metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic14⋊10D4, C42.142D14, C14.912- (1+4), C4.71(D4×D7), (C4×D28)⋊44C2, C7⋊5(Q8⋊5D4), C28.64(C2×D4), C28⋊2D4⋊34C2, C4.4D4⋊11D7, D14⋊15(C4○D4), D14⋊D4⋊41C2, D14⋊3Q8⋊29C2, (C4×Dic14)⋊45C2, (C2×D4).174D14, (C2×C28).81C23, (C2×Q8).137D14, C22⋊C4.73D14, Dic7.28(C2×D4), C14.91(C22×D4), Dic7⋊4D4⋊30C2, (C2×C14).221C24, (C4×C28).186C22, C23.43(C22×D7), D14⋊C4.135C22, Dic7.D4⋊40C2, C22⋊Dic14⋊41C2, (D4×C14).156C22, (C2×D28).223C22, C4⋊Dic7.377C22, (C22×C14).51C23, (Q8×C14).127C22, C22.242(C23×D7), C23.D7.55C22, Dic7⋊C4.121C22, (C2×Dic7).253C23, (C4×Dic7).214C22, (C22×D7).216C23, C2.52(D4.10D14), (C2×Dic14).297C22, (C22×Dic7).143C22, (C2×Q8×D7)⋊11C2, C2.64(C2×D4×D7), C2.77(D7×C4○D4), (C2×D4⋊2D7)⋊19C2, C14.188(C2×C4○D4), (C7×C4.4D4)⋊13C2, (C2×C4×D7).121C22, (C2×C4).196(C22×D7), (C2×C7⋊D4).60C22, (C7×C22⋊C4).65C22, SmallGroup(448,1130)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1356 in 290 conjugacy classes, 105 normal (43 characteristic)
C1, C2 [×3], C2 [×5], C4 [×2], C4 [×12], C22, C22 [×13], C7, C2×C4 [×3], C2×C4 [×2], C2×C4 [×18], D4 [×12], Q8 [×10], C23 [×2], C23 [×2], D7 [×3], C14 [×3], C14 [×2], C42, C42 [×2], C22⋊C4 [×4], C22⋊C4 [×6], C4⋊C4 [×6], C22×C4 [×6], C2×D4, C2×D4 [×5], C2×Q8, C2×Q8 [×7], C4○D4 [×4], Dic7 [×4], Dic7 [×4], C28 [×2], C28 [×4], D14 [×2], D14 [×5], C2×C14, C2×C14 [×6], C4×D4 [×3], C4×Q8, C4⋊D4 [×3], C22⋊Q8 [×3], C4.4D4, C4.4D4 [×2], C22×Q8, C2×C4○D4, Dic14 [×4], Dic14 [×4], C4×D7 [×8], D28 [×2], C2×Dic7 [×2], C2×Dic7 [×4], C2×Dic7 [×4], C7⋊D4 [×8], C2×C28 [×3], C2×C28 [×2], C7×D4 [×2], C7×Q8 [×2], C22×D7 [×2], C22×C14 [×2], Q8⋊5D4, C4×Dic7 [×2], Dic7⋊C4 [×4], C4⋊Dic7 [×2], D14⋊C4 [×2], D14⋊C4 [×2], C23.D7 [×2], C4×C28, C7×C22⋊C4 [×4], C2×Dic14, C2×Dic14 [×2], C2×C4×D7 [×2], C2×C4×D7 [×2], C2×D28, D4⋊2D7 [×4], Q8×D7 [×4], C22×Dic7 [×2], C2×C7⋊D4 [×4], D4×C14, Q8×C14, C4×Dic14, C4×D28, C22⋊Dic14 [×2], Dic7⋊4D4 [×2], D14⋊D4 [×2], Dic7.D4 [×2], C28⋊2D4, D14⋊3Q8, C7×C4.4D4, C2×D4⋊2D7, C2×Q8×D7, Dic14⋊10D4
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⋊5D4, D4×D7 [×2], C23×D7, C2×D4×D7, D7×C4○D4, D4.10D14, Dic14⋊10D4
Generators and relations
G = < a,b,c,d | a28=c4=d2=1, b2=a14, bab-1=a-1, ac=ca, dad=a13, cbc-1=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)
(1 128 15 114)(2 127 16 113)(3 126 17 140)(4 125 18 139)(5 124 19 138)(6 123 20 137)(7 122 21 136)(8 121 22 135)(9 120 23 134)(10 119 24 133)(11 118 25 132)(12 117 26 131)(13 116 27 130)(14 115 28 129)(29 106 43 92)(30 105 44 91)(31 104 45 90)(32 103 46 89)(33 102 47 88)(34 101 48 87)(35 100 49 86)(36 99 50 85)(37 98 51 112)(38 97 52 111)(39 96 53 110)(40 95 54 109)(41 94 55 108)(42 93 56 107)(57 210 71 224)(58 209 72 223)(59 208 73 222)(60 207 74 221)(61 206 75 220)(62 205 76 219)(63 204 77 218)(64 203 78 217)(65 202 79 216)(66 201 80 215)(67 200 81 214)(68 199 82 213)(69 198 83 212)(70 197 84 211)(141 170 155 184)(142 169 156 183)(143 196 157 182)(144 195 158 181)(145 194 159 180)(146 193 160 179)(147 192 161 178)(148 191 162 177)(149 190 163 176)(150 189 164 175)(151 188 165 174)(152 187 166 173)(153 186 167 172)(154 185 168 171)
(1 98 207 167)(2 99 208 168)(3 100 209 141)(4 101 210 142)(5 102 211 143)(6 103 212 144)(7 104 213 145)(8 105 214 146)(9 106 215 147)(10 107 216 148)(11 108 217 149)(12 109 218 150)(13 110 219 151)(14 111 220 152)(15 112 221 153)(16 85 222 154)(17 86 223 155)(18 87 224 156)(19 88 197 157)(20 89 198 158)(21 90 199 159)(22 91 200 160)(23 92 201 161)(24 93 202 162)(25 94 203 163)(26 95 204 164)(27 96 205 165)(28 97 206 166)(29 66 178 120)(30 67 179 121)(31 68 180 122)(32 69 181 123)(33 70 182 124)(34 71 183 125)(35 72 184 126)(36 73 185 127)(37 74 186 128)(38 75 187 129)(39 76 188 130)(40 77 189 131)(41 78 190 132)(42 79 191 133)(43 80 192 134)(44 81 193 135)(45 82 194 136)(46 83 195 137)(47 84 196 138)(48 57 169 139)(49 58 170 140)(50 59 171 113)(51 60 172 114)(52 61 173 115)(53 62 174 116)(54 63 175 117)(55 64 176 118)(56 65 177 119)
(1 112)(2 97)(3 110)(4 95)(5 108)(6 93)(7 106)(8 91)(9 104)(10 89)(11 102)(12 87)(13 100)(14 85)(15 98)(16 111)(17 96)(18 109)(19 94)(20 107)(21 92)(22 105)(23 90)(24 103)(25 88)(26 101)(27 86)(28 99)(29 122)(30 135)(31 120)(32 133)(33 118)(34 131)(35 116)(36 129)(37 114)(38 127)(39 140)(40 125)(41 138)(42 123)(43 136)(44 121)(45 134)(46 119)(47 132)(48 117)(49 130)(50 115)(51 128)(52 113)(53 126)(54 139)(55 124)(56 137)(57 175)(58 188)(59 173)(60 186)(61 171)(62 184)(63 169)(64 182)(65 195)(66 180)(67 193)(68 178)(69 191)(70 176)(71 189)(72 174)(73 187)(74 172)(75 185)(76 170)(77 183)(78 196)(79 181)(80 194)(81 179)(82 192)(83 177)(84 190)(141 219)(142 204)(143 217)(144 202)(145 215)(146 200)(147 213)(148 198)(149 211)(150 224)(151 209)(152 222)(153 207)(154 220)(155 205)(156 218)(157 203)(158 216)(159 201)(160 214)(161 199)(162 212)(163 197)(164 210)(165 223)(166 208)(167 221)(168 206)
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), (1,128,15,114)(2,127,16,113)(3,126,17,140)(4,125,18,139)(5,124,19,138)(6,123,20,137)(7,122,21,136)(8,121,22,135)(9,120,23,134)(10,119,24,133)(11,118,25,132)(12,117,26,131)(13,116,27,130)(14,115,28,129)(29,106,43,92)(30,105,44,91)(31,104,45,90)(32,103,46,89)(33,102,47,88)(34,101,48,87)(35,100,49,86)(36,99,50,85)(37,98,51,112)(38,97,52,111)(39,96,53,110)(40,95,54,109)(41,94,55,108)(42,93,56,107)(57,210,71,224)(58,209,72,223)(59,208,73,222)(60,207,74,221)(61,206,75,220)(62,205,76,219)(63,204,77,218)(64,203,78,217)(65,202,79,216)(66,201,80,215)(67,200,81,214)(68,199,82,213)(69,198,83,212)(70,197,84,211)(141,170,155,184)(142,169,156,183)(143,196,157,182)(144,195,158,181)(145,194,159,180)(146,193,160,179)(147,192,161,178)(148,191,162,177)(149,190,163,176)(150,189,164,175)(151,188,165,174)(152,187,166,173)(153,186,167,172)(154,185,168,171), (1,98,207,167)(2,99,208,168)(3,100,209,141)(4,101,210,142)(5,102,211,143)(6,103,212,144)(7,104,213,145)(8,105,214,146)(9,106,215,147)(10,107,216,148)(11,108,217,149)(12,109,218,150)(13,110,219,151)(14,111,220,152)(15,112,221,153)(16,85,222,154)(17,86,223,155)(18,87,224,156)(19,88,197,157)(20,89,198,158)(21,90,199,159)(22,91,200,160)(23,92,201,161)(24,93,202,162)(25,94,203,163)(26,95,204,164)(27,96,205,165)(28,97,206,166)(29,66,178,120)(30,67,179,121)(31,68,180,122)(32,69,181,123)(33,70,182,124)(34,71,183,125)(35,72,184,126)(36,73,185,127)(37,74,186,128)(38,75,187,129)(39,76,188,130)(40,77,189,131)(41,78,190,132)(42,79,191,133)(43,80,192,134)(44,81,193,135)(45,82,194,136)(46,83,195,137)(47,84,196,138)(48,57,169,139)(49,58,170,140)(50,59,171,113)(51,60,172,114)(52,61,173,115)(53,62,174,116)(54,63,175,117)(55,64,176,118)(56,65,177,119), (1,112)(2,97)(3,110)(4,95)(5,108)(6,93)(7,106)(8,91)(9,104)(10,89)(11,102)(12,87)(13,100)(14,85)(15,98)(16,111)(17,96)(18,109)(19,94)(20,107)(21,92)(22,105)(23,90)(24,103)(25,88)(26,101)(27,86)(28,99)(29,122)(30,135)(31,120)(32,133)(33,118)(34,131)(35,116)(36,129)(37,114)(38,127)(39,140)(40,125)(41,138)(42,123)(43,136)(44,121)(45,134)(46,119)(47,132)(48,117)(49,130)(50,115)(51,128)(52,113)(53,126)(54,139)(55,124)(56,137)(57,175)(58,188)(59,173)(60,186)(61,171)(62,184)(63,169)(64,182)(65,195)(66,180)(67,193)(68,178)(69,191)(70,176)(71,189)(72,174)(73,187)(74,172)(75,185)(76,170)(77,183)(78,196)(79,181)(80,194)(81,179)(82,192)(83,177)(84,190)(141,219)(142,204)(143,217)(144,202)(145,215)(146,200)(147,213)(148,198)(149,211)(150,224)(151,209)(152,222)(153,207)(154,220)(155,205)(156,218)(157,203)(158,216)(159,201)(160,214)(161,199)(162,212)(163,197)(164,210)(165,223)(166,208)(167,221)(168,206)>;
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), (1,128,15,114)(2,127,16,113)(3,126,17,140)(4,125,18,139)(5,124,19,138)(6,123,20,137)(7,122,21,136)(8,121,22,135)(9,120,23,134)(10,119,24,133)(11,118,25,132)(12,117,26,131)(13,116,27,130)(14,115,28,129)(29,106,43,92)(30,105,44,91)(31,104,45,90)(32,103,46,89)(33,102,47,88)(34,101,48,87)(35,100,49,86)(36,99,50,85)(37,98,51,112)(38,97,52,111)(39,96,53,110)(40,95,54,109)(41,94,55,108)(42,93,56,107)(57,210,71,224)(58,209,72,223)(59,208,73,222)(60,207,74,221)(61,206,75,220)(62,205,76,219)(63,204,77,218)(64,203,78,217)(65,202,79,216)(66,201,80,215)(67,200,81,214)(68,199,82,213)(69,198,83,212)(70,197,84,211)(141,170,155,184)(142,169,156,183)(143,196,157,182)(144,195,158,181)(145,194,159,180)(146,193,160,179)(147,192,161,178)(148,191,162,177)(149,190,163,176)(150,189,164,175)(151,188,165,174)(152,187,166,173)(153,186,167,172)(154,185,168,171), (1,98,207,167)(2,99,208,168)(3,100,209,141)(4,101,210,142)(5,102,211,143)(6,103,212,144)(7,104,213,145)(8,105,214,146)(9,106,215,147)(10,107,216,148)(11,108,217,149)(12,109,218,150)(13,110,219,151)(14,111,220,152)(15,112,221,153)(16,85,222,154)(17,86,223,155)(18,87,224,156)(19,88,197,157)(20,89,198,158)(21,90,199,159)(22,91,200,160)(23,92,201,161)(24,93,202,162)(25,94,203,163)(26,95,204,164)(27,96,205,165)(28,97,206,166)(29,66,178,120)(30,67,179,121)(31,68,180,122)(32,69,181,123)(33,70,182,124)(34,71,183,125)(35,72,184,126)(36,73,185,127)(37,74,186,128)(38,75,187,129)(39,76,188,130)(40,77,189,131)(41,78,190,132)(42,79,191,133)(43,80,192,134)(44,81,193,135)(45,82,194,136)(46,83,195,137)(47,84,196,138)(48,57,169,139)(49,58,170,140)(50,59,171,113)(51,60,172,114)(52,61,173,115)(53,62,174,116)(54,63,175,117)(55,64,176,118)(56,65,177,119), (1,112)(2,97)(3,110)(4,95)(5,108)(6,93)(7,106)(8,91)(9,104)(10,89)(11,102)(12,87)(13,100)(14,85)(15,98)(16,111)(17,96)(18,109)(19,94)(20,107)(21,92)(22,105)(23,90)(24,103)(25,88)(26,101)(27,86)(28,99)(29,122)(30,135)(31,120)(32,133)(33,118)(34,131)(35,116)(36,129)(37,114)(38,127)(39,140)(40,125)(41,138)(42,123)(43,136)(44,121)(45,134)(46,119)(47,132)(48,117)(49,130)(50,115)(51,128)(52,113)(53,126)(54,139)(55,124)(56,137)(57,175)(58,188)(59,173)(60,186)(61,171)(62,184)(63,169)(64,182)(65,195)(66,180)(67,193)(68,178)(69,191)(70,176)(71,189)(72,174)(73,187)(74,172)(75,185)(76,170)(77,183)(78,196)(79,181)(80,194)(81,179)(82,192)(83,177)(84,190)(141,219)(142,204)(143,217)(144,202)(145,215)(146,200)(147,213)(148,198)(149,211)(150,224)(151,209)(152,222)(153,207)(154,220)(155,205)(156,218)(157,203)(158,216)(159,201)(160,214)(161,199)(162,212)(163,197)(164,210)(165,223)(166,208)(167,221)(168,206) );
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)], [(1,128,15,114),(2,127,16,113),(3,126,17,140),(4,125,18,139),(5,124,19,138),(6,123,20,137),(7,122,21,136),(8,121,22,135),(9,120,23,134),(10,119,24,133),(11,118,25,132),(12,117,26,131),(13,116,27,130),(14,115,28,129),(29,106,43,92),(30,105,44,91),(31,104,45,90),(32,103,46,89),(33,102,47,88),(34,101,48,87),(35,100,49,86),(36,99,50,85),(37,98,51,112),(38,97,52,111),(39,96,53,110),(40,95,54,109),(41,94,55,108),(42,93,56,107),(57,210,71,224),(58,209,72,223),(59,208,73,222),(60,207,74,221),(61,206,75,220),(62,205,76,219),(63,204,77,218),(64,203,78,217),(65,202,79,216),(66,201,80,215),(67,200,81,214),(68,199,82,213),(69,198,83,212),(70,197,84,211),(141,170,155,184),(142,169,156,183),(143,196,157,182),(144,195,158,181),(145,194,159,180),(146,193,160,179),(147,192,161,178),(148,191,162,177),(149,190,163,176),(150,189,164,175),(151,188,165,174),(152,187,166,173),(153,186,167,172),(154,185,168,171)], [(1,98,207,167),(2,99,208,168),(3,100,209,141),(4,101,210,142),(5,102,211,143),(6,103,212,144),(7,104,213,145),(8,105,214,146),(9,106,215,147),(10,107,216,148),(11,108,217,149),(12,109,218,150),(13,110,219,151),(14,111,220,152),(15,112,221,153),(16,85,222,154),(17,86,223,155),(18,87,224,156),(19,88,197,157),(20,89,198,158),(21,90,199,159),(22,91,200,160),(23,92,201,161),(24,93,202,162),(25,94,203,163),(26,95,204,164),(27,96,205,165),(28,97,206,166),(29,66,178,120),(30,67,179,121),(31,68,180,122),(32,69,181,123),(33,70,182,124),(34,71,183,125),(35,72,184,126),(36,73,185,127),(37,74,186,128),(38,75,187,129),(39,76,188,130),(40,77,189,131),(41,78,190,132),(42,79,191,133),(43,80,192,134),(44,81,193,135),(45,82,194,136),(46,83,195,137),(47,84,196,138),(48,57,169,139),(49,58,170,140),(50,59,171,113),(51,60,172,114),(52,61,173,115),(53,62,174,116),(54,63,175,117),(55,64,176,118),(56,65,177,119)], [(1,112),(2,97),(3,110),(4,95),(5,108),(6,93),(7,106),(8,91),(9,104),(10,89),(11,102),(12,87),(13,100),(14,85),(15,98),(16,111),(17,96),(18,109),(19,94),(20,107),(21,92),(22,105),(23,90),(24,103),(25,88),(26,101),(27,86),(28,99),(29,122),(30,135),(31,120),(32,133),(33,118),(34,131),(35,116),(36,129),(37,114),(38,127),(39,140),(40,125),(41,138),(42,123),(43,136),(44,121),(45,134),(46,119),(47,132),(48,117),(49,130),(50,115),(51,128),(52,113),(53,126),(54,139),(55,124),(56,137),(57,175),(58,188),(59,173),(60,186),(61,171),(62,184),(63,169),(64,182),(65,195),(66,180),(67,193),(68,178),(69,191),(70,176),(71,189),(72,174),(73,187),(74,172),(75,185),(76,170),(77,183),(78,196),(79,181),(80,194),(81,179),(82,192),(83,177),(84,190),(141,219),(142,204),(143,217),(144,202),(145,215),(146,200),(147,213),(148,198),(149,211),(150,224),(151,209),(152,222),(153,207),(154,220),(155,205),(156,218),(157,203),(158,216),(159,201),(160,214),(161,199),(162,212),(163,197),(164,210),(165,223),(166,208),(167,221),(168,206)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 17 | 0 | 0 | 0 | 0 | 0 |
| 2 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 1 | 0 | 0 |
| 0 | 0 | 27 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 26 | 22 | 0 | 0 | 0 | 0 |
| 18 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 3 | 0 | 0 |
| 0 | 0 | 24 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 5 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 24 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 3 | 0 | 0 |
| 0 | 0 | 24 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
G:=sub<GL(6,GF(29))| [17,2,0,0,0,0,0,12,0,0,0,0,0,0,11,27,0,0,0,0,1,21,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[26,18,0,0,0,0,22,3,0,0,0,0,0,0,25,24,0,0,0,0,3,4,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,5,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,0,1,0,0,0,0,28,0],[1,24,0,0,0,0,0,28,0,0,0,0,0,0,25,24,0,0,0,0,3,4,0,0,0,0,0,0,0,1,0,0,0,0,1,0] >;
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | ··· | 4M | 4N | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 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 | 14 | 14 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | D14 | 2- (1+4) | D4×D7 | D7×C4○D4 | D4.10D14 |
| kernel | Dic14⋊10D4 | C4×Dic14 | C4×D28 | C22⋊Dic14 | Dic7⋊4D4 | D14⋊D4 | Dic7.D4 | C28⋊2D4 | D14⋊3Q8 | C7×C4.4D4 | C2×D4⋊2D7 | C2×Q8×D7 | Dic14 | C4.4D4 | D14 | C42 | C22⋊C4 | C2×D4 | C2×Q8 | C14 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 4 | 3 | 4 | 3 | 12 | 3 | 3 | 1 | 6 | 6 | 6 |
In GAP, Magma, Sage, TeX
Dic_{14}\rtimes_{10}D_4 % in TeX
G:=Group("Dic14:10D4"); // GroupNames label
G:=SmallGroup(448,1130);
// by ID
G=gap.SmallGroup(448,1130);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,100,1571,297,192,18822]);
// 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^13,c*b*c^-1=d*b*d=a^14*b,d*c*d=c^-1>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀