(12,177),(13,176),(14,175),(15,174),(16,173),(17,172),(18,171),(19,170),(20,169),(21,196),(22,195),(23,194),(24,193),(25,192),(26,191),(27,190),(28,189),(29,73),(30,72),(31,71),(32,70),(33,69),(34,68),(35,67),(36,66),(37,65),(38,64),(39,63),(40,62),(41,61),(42,60),(43,59),(44,58),(45,57),(46,84),(47,83),(48,82),(49,81),(50,80),(51,79),(52,78),(53,77),(54,76),(55,75),(56,74),(85,135),(86,134),(87,133),(88,132),(89,131),(90,130),(91,129),(92,128),(93,127),(94,126),(95,125),(96,124),(97,123),(98,122),(99,121),(100,120),(101,119),(102,118),(103,117),(104,116),(105,115),(106,114),(107,113),(108,140),(109,139),(110,138),(111,137),(112,136),(141,200),(142,199),(143,198),(144,197),(145,224),(146,223),(147,222),(148,221),(149,220),(150,219),(151,218),(152,217),(153,216),(154,215),(155,214),(156,213),(157,212),(158,211),(159,210),(160,209),(161,208),(162,207),(163,206),(164,205),(165,204),(166,203),(167,202),(168,201)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 16 |
| 0 | 0 | 0 | 0 | 13 | 20 |
| 17 | 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 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 8 | 0 | 0 |
| 0 | 0 | 12 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 22 | 26 | 0 | 0 |
| 0 | 0 | 16 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 0 | 0 | 0 | 28 | 0 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,0,17,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,9,13,0,0,0,0,16,20],[17,0,0,0,0,0,0,12,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[0,28,0,0,0,0,1,0,0,0,0,0,0,0,10,12,0,0,0,0,8,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,22,16,0,0,0,0,26,7,0,0,0,0,0,0,0,28,0,0,0,0,28,0] >;
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 | 28A | ··· | 28R | 28S | ··· | 28AD |
| 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 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 7 | 14 | 14 | 14 | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
70 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | D4×D7 | Q8⋊2D7 |
| kernel | C42.240D14 | D7×C42 | C4⋊D28 | D28⋊C4 | C28⋊1D4 | C28.23D4 | C7×C4⋊Q8 | C2×Q8⋊2D7 | C4×D7 | C4⋊Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | C4 | C4 |
| # reps | 1 | 1 | 1 | 4 | 4 | 2 | 1 | 2 | 4 | 3 | 8 | 3 | 12 | 6 | 6 | 12 |
In GAP, Magma, Sage, TeX
C_4^2._{240}D_{14} % in TeX
G:=Group("C4^2.240D14"); // GroupNames label
G:=SmallGroup(448,1178);
// by ID
G=gap.SmallGroup(448,1178);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,100,675,570,185,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=d^2=1,c^14=b^2,a*b=b*a,c*a*c^-1=d*a*d=a^-1,c*b*c^-1=d*b*d=b^-1,d*c*d=b^2*c^13>;
// generators/relations
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