metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic14⋊23D4, C42.110D14, C14.602- (1+4), (C4×D4)⋊14D7, (D4×C28)⋊16C2, C28⋊7D4⋊8C2, C7⋊1(Q8⋊5D4), C4.141(D4×D7), C4⋊C4.283D14, D14⋊Q8⋊7C2, C28.347(C2×D4), (C4×Dic14)⋊31C2, (C2×D4).215D14, C4.D28⋊17C2, C22⋊1(C4○D28), (C2×C14).96C24, Dic7.17(C2×D4), C14.51(C22×D4), Dic7⋊D4⋊26C2, Dic7⋊4D4⋊47C2, C28.48D4⋊21C2, (C4×C28).153C22, (C2×C28).784C23, D14⋊C4.66C22, C22⋊C4.111D14, Dic7.D4⋊6C2, (C22×Dic14)⋊9C2, (C22×C4).209D14, C23.96(C22×D7), (D4×C14).306C22, (C2×D28).211C22, C4⋊Dic7.298C22, (C22×D7).31C23, C22.121(C23×D7), C23.D7.13C22, Dic7⋊C4.154C22, (C22×C14).166C23, (C22×C28).108C22, (C4×Dic7).204C22, (C2×Dic7).204C23, C2.17(D4.10D14), (C2×Dic14).240C22, (C22×Dic7).96C22, C2.24(C2×D4×D7), (C2×C4○D28)⋊9C2, (C2×C14)⋊3(C4○D4), C14.43(C2×C4○D4), C2.47(C2×C4○D28), (C2×C4×D7).199C22, (C7×C4⋊C4).327C22, (C2×C4).159(C22×D7), (C2×C7⋊D4).114C22, (C7×C22⋊C4).123C22, SmallGroup(448,1005)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1332 in 290 conjugacy classes, 107 normal (51 characteristic)
C1, C2 [×3], C2 [×5], C4 [×2], C4 [×12], C22, C22 [×2], C22 [×11], C7, C2×C4 [×5], C2×C4 [×18], D4 [×12], Q8 [×10], C23 [×2], C23 [×2], D7 [×2], C14 [×3], C14 [×3], C42, C42 [×2], C22⋊C4 [×2], C22⋊C4 [×8], C4⋊C4, C4⋊C4 [×5], C22×C4 [×2], C22×C4 [×4], C2×D4, C2×D4 [×5], C2×Q8 [×8], C4○D4 [×4], Dic7 [×4], Dic7 [×4], C28 [×2], C28 [×4], D14 [×6], C2×C14, C2×C14 [×2], C2×C14 [×5], C4×D4, C4×D4 [×2], C4×Q8, C4⋊D4 [×3], C22⋊Q8 [×3], C4.4D4 [×3], C22×Q8, C2×C4○D4, Dic14 [×4], Dic14 [×6], C4×D7 [×4], D28 [×2], C2×Dic7 [×6], C2×Dic7 [×4], C7⋊D4 [×8], C2×C28 [×5], C2×C28 [×4], C7×D4 [×2], C22×D7 [×2], C22×C14 [×2], Q8⋊5D4, C4×Dic7 [×2], Dic7⋊C4 [×4], C4⋊Dic7, D14⋊C4 [×6], C23.D7 [×2], C4×C28, C7×C22⋊C4 [×2], C7×C4⋊C4, C2×Dic14 [×2], C2×Dic14 [×2], C2×Dic14 [×4], C2×C4×D7 [×2], C2×D28, C4○D28 [×4], C22×Dic7 [×2], C2×C7⋊D4 [×4], C22×C28 [×2], D4×C14, C4×Dic14, C4.D28, Dic7⋊4D4 [×2], Dic7.D4 [×2], D14⋊Q8 [×2], C28.48D4, C28⋊7D4, Dic7⋊D4 [×2], D4×C28, C22×Dic14, C2×C4○D28, Dic14⋊23D4
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, C4○D28 [×2], D4×D7 [×2], C23×D7, C2×C4○D28, C2×D4×D7, D4.10D14, Dic14⋊23D4
Generators and relations
G = < a,b,c,d | a28=c4=d2=1, b2=a14, bab-1=a-1, ac=ca, ad=da, cbc-1=a14b, bd=db, 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)
(1 191 15 177)(2 190 16 176)(3 189 17 175)(4 188 18 174)(5 187 19 173)(6 186 20 172)(7 185 21 171)(8 184 22 170)(9 183 23 169)(10 182 24 196)(11 181 25 195)(12 180 26 194)(13 179 27 193)(14 178 28 192)(29 157 43 143)(30 156 44 142)(31 155 45 141)(32 154 46 168)(33 153 47 167)(34 152 48 166)(35 151 49 165)(36 150 50 164)(37 149 51 163)(38 148 52 162)(39 147 53 161)(40 146 54 160)(41 145 55 159)(42 144 56 158)(57 110 71 96)(58 109 72 95)(59 108 73 94)(60 107 74 93)(61 106 75 92)(62 105 76 91)(63 104 77 90)(64 103 78 89)(65 102 79 88)(66 101 80 87)(67 100 81 86)(68 99 82 85)(69 98 83 112)(70 97 84 111)(113 200 127 214)(114 199 128 213)(115 198 129 212)(116 197 130 211)(117 224 131 210)(118 223 132 209)(119 222 133 208)(120 221 134 207)(121 220 135 206)(122 219 136 205)(123 218 137 204)(124 217 138 203)(125 216 139 202)(126 215 140 201)
(1 69 123 161)(2 70 124 162)(3 71 125 163)(4 72 126 164)(5 73 127 165)(6 74 128 166)(7 75 129 167)(8 76 130 168)(9 77 131 141)(10 78 132 142)(11 79 133 143)(12 80 134 144)(13 81 135 145)(14 82 136 146)(15 83 137 147)(16 84 138 148)(17 57 139 149)(18 58 140 150)(19 59 113 151)(20 60 114 152)(21 61 115 153)(22 62 116 154)(23 63 117 155)(24 64 118 156)(25 65 119 157)(26 66 120 158)(27 67 121 159)(28 68 122 160)(29 195 88 222)(30 196 89 223)(31 169 90 224)(32 170 91 197)(33 171 92 198)(34 172 93 199)(35 173 94 200)(36 174 95 201)(37 175 96 202)(38 176 97 203)(39 177 98 204)(40 178 99 205)(41 179 100 206)(42 180 101 207)(43 181 102 208)(44 182 103 209)(45 183 104 210)(46 184 105 211)(47 185 106 212)(48 186 107 213)(49 187 108 214)(50 188 109 215)(51 189 110 216)(52 190 111 217)(53 191 112 218)(54 192 85 219)(55 193 86 220)(56 194 87 221)
(1 15)(2 16)(3 17)(4 18)(5 19)(6 20)(7 21)(8 22)(9 23)(10 24)(11 25)(12 26)(13 27)(14 28)(29 102)(30 103)(31 104)(32 105)(33 106)(34 107)(35 108)(36 109)(37 110)(38 111)(39 112)(40 85)(41 86)(42 87)(43 88)(44 89)(45 90)(46 91)(47 92)(48 93)(49 94)(50 95)(51 96)(52 97)(53 98)(54 99)(55 100)(56 101)(57 163)(58 164)(59 165)(60 166)(61 167)(62 168)(63 141)(64 142)(65 143)(66 144)(67 145)(68 146)(69 147)(70 148)(71 149)(72 150)(73 151)(74 152)(75 153)(76 154)(77 155)(78 156)(79 157)(80 158)(81 159)(82 160)(83 161)(84 162)(113 127)(114 128)(115 129)(116 130)(117 131)(118 132)(119 133)(120 134)(121 135)(122 136)(123 137)(124 138)(125 139)(126 140)(169 183)(170 184)(171 185)(172 186)(173 187)(174 188)(175 189)(176 190)(177 191)(178 192)(179 193)(180 194)(181 195)(182 196)(197 211)(198 212)(199 213)(200 214)(201 215)(202 216)(203 217)(204 218)(205 219)(206 220)(207 221)(208 222)(209 223)(210 224)
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), (1,191,15,177)(2,190,16,176)(3,189,17,175)(4,188,18,174)(5,187,19,173)(6,186,20,172)(7,185,21,171)(8,184,22,170)(9,183,23,169)(10,182,24,196)(11,181,25,195)(12,180,26,194)(13,179,27,193)(14,178,28,192)(29,157,43,143)(30,156,44,142)(31,155,45,141)(32,154,46,168)(33,153,47,167)(34,152,48,166)(35,151,49,165)(36,150,50,164)(37,149,51,163)(38,148,52,162)(39,147,53,161)(40,146,54,160)(41,145,55,159)(42,144,56,158)(57,110,71,96)(58,109,72,95)(59,108,73,94)(60,107,74,93)(61,106,75,92)(62,105,76,91)(63,104,77,90)(64,103,78,89)(65,102,79,88)(66,101,80,87)(67,100,81,86)(68,99,82,85)(69,98,83,112)(70,97,84,111)(113,200,127,214)(114,199,128,213)(115,198,129,212)(116,197,130,211)(117,224,131,210)(118,223,132,209)(119,222,133,208)(120,221,134,207)(121,220,135,206)(122,219,136,205)(123,218,137,204)(124,217,138,203)(125,216,139,202)(126,215,140,201), (1,69,123,161)(2,70,124,162)(3,71,125,163)(4,72,126,164)(5,73,127,165)(6,74,128,166)(7,75,129,167)(8,76,130,168)(9,77,131,141)(10,78,132,142)(11,79,133,143)(12,80,134,144)(13,81,135,145)(14,82,136,146)(15,83,137,147)(16,84,138,148)(17,57,139,149)(18,58,140,150)(19,59,113,151)(20,60,114,152)(21,61,115,153)(22,62,116,154)(23,63,117,155)(24,64,118,156)(25,65,119,157)(26,66,120,158)(27,67,121,159)(28,68,122,160)(29,195,88,222)(30,196,89,223)(31,169,90,224)(32,170,91,197)(33,171,92,198)(34,172,93,199)(35,173,94,200)(36,174,95,201)(37,175,96,202)(38,176,97,203)(39,177,98,204)(40,178,99,205)(41,179,100,206)(42,180,101,207)(43,181,102,208)(44,182,103,209)(45,183,104,210)(46,184,105,211)(47,185,106,212)(48,186,107,213)(49,187,108,214)(50,188,109,215)(51,189,110,216)(52,190,111,217)(53,191,112,218)(54,192,85,219)(55,193,86,220)(56,194,87,221), (1,15)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(29,102)(30,103)(31,104)(32,105)(33,106)(34,107)(35,108)(36,109)(37,110)(38,111)(39,112)(40,85)(41,86)(42,87)(43,88)(44,89)(45,90)(46,91)(47,92)(48,93)(49,94)(50,95)(51,96)(52,97)(53,98)(54,99)(55,100)(56,101)(57,163)(58,164)(59,165)(60,166)(61,167)(62,168)(63,141)(64,142)(65,143)(66,144)(67,145)(68,146)(69,147)(70,148)(71,149)(72,150)(73,151)(74,152)(75,153)(76,154)(77,155)(78,156)(79,157)(80,158)(81,159)(82,160)(83,161)(84,162)(113,127)(114,128)(115,129)(116,130)(117,131)(118,132)(119,133)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224)>;
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), (1,191,15,177)(2,190,16,176)(3,189,17,175)(4,188,18,174)(5,187,19,173)(6,186,20,172)(7,185,21,171)(8,184,22,170)(9,183,23,169)(10,182,24,196)(11,181,25,195)(12,180,26,194)(13,179,27,193)(14,178,28,192)(29,157,43,143)(30,156,44,142)(31,155,45,141)(32,154,46,168)(33,153,47,167)(34,152,48,166)(35,151,49,165)(36,150,50,164)(37,149,51,163)(38,148,52,162)(39,147,53,161)(40,146,54,160)(41,145,55,159)(42,144,56,158)(57,110,71,96)(58,109,72,95)(59,108,73,94)(60,107,74,93)(61,106,75,92)(62,105,76,91)(63,104,77,90)(64,103,78,89)(65,102,79,88)(66,101,80,87)(67,100,81,86)(68,99,82,85)(69,98,83,112)(70,97,84,111)(113,200,127,214)(114,199,128,213)(115,198,129,212)(116,197,130,211)(117,224,131,210)(118,223,132,209)(119,222,133,208)(120,221,134,207)(121,220,135,206)(122,219,136,205)(123,218,137,204)(124,217,138,203)(125,216,139,202)(126,215,140,201), (1,69,123,161)(2,70,124,162)(3,71,125,163)(4,72,126,164)(5,73,127,165)(6,74,128,166)(7,75,129,167)(8,76,130,168)(9,77,131,141)(10,78,132,142)(11,79,133,143)(12,80,134,144)(13,81,135,145)(14,82,136,146)(15,83,137,147)(16,84,138,148)(17,57,139,149)(18,58,140,150)(19,59,113,151)(20,60,114,152)(21,61,115,153)(22,62,116,154)(23,63,117,155)(24,64,118,156)(25,65,119,157)(26,66,120,158)(27,67,121,159)(28,68,122,160)(29,195,88,222)(30,196,89,223)(31,169,90,224)(32,170,91,197)(33,171,92,198)(34,172,93,199)(35,173,94,200)(36,174,95,201)(37,175,96,202)(38,176,97,203)(39,177,98,204)(40,178,99,205)(41,179,100,206)(42,180,101,207)(43,181,102,208)(44,182,103,209)(45,183,104,210)(46,184,105,211)(47,185,106,212)(48,186,107,213)(49,187,108,214)(50,188,109,215)(51,189,110,216)(52,190,111,217)(53,191,112,218)(54,192,85,219)(55,193,86,220)(56,194,87,221), (1,15)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(29,102)(30,103)(31,104)(32,105)(33,106)(34,107)(35,108)(36,109)(37,110)(38,111)(39,112)(40,85)(41,86)(42,87)(43,88)(44,89)(45,90)(46,91)(47,92)(48,93)(49,94)(50,95)(51,96)(52,97)(53,98)(54,99)(55,100)(56,101)(57,163)(58,164)(59,165)(60,166)(61,167)(62,168)(63,141)(64,142)(65,143)(66,144)(67,145)(68,146)(69,147)(70,148)(71,149)(72,150)(73,151)(74,152)(75,153)(76,154)(77,155)(78,156)(79,157)(80,158)(81,159)(82,160)(83,161)(84,162)(113,127)(114,128)(115,129)(116,130)(117,131)(118,132)(119,133)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224) );
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)], [(1,191,15,177),(2,190,16,176),(3,189,17,175),(4,188,18,174),(5,187,19,173),(6,186,20,172),(7,185,21,171),(8,184,22,170),(9,183,23,169),(10,182,24,196),(11,181,25,195),(12,180,26,194),(13,179,27,193),(14,178,28,192),(29,157,43,143),(30,156,44,142),(31,155,45,141),(32,154,46,168),(33,153,47,167),(34,152,48,166),(35,151,49,165),(36,150,50,164),(37,149,51,163),(38,148,52,162),(39,147,53,161),(40,146,54,160),(41,145,55,159),(42,144,56,158),(57,110,71,96),(58,109,72,95),(59,108,73,94),(60,107,74,93),(61,106,75,92),(62,105,76,91),(63,104,77,90),(64,103,78,89),(65,102,79,88),(66,101,80,87),(67,100,81,86),(68,99,82,85),(69,98,83,112),(70,97,84,111),(113,200,127,214),(114,199,128,213),(115,198,129,212),(116,197,130,211),(117,224,131,210),(118,223,132,209),(119,222,133,208),(120,221,134,207),(121,220,135,206),(122,219,136,205),(123,218,137,204),(124,217,138,203),(125,216,139,202),(126,215,140,201)], [(1,69,123,161),(2,70,124,162),(3,71,125,163),(4,72,126,164),(5,73,127,165),(6,74,128,166),(7,75,129,167),(8,76,130,168),(9,77,131,141),(10,78,132,142),(11,79,133,143),(12,80,134,144),(13,81,135,145),(14,82,136,146),(15,83,137,147),(16,84,138,148),(17,57,139,149),(18,58,140,150),(19,59,113,151),(20,60,114,152),(21,61,115,153),(22,62,116,154),(23,63,117,155),(24,64,118,156),(25,65,119,157),(26,66,120,158),(27,67,121,159),(28,68,122,160),(29,195,88,222),(30,196,89,223),(31,169,90,224),(32,170,91,197),(33,171,92,198),(34,172,93,199),(35,173,94,200),(36,174,95,201),(37,175,96,202),(38,176,97,203),(39,177,98,204),(40,178,99,205),(41,179,100,206),(42,180,101,207),(43,181,102,208),(44,182,103,209),(45,183,104,210),(46,184,105,211),(47,185,106,212),(48,186,107,213),(49,187,108,214),(50,188,109,215),(51,189,110,216),(52,190,111,217),(53,191,112,218),(54,192,85,219),(55,193,86,220),(56,194,87,221)], [(1,15),(2,16),(3,17),(4,18),(5,19),(6,20),(7,21),(8,22),(9,23),(10,24),(11,25),(12,26),(13,27),(14,28),(29,102),(30,103),(31,104),(32,105),(33,106),(34,107),(35,108),(36,109),(37,110),(38,111),(39,112),(40,85),(41,86),(42,87),(43,88),(44,89),(45,90),(46,91),(47,92),(48,93),(49,94),(50,95),(51,96),(52,97),(53,98),(54,99),(55,100),(56,101),(57,163),(58,164),(59,165),(60,166),(61,167),(62,168),(63,141),(64,142),(65,143),(66,144),(67,145),(68,146),(69,147),(70,148),(71,149),(72,150),(73,151),(74,152),(75,153),(76,154),(77,155),(78,156),(79,157),(80,158),(81,159),(82,160),(83,161),(84,162),(113,127),(114,128),(115,129),(116,130),(117,131),(118,132),(119,133),(120,134),(121,135),(122,136),(123,137),(124,138),(125,139),(126,140),(169,183),(170,184),(171,185),(172,186),(173,187),(174,188),(175,189),(176,190),(177,191),(178,192),(179,193),(180,194),(181,195),(182,196),(197,211),(198,212),(199,213),(200,214),(201,215),(202,216),(203,217),(204,218),(205,219),(206,220),(207,221),(208,222),(209,223),(210,224)])
Matrix representation ►G ⊆ GL4(𝔽29) generated by
| 28 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 9 | 16 |
| 0 | 0 | 28 | 8 |
| 28 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 4 | 17 |
| 0 | 0 | 28 | 25 |
| 0 | 1 | 0 | 0 |
| 28 | 0 | 0 | 0 |
| 0 | 0 | 20 | 2 |
| 0 | 0 | 18 | 9 |
| 28 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 28 |
G:=sub<GL(4,GF(29))| [28,0,0,0,0,28,0,0,0,0,9,28,0,0,16,8],[28,0,0,0,0,28,0,0,0,0,4,28,0,0,17,25],[0,28,0,0,1,0,0,0,0,0,20,18,0,0,2,9],[28,0,0,0,0,1,0,0,0,0,28,0,0,0,0,28] >;
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| 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 | 2 | 2 | 4 | 28 | 28 | 2 | ··· | 2 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 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 | 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 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | D14 | D14 | C4○D28 | 2- (1+4) | D4×D7 | D4.10D14 |
| kernel | Dic14⋊23D4 | C4×Dic14 | C4.D28 | Dic7⋊4D4 | Dic7.D4 | D14⋊Q8 | C28.48D4 | C28⋊7D4 | Dic7⋊D4 | D4×C28 | C22×Dic14 | C2×C4○D28 | Dic14 | C4×D4 | C2×C14 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C22 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 2 | 1 | 1 | 2 | 1 | 1 | 1 | 4 | 3 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 1 | 6 | 6 |
In GAP, Magma, Sage, TeX
Dic_{14}\rtimes_{23}D_4 % in TeX
G:=Group("Dic14:23D4"); // GroupNames label
G:=SmallGroup(448,1005);
// by ID
G=gap.SmallGroup(448,1005);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,387,100,675,570,18822]);
// 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,c*b*c^-1=a^14*b,b*d=d*b,d*c*d=c^-1>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀