metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic14⋊11D4, C42.167D14, C14.782+ (1+4), C4⋊1D4⋊7D7, C4.72(D4×D7), (C4×D28)⋊50C2, C28⋊5(C4○D4), C7⋊4(Q8⋊6D4), C28.67(C2×D4), C4⋊1(D4⋊2D7), C28⋊2D4⋊37C2, C28⋊D4⋊27C2, (D4×Dic7)⋊35C2, (C4×Dic14)⋊51C2, (C2×D4).115D14, Dic7.29(C2×D4), C14.96(C22×D4), Dic7⋊D4⋊37C2, (C2×C28).636C23, (C2×C14).262C24, (C4×C28).204C22, C2.82(D4⋊6D14), C23.68(C22×D7), D14⋊C4.149C22, (C2×D28).270C22, (D4×C14).214C22, C4⋊Dic7.381C22, (C22×C14).76C23, C22.283(C23×D7), C23.D7.73C22, Dic7⋊C4.164C22, (C2×Dic7).269C23, (C4×Dic7).155C22, (C22×D7).116C23, (C2×Dic14).301C22, (C22×Dic7).158C22, C2.69(C2×D4×D7), (C7×C4⋊1D4)⋊9C2, C14.97(C2×C4○D4), (C2×D4⋊2D7)⋊22C2, C2.61(C2×D4⋊2D7), (C2×C4×D7).139C22, (C2×C4).598(C22×D7), (C2×C7⋊D4).78C22, SmallGroup(448,1171)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1484 in 312 conjugacy classes, 107 normal (27 characteristic)
C1, C2 [×3], C2 [×6], C4 [×4], C4 [×9], C22, C22 [×18], C7, C2×C4 [×3], C2×C4 [×18], D4 [×24], Q8 [×4], C23 [×4], C23 [×2], D7 [×2], C14 [×3], C14 [×4], C42, C42 [×2], C22⋊C4 [×6], C4⋊C4 [×4], C22×C4 [×6], C2×D4 [×6], C2×D4 [×9], C2×Q8, C4○D4 [×8], Dic7 [×4], Dic7 [×4], C28 [×4], C28, D14 [×6], C2×C14, C2×C14 [×12], C4×D4 [×3], C4×Q8, C4⋊D4 [×6], C4⋊1D4, C4⋊1D4 [×2], C2×C4○D4 [×2], Dic14 [×4], C4×D7 [×4], D28 [×2], C2×Dic7 [×6], C2×Dic7 [×8], C7⋊D4 [×12], C2×C28 [×3], C7×D4 [×10], C22×D7 [×2], C22×C14 [×4], Q8⋊6D4, C4×Dic7 [×2], Dic7⋊C4 [×2], C4⋊Dic7 [×2], D14⋊C4 [×2], C23.D7 [×4], C4×C28, C2×Dic14, C2×C4×D7 [×2], C2×D28, D4⋊2D7 [×8], C22×Dic7 [×4], C2×C7⋊D4 [×8], D4×C14 [×6], C4×Dic14, C4×D28, D4×Dic7 [×2], C28⋊2D4 [×2], Dic7⋊D4 [×4], C28⋊D4 [×2], C7×C4⋊1D4, C2×D4⋊2D7 [×2], Dic14⋊11D4
Quotients:
C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D7, C2×D4 [×6], C4○D4 [×2], C24, D14 [×7], C22×D4, C2×C4○D4, 2+ (1+4), C22×D7 [×7], Q8⋊6D4, D4×D7 [×2], D4⋊2D7 [×2], C23×D7, C2×D4×D7, C2×D4⋊2D7, D4⋊6D14, Dic14⋊11D4
Generators and relations
G = < a,b,c,d | a28=c4=d2=1, b2=a14, bab-1=a-1, ac=ca, dad=a15, bc=cb, dbd=a14b, dcd=c-1 >
►On 224 points
Generators in S224
(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 50 15 36)(2 49 16 35)(3 48 17 34)(4 47 18 33)(5 46 19 32)(6 45 20 31)(7 44 21 30)(8 43 22 29)(9 42 23 56)(10 41 24 55)(11 40 25 54)(12 39 26 53)(13 38 27 52)(14 37 28 51)(57 112 71 98)(58 111 72 97)(59 110 73 96)(60 109 74 95)(61 108 75 94)(62 107 76 93)(63 106 77 92)(64 105 78 91)(65 104 79 90)(66 103 80 89)(67 102 81 88)(68 101 82 87)(69 100 83 86)(70 99 84 85)(113 204 127 218)(114 203 128 217)(115 202 129 216)(116 201 130 215)(117 200 131 214)(118 199 132 213)(119 198 133 212)(120 197 134 211)(121 224 135 210)(122 223 136 209)(123 222 137 208)(124 221 138 207)(125 220 139 206)(126 219 140 205)(141 196 155 182)(142 195 156 181)(143 194 157 180)(144 193 158 179)(145 192 159 178)(146 191 160 177)(147 190 161 176)(148 189 162 175)(149 188 163 174)(150 187 164 173)(151 186 165 172)(152 185 166 171)(153 184 167 170)(154 183 168 169)
(1 195 78 210)(2 196 79 211)(3 169 80 212)(4 170 81 213)(5 171 82 214)(6 172 83 215)(7 173 84 216)(8 174 57 217)(9 175 58 218)(10 176 59 219)(11 177 60 220)(12 178 61 221)(13 179 62 222)(14 180 63 223)(15 181 64 224)(16 182 65 197)(17 183 66 198)(18 184 67 199)(19 185 68 200)(20 186 69 201)(21 187 70 202)(22 188 71 203)(23 189 72 204)(24 190 73 205)(25 191 74 206)(26 192 75 207)(27 193 76 208)(28 194 77 209)(29 163 98 128)(30 164 99 129)(31 165 100 130)(32 166 101 131)(33 167 102 132)(34 168 103 133)(35 141 104 134)(36 142 105 135)(37 143 106 136)(38 144 107 137)(39 145 108 138)(40 146 109 139)(41 147 110 140)(42 148 111 113)(43 149 112 114)(44 150 85 115)(45 151 86 116)(46 152 87 117)(47 153 88 118)(48 154 89 119)(49 155 90 120)(50 156 91 121)(51 157 92 122)(52 158 93 123)(53 159 94 124)(54 160 95 125)(55 161 96 126)(56 162 97 127)
(1 91)(2 106)(3 93)(4 108)(5 95)(6 110)(7 97)(8 112)(9 99)(10 86)(11 101)(12 88)(13 103)(14 90)(15 105)(16 92)(17 107)(18 94)(19 109)(20 96)(21 111)(22 98)(23 85)(24 100)(25 87)(26 102)(27 89)(28 104)(29 71)(30 58)(31 73)(32 60)(33 75)(34 62)(35 77)(36 64)(37 79)(38 66)(39 81)(40 68)(41 83)(42 70)(43 57)(44 72)(45 59)(46 74)(47 61)(48 76)(49 63)(50 78)(51 65)(52 80)(53 67)(54 82)(55 69)(56 84)(113 202)(114 217)(115 204)(116 219)(117 206)(118 221)(119 208)(120 223)(121 210)(122 197)(123 212)(124 199)(125 214)(126 201)(127 216)(128 203)(129 218)(130 205)(131 220)(132 207)(133 222)(134 209)(135 224)(136 211)(137 198)(138 213)(139 200)(140 215)(141 194)(142 181)(143 196)(144 183)(145 170)(146 185)(147 172)(148 187)(149 174)(150 189)(151 176)(152 191)(153 178)(154 193)(155 180)(156 195)(157 182)(158 169)(159 184)(160 171)(161 186)(162 173)(163 188)(164 175)(165 190)(166 177)(167 192)(168 179)
G:=sub<Sym(224)| (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), (1,50,15,36)(2,49,16,35)(3,48,17,34)(4,47,18,33)(5,46,19,32)(6,45,20,31)(7,44,21,30)(8,43,22,29)(9,42,23,56)(10,41,24,55)(11,40,25,54)(12,39,26,53)(13,38,27,52)(14,37,28,51)(57,112,71,98)(58,111,72,97)(59,110,73,96)(60,109,74,95)(61,108,75,94)(62,107,76,93)(63,106,77,92)(64,105,78,91)(65,104,79,90)(66,103,80,89)(67,102,81,88)(68,101,82,87)(69,100,83,86)(70,99,84,85)(113,204,127,218)(114,203,128,217)(115,202,129,216)(116,201,130,215)(117,200,131,214)(118,199,132,213)(119,198,133,212)(120,197,134,211)(121,224,135,210)(122,223,136,209)(123,222,137,208)(124,221,138,207)(125,220,139,206)(126,219,140,205)(141,196,155,182)(142,195,156,181)(143,194,157,180)(144,193,158,179)(145,192,159,178)(146,191,160,177)(147,190,161,176)(148,189,162,175)(149,188,163,174)(150,187,164,173)(151,186,165,172)(152,185,166,171)(153,184,167,170)(154,183,168,169), (1,195,78,210)(2,196,79,211)(3,169,80,212)(4,170,81,213)(5,171,82,214)(6,172,83,215)(7,173,84,216)(8,174,57,217)(9,175,58,218)(10,176,59,219)(11,177,60,220)(12,178,61,221)(13,179,62,222)(14,180,63,223)(15,181,64,224)(16,182,65,197)(17,183,66,198)(18,184,67,199)(19,185,68,200)(20,186,69,201)(21,187,70,202)(22,188,71,203)(23,189,72,204)(24,190,73,205)(25,191,74,206)(26,192,75,207)(27,193,76,208)(28,194,77,209)(29,163,98,128)(30,164,99,129)(31,165,100,130)(32,166,101,131)(33,167,102,132)(34,168,103,133)(35,141,104,134)(36,142,105,135)(37,143,106,136)(38,144,107,137)(39,145,108,138)(40,146,109,139)(41,147,110,140)(42,148,111,113)(43,149,112,114)(44,150,85,115)(45,151,86,116)(46,152,87,117)(47,153,88,118)(48,154,89,119)(49,155,90,120)(50,156,91,121)(51,157,92,122)(52,158,93,123)(53,159,94,124)(54,160,95,125)(55,161,96,126)(56,162,97,127), (1,91)(2,106)(3,93)(4,108)(5,95)(6,110)(7,97)(8,112)(9,99)(10,86)(11,101)(12,88)(13,103)(14,90)(15,105)(16,92)(17,107)(18,94)(19,109)(20,96)(21,111)(22,98)(23,85)(24,100)(25,87)(26,102)(27,89)(28,104)(29,71)(30,58)(31,73)(32,60)(33,75)(34,62)(35,77)(36,64)(37,79)(38,66)(39,81)(40,68)(41,83)(42,70)(43,57)(44,72)(45,59)(46,74)(47,61)(48,76)(49,63)(50,78)(51,65)(52,80)(53,67)(54,82)(55,69)(56,84)(113,202)(114,217)(115,204)(116,219)(117,206)(118,221)(119,208)(120,223)(121,210)(122,197)(123,212)(124,199)(125,214)(126,201)(127,216)(128,203)(129,218)(130,205)(131,220)(132,207)(133,222)(134,209)(135,224)(136,211)(137,198)(138,213)(139,200)(140,215)(141,194)(142,181)(143,196)(144,183)(145,170)(146,185)(147,172)(148,187)(149,174)(150,189)(151,176)(152,191)(153,178)(154,193)(155,180)(156,195)(157,182)(158,169)(159,184)(160,171)(161,186)(162,173)(163,188)(164,175)(165,190)(166,177)(167,192)(168,179)>;
G:=Group( (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), (1,50,15,36)(2,49,16,35)(3,48,17,34)(4,47,18,33)(5,46,19,32)(6,45,20,31)(7,44,21,30)(8,43,22,29)(9,42,23,56)(10,41,24,55)(11,40,25,54)(12,39,26,53)(13,38,27,52)(14,37,28,51)(57,112,71,98)(58,111,72,97)(59,110,73,96)(60,109,74,95)(61,108,75,94)(62,107,76,93)(63,106,77,92)(64,105,78,91)(65,104,79,90)(66,103,80,89)(67,102,81,88)(68,101,82,87)(69,100,83,86)(70,99,84,85)(113,204,127,218)(114,203,128,217)(115,202,129,216)(116,201,130,215)(117,200,131,214)(118,199,132,213)(119,198,133,212)(120,197,134,211)(121,224,135,210)(122,223,136,209)(123,222,137,208)(124,221,138,207)(125,220,139,206)(126,219,140,205)(141,196,155,182)(142,195,156,181)(143,194,157,180)(144,193,158,179)(145,192,159,178)(146,191,160,177)(147,190,161,176)(148,189,162,175)(149,188,163,174)(150,187,164,173)(151,186,165,172)(152,185,166,171)(153,184,167,170)(154,183,168,169), (1,195,78,210)(2,196,79,211)(3,169,80,212)(4,170,81,213)(5,171,82,214)(6,172,83,215)(7,173,84,216)(8,174,57,217)(9,175,58,218)(10,176,59,219)(11,177,60,220)(12,178,61,221)(13,179,62,222)(14,180,63,223)(15,181,64,224)(16,182,65,197)(17,183,66,198)(18,184,67,199)(19,185,68,200)(20,186,69,201)(21,187,70,202)(22,188,71,203)(23,189,72,204)(24,190,73,205)(25,191,74,206)(26,192,75,207)(27,193,76,208)(28,194,77,209)(29,163,98,128)(30,164,99,129)(31,165,100,130)(32,166,101,131)(33,167,102,132)(34,168,103,133)(35,141,104,134)(36,142,105,135)(37,143,106,136)(38,144,107,137)(39,145,108,138)(40,146,109,139)(41,147,110,140)(42,148,111,113)(43,149,112,114)(44,150,85,115)(45,151,86,116)(46,152,87,117)(47,153,88,118)(48,154,89,119)(49,155,90,120)(50,156,91,121)(51,157,92,122)(52,158,93,123)(53,159,94,124)(54,160,95,125)(55,161,96,126)(56,162,97,127), (1,91)(2,106)(3,93)(4,108)(5,95)(6,110)(7,97)(8,112)(9,99)(10,86)(11,101)(12,88)(13,103)(14,90)(15,105)(16,92)(17,107)(18,94)(19,109)(20,96)(21,111)(22,98)(23,85)(24,100)(25,87)(26,102)(27,89)(28,104)(29,71)(30,58)(31,73)(32,60)(33,75)(34,62)(35,77)(36,64)(37,79)(38,66)(39,81)(40,68)(41,83)(42,70)(43,57)(44,72)(45,59)(46,74)(47,61)(48,76)(49,63)(50,78)(51,65)(52,80)(53,67)(54,82)(55,69)(56,84)(113,202)(114,217)(115,204)(116,219)(117,206)(118,221)(119,208)(120,223)(121,210)(122,197)(123,212)(124,199)(125,214)(126,201)(127,216)(128,203)(129,218)(130,205)(131,220)(132,207)(133,222)(134,209)(135,224)(136,211)(137,198)(138,213)(139,200)(140,215)(141,194)(142,181)(143,196)(144,183)(145,170)(146,185)(147,172)(148,187)(149,174)(150,189)(151,176)(152,191)(153,178)(154,193)(155,180)(156,195)(157,182)(158,169)(159,184)(160,171)(161,186)(162,173)(163,188)(164,175)(165,190)(166,177)(167,192)(168,179) );
G=PermutationGroup([(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)], [(1,50,15,36),(2,49,16,35),(3,48,17,34),(4,47,18,33),(5,46,19,32),(6,45,20,31),(7,44,21,30),(8,43,22,29),(9,42,23,56),(10,41,24,55),(11,40,25,54),(12,39,26,53),(13,38,27,52),(14,37,28,51),(57,112,71,98),(58,111,72,97),(59,110,73,96),(60,109,74,95),(61,108,75,94),(62,107,76,93),(63,106,77,92),(64,105,78,91),(65,104,79,90),(66,103,80,89),(67,102,81,88),(68,101,82,87),(69,100,83,86),(70,99,84,85),(113,204,127,218),(114,203,128,217),(115,202,129,216),(116,201,130,215),(117,200,131,214),(118,199,132,213),(119,198,133,212),(120,197,134,211),(121,224,135,210),(122,223,136,209),(123,222,137,208),(124,221,138,207),(125,220,139,206),(126,219,140,205),(141,196,155,182),(142,195,156,181),(143,194,157,180),(144,193,158,179),(145,192,159,178),(146,191,160,177),(147,190,161,176),(148,189,162,175),(149,188,163,174),(150,187,164,173),(151,186,165,172),(152,185,166,171),(153,184,167,170),(154,183,168,169)], [(1,195,78,210),(2,196,79,211),(3,169,80,212),(4,170,81,213),(5,171,82,214),(6,172,83,215),(7,173,84,216),(8,174,57,217),(9,175,58,218),(10,176,59,219),(11,177,60,220),(12,178,61,221),(13,179,62,222),(14,180,63,223),(15,181,64,224),(16,182,65,197),(17,183,66,198),(18,184,67,199),(19,185,68,200),(20,186,69,201),(21,187,70,202),(22,188,71,203),(23,189,72,204),(24,190,73,205),(25,191,74,206),(26,192,75,207),(27,193,76,208),(28,194,77,209),(29,163,98,128),(30,164,99,129),(31,165,100,130),(32,166,101,131),(33,167,102,132),(34,168,103,133),(35,141,104,134),(36,142,105,135),(37,143,106,136),(38,144,107,137),(39,145,108,138),(40,146,109,139),(41,147,110,140),(42,148,111,113),(43,149,112,114),(44,150,85,115),(45,151,86,116),(46,152,87,117),(47,153,88,118),(48,154,89,119),(49,155,90,120),(50,156,91,121),(51,157,92,122),(52,158,93,123),(53,159,94,124),(54,160,95,125),(55,161,96,126),(56,162,97,127)], [(1,91),(2,106),(3,93),(4,108),(5,95),(6,110),(7,97),(8,112),(9,99),(10,86),(11,101),(12,88),(13,103),(14,90),(15,105),(16,92),(17,107),(18,94),(19,109),(20,96),(21,111),(22,98),(23,85),(24,100),(25,87),(26,102),(27,89),(28,104),(29,71),(30,58),(31,73),(32,60),(33,75),(34,62),(35,77),(36,64),(37,79),(38,66),(39,81),(40,68),(41,83),(42,70),(43,57),(44,72),(45,59),(46,74),(47,61),(48,76),(49,63),(50,78),(51,65),(52,80),(53,67),(54,82),(55,69),(56,84),(113,202),(114,217),(115,204),(116,219),(117,206),(118,221),(119,208),(120,223),(121,210),(122,197),(123,212),(124,199),(125,214),(126,201),(127,216),(128,203),(129,218),(130,205),(131,220),(132,207),(133,222),(134,209),(135,224),(136,211),(137,198),(138,213),(139,200),(140,215),(141,194),(142,181),(143,196),(144,183),(145,170),(146,185),(147,172),(148,187),(149,174),(150,189),(151,176),(152,191),(153,178),(154,193),(155,180),(156,195),(157,182),(158,169),(159,184),(160,171),(161,186),(162,173),(163,188),(164,175),(165,190),(166,177),(167,192),(168,179)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 0 | 28 | 0 | 0 | 0 | 0 |
| 1 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 11 | 1 | 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 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 0 | 0 | 0 | 28 | 0 |
G:=sub<GL(6,GF(29))| [0,1,0,0,0,0,28,11,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,17,0,0,0,0,0,0,12],[28,11,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,1,0],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,0,28,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,28,0] >;
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | ··· | 4M | 4N | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28R |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 4 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 14 | ··· | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 |
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 | D4 | D7 | C4○D4 | D14 | D14 | 2+ (1+4) | D4×D7 | D4⋊2D7 | D4⋊6D14 |
| kernel | Dic14⋊11D4 | C4×Dic14 | C4×D28 | D4×Dic7 | C28⋊2D4 | Dic7⋊D4 | C28⋊D4 | C7×C4⋊1D4 | C2×D4⋊2D7 | Dic14 | C4⋊1D4 | C28 | C42 | C2×D4 | C14 | C4 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 4 | 2 | 1 | 2 | 4 | 3 | 4 | 3 | 18 | 1 | 6 | 6 | 6 |
In GAP, Magma, Sage, TeX
Dic_{14}\rtimes_{11}D_4 % in TeX
G:=Group("Dic14:11D4"); // GroupNames label
G:=SmallGroup(448,1171);
// by ID
G=gap.SmallGroup(448,1171);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,232,100,675,570,185,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=c^4=d^2=1,b^2=a^14,b*a*b^-1=a^-1,a*c=c*a,d*a*d=a^15,b*c=c*b,d*b*d=a^14*b,d*c*d=c^-1>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀