metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic14⋊24D4, C42.111D14, C14.1042+ (1+4), (C4×D4)⋊15D7, (D4×C28)⋊17C2, C4⋊1(C4○D28), C28⋊3(C4○D4), C28⋊D4⋊9C2, C7⋊1(Q8⋊6D4), C4.142(D4×D7), D14⋊D4⋊8C2, C4⋊D28⋊12C2, C28⋊7D4⋊19C2, C4⋊C4.317D14, C28.348(C2×D4), D28⋊C4⋊15C2, (C4×Dic14)⋊32C2, (C2×D4).216D14, (C2×C14).97C24, Dic7.18(C2×D4), C14.52(C22×D4), (C2×C28).785C23, (C4×C28).154C22, D14⋊C4.54C22, C22⋊C4.112D14, (C22×C4).210D14, C2.16(D4⋊8D14), C23.97(C22×D7), (D4×C14).258C22, (C2×D28).138C22, C4⋊Dic7.299C22, (C4×Dic7).75C22, (C22×D7).32C23, C22.122(C23×D7), Dic7⋊C4.111C22, (C22×C28).109C22, (C22×C14).167C23, (C2×Dic7).205C23, (C2×Dic14).316C22, C2.25(C2×D4×D7), (C2×C4○D28)⋊10C2, C2.48(C2×C4○D28), C14.44(C2×C4○D4), (C2×C4×D7).200C22, (C7×C4⋊C4).328C22, (C2×C4).580(C22×D7), (C2×C7⋊D4).14C22, (C7×C22⋊C4).124C22, SmallGroup(448,1006)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1652 in 312 conjugacy classes, 107 normal (29 characteristic)
C1, C2 [×3], C2 [×6], C4 [×4], C4 [×9], C22, C22 [×18], C7, C2×C4 [×3], C2×C4 [×2], C2×C4 [×16], D4 [×24], Q8 [×4], C23 [×2], C23 [×4], D7 [×4], C14 [×3], C14 [×2], C42, C42 [×2], C22⋊C4 [×2], C22⋊C4 [×4], C4⋊C4, C4⋊C4 [×3], C22×C4 [×2], C22×C4 [×4], C2×D4, C2×D4 [×14], C2×Q8, C4○D4 [×8], Dic7 [×4], Dic7 [×2], C28 [×4], C28 [×3], D14 [×12], C2×C14, C2×C14 [×6], C4×D4, C4×D4 [×2], C4×Q8, C4⋊D4 [×6], C4⋊1D4 [×3], C2×C4○D4 [×2], Dic14 [×4], C4×D7 [×8], D28 [×10], C2×Dic7 [×4], C7⋊D4 [×12], C2×C28 [×3], C2×C28 [×2], C2×C28 [×4], C7×D4 [×2], C22×D7 [×4], C22×C14 [×2], Q8⋊6D4, C4×Dic7 [×2], Dic7⋊C4 [×2], C4⋊Dic7, D14⋊C4 [×4], C4×C28, C7×C22⋊C4 [×2], C7×C4⋊C4, C2×Dic14, C2×C4×D7 [×4], C2×D28 [×6], C4○D28 [×8], C2×C7⋊D4 [×8], C22×C28 [×2], D4×C14, C4×Dic14, C4⋊D28, D14⋊D4 [×4], D28⋊C4 [×2], C28⋊7D4 [×2], C28⋊D4 [×2], D4×C28, C2×C4○D28 [×2], Dic14⋊24D4
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, C4○D28 [×2], D4×D7 [×2], C23×D7, C2×C4○D28, C2×D4×D7, D4⋊8D14, Dic14⋊24D4
Generators and relations
G = < a,b,c,d | a28=c4=d2=1, b2=a14, bab-1=a-1, ac=ca, ad=da, 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 36 15 50)(2 35 16 49)(3 34 17 48)(4 33 18 47)(5 32 19 46)(6 31 20 45)(7 30 21 44)(8 29 22 43)(9 56 23 42)(10 55 24 41)(11 54 25 40)(12 53 26 39)(13 52 27 38)(14 51 28 37)(57 117 71 131)(58 116 72 130)(59 115 73 129)(60 114 74 128)(61 113 75 127)(62 140 76 126)(63 139 77 125)(64 138 78 124)(65 137 79 123)(66 136 80 122)(67 135 81 121)(68 134 82 120)(69 133 83 119)(70 132 84 118)(85 171 99 185)(86 170 100 184)(87 169 101 183)(88 196 102 182)(89 195 103 181)(90 194 104 180)(91 193 105 179)(92 192 106 178)(93 191 107 177)(94 190 108 176)(95 189 109 175)(96 188 110 174)(97 187 111 173)(98 186 112 172)(141 217 155 203)(142 216 156 202)(143 215 157 201)(144 214 158 200)(145 213 159 199)(146 212 160 198)(147 211 161 197)(148 210 162 224)(149 209 163 223)(150 208 164 222)(151 207 165 221)(152 206 166 220)(153 205 167 219)(154 204 168 218)
(1 135 196 216)(2 136 169 217)(3 137 170 218)(4 138 171 219)(5 139 172 220)(6 140 173 221)(7 113 174 222)(8 114 175 223)(9 115 176 224)(10 116 177 197)(11 117 178 198)(12 118 179 199)(13 119 180 200)(14 120 181 201)(15 121 182 202)(16 122 183 203)(17 123 184 204)(18 124 185 205)(19 125 186 206)(20 126 187 207)(21 127 188 208)(22 128 189 209)(23 129 190 210)(24 130 191 211)(25 131 192 212)(26 132 193 213)(27 133 194 214)(28 134 195 215)(29 74 95 149)(30 75 96 150)(31 76 97 151)(32 77 98 152)(33 78 99 153)(34 79 100 154)(35 80 101 155)(36 81 102 156)(37 82 103 157)(38 83 104 158)(39 84 105 159)(40 57 106 160)(41 58 107 161)(42 59 108 162)(43 60 109 163)(44 61 110 164)(45 62 111 165)(46 63 112 166)(47 64 85 167)(48 65 86 168)(49 66 87 141)(50 67 88 142)(51 68 89 143)(52 69 90 144)(53 70 91 145)(54 71 92 146)(55 72 93 147)(56 73 94 148)
(1 102)(2 103)(3 104)(4 105)(5 106)(6 107)(7 108)(8 109)(9 110)(10 111)(11 112)(12 85)(13 86)(14 87)(15 88)(16 89)(17 90)(18 91)(19 92)(20 93)(21 94)(22 95)(23 96)(24 97)(25 98)(26 99)(27 100)(28 101)(29 189)(30 190)(31 191)(32 192)(33 193)(34 194)(35 195)(36 196)(37 169)(38 170)(39 171)(40 172)(41 173)(42 174)(43 175)(44 176)(45 177)(46 178)(47 179)(48 180)(49 181)(50 182)(51 183)(52 184)(53 185)(54 186)(55 187)(56 188)(57 139)(58 140)(59 113)(60 114)(61 115)(62 116)(63 117)(64 118)(65 119)(66 120)(67 121)(68 122)(69 123)(70 124)(71 125)(72 126)(73 127)(74 128)(75 129)(76 130)(77 131)(78 132)(79 133)(80 134)(81 135)(82 136)(83 137)(84 138)(141 201)(142 202)(143 203)(144 204)(145 205)(146 206)(147 207)(148 208)(149 209)(150 210)(151 211)(152 212)(153 213)(154 214)(155 215)(156 216)(157 217)(158 218)(159 219)(160 220)(161 221)(162 222)(163 223)(164 224)(165 197)(166 198)(167 199)(168 200)
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), (1,36,15,50)(2,35,16,49)(3,34,17,48)(4,33,18,47)(5,32,19,46)(6,31,20,45)(7,30,21,44)(8,29,22,43)(9,56,23,42)(10,55,24,41)(11,54,25,40)(12,53,26,39)(13,52,27,38)(14,51,28,37)(57,117,71,131)(58,116,72,130)(59,115,73,129)(60,114,74,128)(61,113,75,127)(62,140,76,126)(63,139,77,125)(64,138,78,124)(65,137,79,123)(66,136,80,122)(67,135,81,121)(68,134,82,120)(69,133,83,119)(70,132,84,118)(85,171,99,185)(86,170,100,184)(87,169,101,183)(88,196,102,182)(89,195,103,181)(90,194,104,180)(91,193,105,179)(92,192,106,178)(93,191,107,177)(94,190,108,176)(95,189,109,175)(96,188,110,174)(97,187,111,173)(98,186,112,172)(141,217,155,203)(142,216,156,202)(143,215,157,201)(144,214,158,200)(145,213,159,199)(146,212,160,198)(147,211,161,197)(148,210,162,224)(149,209,163,223)(150,208,164,222)(151,207,165,221)(152,206,166,220)(153,205,167,219)(154,204,168,218), (1,135,196,216)(2,136,169,217)(3,137,170,218)(4,138,171,219)(5,139,172,220)(6,140,173,221)(7,113,174,222)(8,114,175,223)(9,115,176,224)(10,116,177,197)(11,117,178,198)(12,118,179,199)(13,119,180,200)(14,120,181,201)(15,121,182,202)(16,122,183,203)(17,123,184,204)(18,124,185,205)(19,125,186,206)(20,126,187,207)(21,127,188,208)(22,128,189,209)(23,129,190,210)(24,130,191,211)(25,131,192,212)(26,132,193,213)(27,133,194,214)(28,134,195,215)(29,74,95,149)(30,75,96,150)(31,76,97,151)(32,77,98,152)(33,78,99,153)(34,79,100,154)(35,80,101,155)(36,81,102,156)(37,82,103,157)(38,83,104,158)(39,84,105,159)(40,57,106,160)(41,58,107,161)(42,59,108,162)(43,60,109,163)(44,61,110,164)(45,62,111,165)(46,63,112,166)(47,64,85,167)(48,65,86,168)(49,66,87,141)(50,67,88,142)(51,68,89,143)(52,69,90,144)(53,70,91,145)(54,71,92,146)(55,72,93,147)(56,73,94,148), (1,102)(2,103)(3,104)(4,105)(5,106)(6,107)(7,108)(8,109)(9,110)(10,111)(11,112)(12,85)(13,86)(14,87)(15,88)(16,89)(17,90)(18,91)(19,92)(20,93)(21,94)(22,95)(23,96)(24,97)(25,98)(26,99)(27,100)(28,101)(29,189)(30,190)(31,191)(32,192)(33,193)(34,194)(35,195)(36,196)(37,169)(38,170)(39,171)(40,172)(41,173)(42,174)(43,175)(44,176)(45,177)(46,178)(47,179)(48,180)(49,181)(50,182)(51,183)(52,184)(53,185)(54,186)(55,187)(56,188)(57,139)(58,140)(59,113)(60,114)(61,115)(62,116)(63,117)(64,118)(65,119)(66,120)(67,121)(68,122)(69,123)(70,124)(71,125)(72,126)(73,127)(74,128)(75,129)(76,130)(77,131)(78,132)(79,133)(80,134)(81,135)(82,136)(83,137)(84,138)(141,201)(142,202)(143,203)(144,204)(145,205)(146,206)(147,207)(148,208)(149,209)(150,210)(151,211)(152,212)(153,213)(154,214)(155,215)(156,216)(157,217)(158,218)(159,219)(160,220)(161,221)(162,222)(163,223)(164,224)(165,197)(166,198)(167,199)(168,200)>;
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), (1,36,15,50)(2,35,16,49)(3,34,17,48)(4,33,18,47)(5,32,19,46)(6,31,20,45)(7,30,21,44)(8,29,22,43)(9,56,23,42)(10,55,24,41)(11,54,25,40)(12,53,26,39)(13,52,27,38)(14,51,28,37)(57,117,71,131)(58,116,72,130)(59,115,73,129)(60,114,74,128)(61,113,75,127)(62,140,76,126)(63,139,77,125)(64,138,78,124)(65,137,79,123)(66,136,80,122)(67,135,81,121)(68,134,82,120)(69,133,83,119)(70,132,84,118)(85,171,99,185)(86,170,100,184)(87,169,101,183)(88,196,102,182)(89,195,103,181)(90,194,104,180)(91,193,105,179)(92,192,106,178)(93,191,107,177)(94,190,108,176)(95,189,109,175)(96,188,110,174)(97,187,111,173)(98,186,112,172)(141,217,155,203)(142,216,156,202)(143,215,157,201)(144,214,158,200)(145,213,159,199)(146,212,160,198)(147,211,161,197)(148,210,162,224)(149,209,163,223)(150,208,164,222)(151,207,165,221)(152,206,166,220)(153,205,167,219)(154,204,168,218), (1,135,196,216)(2,136,169,217)(3,137,170,218)(4,138,171,219)(5,139,172,220)(6,140,173,221)(7,113,174,222)(8,114,175,223)(9,115,176,224)(10,116,177,197)(11,117,178,198)(12,118,179,199)(13,119,180,200)(14,120,181,201)(15,121,182,202)(16,122,183,203)(17,123,184,204)(18,124,185,205)(19,125,186,206)(20,126,187,207)(21,127,188,208)(22,128,189,209)(23,129,190,210)(24,130,191,211)(25,131,192,212)(26,132,193,213)(27,133,194,214)(28,134,195,215)(29,74,95,149)(30,75,96,150)(31,76,97,151)(32,77,98,152)(33,78,99,153)(34,79,100,154)(35,80,101,155)(36,81,102,156)(37,82,103,157)(38,83,104,158)(39,84,105,159)(40,57,106,160)(41,58,107,161)(42,59,108,162)(43,60,109,163)(44,61,110,164)(45,62,111,165)(46,63,112,166)(47,64,85,167)(48,65,86,168)(49,66,87,141)(50,67,88,142)(51,68,89,143)(52,69,90,144)(53,70,91,145)(54,71,92,146)(55,72,93,147)(56,73,94,148), (1,102)(2,103)(3,104)(4,105)(5,106)(6,107)(7,108)(8,109)(9,110)(10,111)(11,112)(12,85)(13,86)(14,87)(15,88)(16,89)(17,90)(18,91)(19,92)(20,93)(21,94)(22,95)(23,96)(24,97)(25,98)(26,99)(27,100)(28,101)(29,189)(30,190)(31,191)(32,192)(33,193)(34,194)(35,195)(36,196)(37,169)(38,170)(39,171)(40,172)(41,173)(42,174)(43,175)(44,176)(45,177)(46,178)(47,179)(48,180)(49,181)(50,182)(51,183)(52,184)(53,185)(54,186)(55,187)(56,188)(57,139)(58,140)(59,113)(60,114)(61,115)(62,116)(63,117)(64,118)(65,119)(66,120)(67,121)(68,122)(69,123)(70,124)(71,125)(72,126)(73,127)(74,128)(75,129)(76,130)(77,131)(78,132)(79,133)(80,134)(81,135)(82,136)(83,137)(84,138)(141,201)(142,202)(143,203)(144,204)(145,205)(146,206)(147,207)(148,208)(149,209)(150,210)(151,211)(152,212)(153,213)(154,214)(155,215)(156,216)(157,217)(158,218)(159,219)(160,220)(161,221)(162,222)(163,223)(164,224)(165,197)(166,198)(167,199)(168,200) );
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)], [(1,36,15,50),(2,35,16,49),(3,34,17,48),(4,33,18,47),(5,32,19,46),(6,31,20,45),(7,30,21,44),(8,29,22,43),(9,56,23,42),(10,55,24,41),(11,54,25,40),(12,53,26,39),(13,52,27,38),(14,51,28,37),(57,117,71,131),(58,116,72,130),(59,115,73,129),(60,114,74,128),(61,113,75,127),(62,140,76,126),(63,139,77,125),(64,138,78,124),(65,137,79,123),(66,136,80,122),(67,135,81,121),(68,134,82,120),(69,133,83,119),(70,132,84,118),(85,171,99,185),(86,170,100,184),(87,169,101,183),(88,196,102,182),(89,195,103,181),(90,194,104,180),(91,193,105,179),(92,192,106,178),(93,191,107,177),(94,190,108,176),(95,189,109,175),(96,188,110,174),(97,187,111,173),(98,186,112,172),(141,217,155,203),(142,216,156,202),(143,215,157,201),(144,214,158,200),(145,213,159,199),(146,212,160,198),(147,211,161,197),(148,210,162,224),(149,209,163,223),(150,208,164,222),(151,207,165,221),(152,206,166,220),(153,205,167,219),(154,204,168,218)], [(1,135,196,216),(2,136,169,217),(3,137,170,218),(4,138,171,219),(5,139,172,220),(6,140,173,221),(7,113,174,222),(8,114,175,223),(9,115,176,224),(10,116,177,197),(11,117,178,198),(12,118,179,199),(13,119,180,200),(14,120,181,201),(15,121,182,202),(16,122,183,203),(17,123,184,204),(18,124,185,205),(19,125,186,206),(20,126,187,207),(21,127,188,208),(22,128,189,209),(23,129,190,210),(24,130,191,211),(25,131,192,212),(26,132,193,213),(27,133,194,214),(28,134,195,215),(29,74,95,149),(30,75,96,150),(31,76,97,151),(32,77,98,152),(33,78,99,153),(34,79,100,154),(35,80,101,155),(36,81,102,156),(37,82,103,157),(38,83,104,158),(39,84,105,159),(40,57,106,160),(41,58,107,161),(42,59,108,162),(43,60,109,163),(44,61,110,164),(45,62,111,165),(46,63,112,166),(47,64,85,167),(48,65,86,168),(49,66,87,141),(50,67,88,142),(51,68,89,143),(52,69,90,144),(53,70,91,145),(54,71,92,146),(55,72,93,147),(56,73,94,148)], [(1,102),(2,103),(3,104),(4,105),(5,106),(6,107),(7,108),(8,109),(9,110),(10,111),(11,112),(12,85),(13,86),(14,87),(15,88),(16,89),(17,90),(18,91),(19,92),(20,93),(21,94),(22,95),(23,96),(24,97),(25,98),(26,99),(27,100),(28,101),(29,189),(30,190),(31,191),(32,192),(33,193),(34,194),(35,195),(36,196),(37,169),(38,170),(39,171),(40,172),(41,173),(42,174),(43,175),(44,176),(45,177),(46,178),(47,179),(48,180),(49,181),(50,182),(51,183),(52,184),(53,185),(54,186),(55,187),(56,188),(57,139),(58,140),(59,113),(60,114),(61,115),(62,116),(63,117),(64,118),(65,119),(66,120),(67,121),(68,122),(69,123),(70,124),(71,125),(72,126),(73,127),(74,128),(75,129),(76,130),(77,131),(78,132),(79,133),(80,134),(81,135),(82,136),(83,137),(84,138),(141,201),(142,202),(143,203),(144,204),(145,205),(146,206),(147,207),(148,208),(149,209),(150,210),(151,211),(152,212),(153,213),(154,214),(155,215),(156,216),(157,217),(158,218),(159,219),(160,220),(161,221),(162,222),(163,223),(164,224),(165,197),(166,198),(167,199),(168,200)])
Matrix representation ►G ⊆ GL4(𝔽29) generated by
| 17 | 21 | 0 | 0 |
| 14 | 2 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 28 |
| 13 | 21 | 0 | 0 |
| 14 | 16 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 28 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 28 |
| 0 | 0 | 1 | 0 |
| 24 | 15 | 0 | 0 |
| 10 | 5 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 28 |
G:=sub<GL(4,GF(29))| [17,14,0,0,21,2,0,0,0,0,28,0,0,0,0,28],[13,14,0,0,21,16,0,0,0,0,28,0,0,0,0,28],[1,0,0,0,0,1,0,0,0,0,0,1,0,0,28,0],[24,10,0,0,15,5,0,0,0,0,1,0,0,0,0,28] >;
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| 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 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | D14 | D14 | C4○D28 | 2+ (1+4) | D4×D7 | D4⋊8D14 |
| kernel | Dic14⋊24D4 | C4×Dic14 | C4⋊D28 | D14⋊D4 | D28⋊C4 | C28⋊7D4 | C28⋊D4 | D4×C28 | C2×C4○D28 | Dic14 | C4×D4 | C28 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C4 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 4 | 2 | 2 | 2 | 1 | 2 | 4 | 3 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 1 | 6 | 6 |
In GAP, Magma, Sage, TeX
Dic_{14}\rtimes_{24}D_4 % in TeX
G:=Group("Dic14:24D4"); // GroupNames label
G:=SmallGroup(448,1006);
// by ID
G=gap.SmallGroup(448,1006);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,232,387,100,675,570,18822]);
// 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,a*d=d*a,b*c=c*b,d*b*d=a^14*b,d*c*d=c^-1>;
// generators/relations
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