metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.137D14, C14.872- (1+4), C14.702+ (1+4), C4.4D4⋊6D7, C42⋊2D7⋊7C2, (C2×Q8).81D14, D14⋊3Q8⋊27C2, (C4×Dic14)⋊43C2, (C2×D4).107D14, C22⋊C4.71D14, Dic7⋊Q8⋊20C2, Dic7⋊4D4⋊28C2, D14.D4⋊40C2, (C2×C28).629C23, (C2×C14).213C24, (C4×C28).183C22, D14⋊C4.59C22, Dic7⋊D4.5C2, C2.72(D4⋊6D14), C23.35(C22×D7), Dic7.11(C4○D4), C22⋊Dic14⋊37C2, Dic7.D4⋊37C2, (D4×C14).207C22, C23.D14⋊36C2, Dic7⋊C4.82C22, C4⋊Dic7.232C22, (C22×C14).43C23, (Q8×C14).122C22, (C22×D7).93C23, C22.234(C23×D7), C23.D7.50C22, C23.11D14⋊16C2, C23.18D14⋊24C2, C7⋊8(C22.36C24), (C4×Dic7).213C22, (C2×Dic7).250C23, C2.48(D4.10D14), (C2×Dic14).174C22, (C22×Dic7).138C22, C2.72(D7×C4○D4), (C7×C4.4D4)⋊7C2, C14.184(C2×C4○D4), (C2×C4×D7).119C22, (C2×C4).191(C22×D7), (C2×C7⋊D4).56C22, (C7×C22⋊C4).60C22, SmallGroup(448,1122)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 940 in 216 conjugacy classes, 93 normal (91 characteristic)
C1, C2 [×3], C2 [×3], C4 [×13], C22, C22 [×9], C7, C2×C4 [×5], C2×C4 [×11], D4 [×4], Q8 [×4], C23 [×2], C23, D7, C14 [×3], C14 [×2], C42, C42 [×3], C22⋊C4 [×4], C22⋊C4 [×8], C4⋊C4 [×10], C22×C4 [×3], C2×D4, C2×D4 [×2], C2×Q8, C2×Q8 [×2], Dic7 [×2], Dic7 [×6], C28 [×5], D14 [×3], C2×C14, C2×C14 [×6], C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8 [×3], C22.D4 [×2], C4.4D4, C4.4D4 [×2], C42⋊2C2 [×2], C4⋊Q8, Dic14 [×3], C4×D7, C2×Dic7 [×7], C2×Dic7 [×3], C7⋊D4 [×3], C2×C28 [×5], C7×D4, C7×Q8, C22×D7, C22×C14 [×2], C22.36C24, C4×Dic7 [×3], Dic7⋊C4 [×8], C4⋊Dic7 [×2], D14⋊C4 [×4], C23.D7 [×4], C4×C28, C7×C22⋊C4 [×4], C2×Dic14 [×2], C2×C4×D7, C22×Dic7 [×2], C2×C7⋊D4 [×2], D4×C14, Q8×C14, C4×Dic14, C42⋊2D7, C23.11D14, C22⋊Dic14 [×2], C23.D14, Dic7⋊4D4, D14.D4, Dic7.D4 [×2], C23.18D14, Dic7⋊D4, Dic7⋊Q8, D14⋊3Q8, C7×C4.4D4, C42.137D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×2], C24, D14 [×7], C2×C4○D4, 2+ (1+4), 2- (1+4), C22×D7 [×7], C22.36C24, C23×D7, D4⋊6D14, D7×C4○D4, D4.10D14, C42.137D14
Generators and relations
G = < a,b,c,d | a4=b4=c14=1, d2=b2, ab=ba, cac-1=dad-1=ab2, cbc-1=a2b, dbd-1=a2b-1, dcd-1=c-1 >
►On 224 points
Generators in S224
(1 154 56 134)(2 148 50 128)(3 142 51 136)(4 150 52 130)(5 144 53 138)(6 152 54 132)(7 146 55 140)(8 206 22 218)(9 200 23 212)(10 208 24 220)(11 202 25 214)(12 210 26 222)(13 204 27 216)(14 198 28 224)(15 211 41 199)(16 219 42 207)(17 213 36 201)(18 221 37 209)(19 215 38 203)(20 223 39 197)(21 217 40 205)(29 127 49 147)(30 135 43 141)(31 129 44 149)(32 137 45 143)(33 131 46 151)(34 139 47 145)(35 133 48 153)(57 121 192 114)(58 166 193 159)(59 123 194 116)(60 168 195 161)(61 125 196 118)(62 156 183 163)(63 113 184 120)(64 158 185 165)(65 115 186 122)(66 160 187 167)(67 117 188 124)(68 162 189 155)(69 119 190 126)(70 164 191 157)(71 179 102 172)(72 91 103 98)(73 181 104 174)(74 93 105 86)(75 169 106 176)(76 95 107 88)(77 171 108 178)(78 97 109 90)(79 173 110 180)(80 85 111 92)(81 175 112 182)(82 87 99 94)(83 177 100 170)(84 89 101 96)
(1 168 49 124)(2 162 43 118)(3 156 44 126)(4 164 45 120)(5 158 46 114)(6 166 47 122)(7 160 48 116)(8 97 41 172)(9 91 42 180)(10 85 36 174)(11 93 37 182)(12 87 38 176)(13 95 39 170)(14 89 40 178)(15 179 22 90)(16 173 23 98)(17 181 24 92)(18 175 25 86)(19 169 26 94)(20 177 27 88)(21 171 28 96)(29 117 56 161)(30 125 50 155)(31 119 51 163)(32 113 52 157)(33 121 53 165)(34 115 54 159)(35 123 55 167)(57 144 185 151)(58 139 186 132)(59 146 187 153)(60 127 188 134)(61 148 189 141)(62 129 190 136)(63 150 191 143)(64 131 192 138)(65 152 193 145)(66 133 194 140)(67 154 195 147)(68 135 196 128)(69 142 183 149)(70 137 184 130)(71 206 109 199)(72 219 110 212)(73 208 111 201)(74 221 112 214)(75 210 99 203)(76 223 100 216)(77 198 101 205)(78 211 102 218)(79 200 103 207)(80 213 104 220)(81 202 105 209)(82 215 106 222)(83 204 107 197)(84 217 108 224)
(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 39 49 13)(2 38 43 12)(3 37 44 11)(4 36 45 10)(5 42 46 9)(6 41 47 8)(7 40 48 14)(15 34 22 54)(16 33 23 53)(17 32 24 52)(18 31 25 51)(19 30 26 50)(20 29 27 56)(21 35 28 55)(57 72 185 110)(58 71 186 109)(59 84 187 108)(60 83 188 107)(61 82 189 106)(62 81 190 105)(63 80 191 104)(64 79 192 103)(65 78 193 102)(66 77 194 101)(67 76 195 100)(68 75 196 99)(69 74 183 112)(70 73 184 111)(85 113 174 157)(86 126 175 156)(87 125 176 155)(88 124 177 168)(89 123 178 167)(90 122 179 166)(91 121 180 165)(92 120 181 164)(93 119 182 163)(94 118 169 162)(95 117 170 161)(96 116 171 160)(97 115 172 159)(98 114 173 158)(127 223 134 216)(128 222 135 215)(129 221 136 214)(130 220 137 213)(131 219 138 212)(132 218 139 211)(133 217 140 224)(141 203 148 210)(142 202 149 209)(143 201 150 208)(144 200 151 207)(145 199 152 206)(146 198 153 205)(147 197 154 204)
G:=sub<Sym(224)| (1,154,56,134)(2,148,50,128)(3,142,51,136)(4,150,52,130)(5,144,53,138)(6,152,54,132)(7,146,55,140)(8,206,22,218)(9,200,23,212)(10,208,24,220)(11,202,25,214)(12,210,26,222)(13,204,27,216)(14,198,28,224)(15,211,41,199)(16,219,42,207)(17,213,36,201)(18,221,37,209)(19,215,38,203)(20,223,39,197)(21,217,40,205)(29,127,49,147)(30,135,43,141)(31,129,44,149)(32,137,45,143)(33,131,46,151)(34,139,47,145)(35,133,48,153)(57,121,192,114)(58,166,193,159)(59,123,194,116)(60,168,195,161)(61,125,196,118)(62,156,183,163)(63,113,184,120)(64,158,185,165)(65,115,186,122)(66,160,187,167)(67,117,188,124)(68,162,189,155)(69,119,190,126)(70,164,191,157)(71,179,102,172)(72,91,103,98)(73,181,104,174)(74,93,105,86)(75,169,106,176)(76,95,107,88)(77,171,108,178)(78,97,109,90)(79,173,110,180)(80,85,111,92)(81,175,112,182)(82,87,99,94)(83,177,100,170)(84,89,101,96), (1,168,49,124)(2,162,43,118)(3,156,44,126)(4,164,45,120)(5,158,46,114)(6,166,47,122)(7,160,48,116)(8,97,41,172)(9,91,42,180)(10,85,36,174)(11,93,37,182)(12,87,38,176)(13,95,39,170)(14,89,40,178)(15,179,22,90)(16,173,23,98)(17,181,24,92)(18,175,25,86)(19,169,26,94)(20,177,27,88)(21,171,28,96)(29,117,56,161)(30,125,50,155)(31,119,51,163)(32,113,52,157)(33,121,53,165)(34,115,54,159)(35,123,55,167)(57,144,185,151)(58,139,186,132)(59,146,187,153)(60,127,188,134)(61,148,189,141)(62,129,190,136)(63,150,191,143)(64,131,192,138)(65,152,193,145)(66,133,194,140)(67,154,195,147)(68,135,196,128)(69,142,183,149)(70,137,184,130)(71,206,109,199)(72,219,110,212)(73,208,111,201)(74,221,112,214)(75,210,99,203)(76,223,100,216)(77,198,101,205)(78,211,102,218)(79,200,103,207)(80,213,104,220)(81,202,105,209)(82,215,106,222)(83,204,107,197)(84,217,108,224), (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), (1,39,49,13)(2,38,43,12)(3,37,44,11)(4,36,45,10)(5,42,46,9)(6,41,47,8)(7,40,48,14)(15,34,22,54)(16,33,23,53)(17,32,24,52)(18,31,25,51)(19,30,26,50)(20,29,27,56)(21,35,28,55)(57,72,185,110)(58,71,186,109)(59,84,187,108)(60,83,188,107)(61,82,189,106)(62,81,190,105)(63,80,191,104)(64,79,192,103)(65,78,193,102)(66,77,194,101)(67,76,195,100)(68,75,196,99)(69,74,183,112)(70,73,184,111)(85,113,174,157)(86,126,175,156)(87,125,176,155)(88,124,177,168)(89,123,178,167)(90,122,179,166)(91,121,180,165)(92,120,181,164)(93,119,182,163)(94,118,169,162)(95,117,170,161)(96,116,171,160)(97,115,172,159)(98,114,173,158)(127,223,134,216)(128,222,135,215)(129,221,136,214)(130,220,137,213)(131,219,138,212)(132,218,139,211)(133,217,140,224)(141,203,148,210)(142,202,149,209)(143,201,150,208)(144,200,151,207)(145,199,152,206)(146,198,153,205)(147,197,154,204)>;
G:=Group( (1,154,56,134)(2,148,50,128)(3,142,51,136)(4,150,52,130)(5,144,53,138)(6,152,54,132)(7,146,55,140)(8,206,22,218)(9,200,23,212)(10,208,24,220)(11,202,25,214)(12,210,26,222)(13,204,27,216)(14,198,28,224)(15,211,41,199)(16,219,42,207)(17,213,36,201)(18,221,37,209)(19,215,38,203)(20,223,39,197)(21,217,40,205)(29,127,49,147)(30,135,43,141)(31,129,44,149)(32,137,45,143)(33,131,46,151)(34,139,47,145)(35,133,48,153)(57,121,192,114)(58,166,193,159)(59,123,194,116)(60,168,195,161)(61,125,196,118)(62,156,183,163)(63,113,184,120)(64,158,185,165)(65,115,186,122)(66,160,187,167)(67,117,188,124)(68,162,189,155)(69,119,190,126)(70,164,191,157)(71,179,102,172)(72,91,103,98)(73,181,104,174)(74,93,105,86)(75,169,106,176)(76,95,107,88)(77,171,108,178)(78,97,109,90)(79,173,110,180)(80,85,111,92)(81,175,112,182)(82,87,99,94)(83,177,100,170)(84,89,101,96), (1,168,49,124)(2,162,43,118)(3,156,44,126)(4,164,45,120)(5,158,46,114)(6,166,47,122)(7,160,48,116)(8,97,41,172)(9,91,42,180)(10,85,36,174)(11,93,37,182)(12,87,38,176)(13,95,39,170)(14,89,40,178)(15,179,22,90)(16,173,23,98)(17,181,24,92)(18,175,25,86)(19,169,26,94)(20,177,27,88)(21,171,28,96)(29,117,56,161)(30,125,50,155)(31,119,51,163)(32,113,52,157)(33,121,53,165)(34,115,54,159)(35,123,55,167)(57,144,185,151)(58,139,186,132)(59,146,187,153)(60,127,188,134)(61,148,189,141)(62,129,190,136)(63,150,191,143)(64,131,192,138)(65,152,193,145)(66,133,194,140)(67,154,195,147)(68,135,196,128)(69,142,183,149)(70,137,184,130)(71,206,109,199)(72,219,110,212)(73,208,111,201)(74,221,112,214)(75,210,99,203)(76,223,100,216)(77,198,101,205)(78,211,102,218)(79,200,103,207)(80,213,104,220)(81,202,105,209)(82,215,106,222)(83,204,107,197)(84,217,108,224), (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), (1,39,49,13)(2,38,43,12)(3,37,44,11)(4,36,45,10)(5,42,46,9)(6,41,47,8)(7,40,48,14)(15,34,22,54)(16,33,23,53)(17,32,24,52)(18,31,25,51)(19,30,26,50)(20,29,27,56)(21,35,28,55)(57,72,185,110)(58,71,186,109)(59,84,187,108)(60,83,188,107)(61,82,189,106)(62,81,190,105)(63,80,191,104)(64,79,192,103)(65,78,193,102)(66,77,194,101)(67,76,195,100)(68,75,196,99)(69,74,183,112)(70,73,184,111)(85,113,174,157)(86,126,175,156)(87,125,176,155)(88,124,177,168)(89,123,178,167)(90,122,179,166)(91,121,180,165)(92,120,181,164)(93,119,182,163)(94,118,169,162)(95,117,170,161)(96,116,171,160)(97,115,172,159)(98,114,173,158)(127,223,134,216)(128,222,135,215)(129,221,136,214)(130,220,137,213)(131,219,138,212)(132,218,139,211)(133,217,140,224)(141,203,148,210)(142,202,149,209)(143,201,150,208)(144,200,151,207)(145,199,152,206)(146,198,153,205)(147,197,154,204) );
G=PermutationGroup([(1,154,56,134),(2,148,50,128),(3,142,51,136),(4,150,52,130),(5,144,53,138),(6,152,54,132),(7,146,55,140),(8,206,22,218),(9,200,23,212),(10,208,24,220),(11,202,25,214),(12,210,26,222),(13,204,27,216),(14,198,28,224),(15,211,41,199),(16,219,42,207),(17,213,36,201),(18,221,37,209),(19,215,38,203),(20,223,39,197),(21,217,40,205),(29,127,49,147),(30,135,43,141),(31,129,44,149),(32,137,45,143),(33,131,46,151),(34,139,47,145),(35,133,48,153),(57,121,192,114),(58,166,193,159),(59,123,194,116),(60,168,195,161),(61,125,196,118),(62,156,183,163),(63,113,184,120),(64,158,185,165),(65,115,186,122),(66,160,187,167),(67,117,188,124),(68,162,189,155),(69,119,190,126),(70,164,191,157),(71,179,102,172),(72,91,103,98),(73,181,104,174),(74,93,105,86),(75,169,106,176),(76,95,107,88),(77,171,108,178),(78,97,109,90),(79,173,110,180),(80,85,111,92),(81,175,112,182),(82,87,99,94),(83,177,100,170),(84,89,101,96)], [(1,168,49,124),(2,162,43,118),(3,156,44,126),(4,164,45,120),(5,158,46,114),(6,166,47,122),(7,160,48,116),(8,97,41,172),(9,91,42,180),(10,85,36,174),(11,93,37,182),(12,87,38,176),(13,95,39,170),(14,89,40,178),(15,179,22,90),(16,173,23,98),(17,181,24,92),(18,175,25,86),(19,169,26,94),(20,177,27,88),(21,171,28,96),(29,117,56,161),(30,125,50,155),(31,119,51,163),(32,113,52,157),(33,121,53,165),(34,115,54,159),(35,123,55,167),(57,144,185,151),(58,139,186,132),(59,146,187,153),(60,127,188,134),(61,148,189,141),(62,129,190,136),(63,150,191,143),(64,131,192,138),(65,152,193,145),(66,133,194,140),(67,154,195,147),(68,135,196,128),(69,142,183,149),(70,137,184,130),(71,206,109,199),(72,219,110,212),(73,208,111,201),(74,221,112,214),(75,210,99,203),(76,223,100,216),(77,198,101,205),(78,211,102,218),(79,200,103,207),(80,213,104,220),(81,202,105,209),(82,215,106,222),(83,204,107,197),(84,217,108,224)], [(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)], [(1,39,49,13),(2,38,43,12),(3,37,44,11),(4,36,45,10),(5,42,46,9),(6,41,47,8),(7,40,48,14),(15,34,22,54),(16,33,23,53),(17,32,24,52),(18,31,25,51),(19,30,26,50),(20,29,27,56),(21,35,28,55),(57,72,185,110),(58,71,186,109),(59,84,187,108),(60,83,188,107),(61,82,189,106),(62,81,190,105),(63,80,191,104),(64,79,192,103),(65,78,193,102),(66,77,194,101),(67,76,195,100),(68,75,196,99),(69,74,183,112),(70,73,184,111),(85,113,174,157),(86,126,175,156),(87,125,176,155),(88,124,177,168),(89,123,178,167),(90,122,179,166),(91,121,180,165),(92,120,181,164),(93,119,182,163),(94,118,169,162),(95,117,170,161),(96,116,171,160),(97,115,172,159),(98,114,173,158),(127,223,134,216),(128,222,135,215),(129,221,136,214),(130,220,137,213),(131,219,138,212),(132,218,139,211),(133,217,140,224),(141,203,148,210),(142,202,149,209),(143,201,150,208),(144,200,151,207),(145,199,152,206),(146,198,153,205),(147,197,154,204)])
Matrix representation ►G ⊆ GL8(𝔽29)
| 17 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 20 | 14 |
| 0 | 0 | 0 | 0 | 0 | 0 | 15 | 9 |
| 0 | 0 | 0 | 0 | 9 | 15 | 0 | 0 |
| 0 | 0 | 0 | 0 | 14 | 20 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 | 0 | 0 |
| 22 | 10 | 0 | 0 | 0 | 0 | 0 | 0 |
| 19 | 10 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 22 | 10 | 0 | 0 |
| 0 | 0 | 0 | 0 | 19 | 10 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 7 | 19 |
| 0 | 0 | 0 | 0 | 0 | 0 | 10 | 19 |
| 4 | 20 | 0 | 0 | 0 | 0 | 0 | 0 |
| 21 | 25 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 3 | 17 |
G:=sub<GL(8,GF(29))| [17,0,0,0,0,0,0,0,0,17,0,0,0,0,0,0,0,0,17,0,0,0,0,0,0,0,0,17,0,0,0,0,0,0,0,0,0,0,9,14,0,0,0,0,0,0,15,20,0,0,0,0,20,15,0,0,0,0,0,0,14,9,0,0],[0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0],[22,19,0,0,0,0,0,0,10,10,0,0,0,0,0,0,0,0,7,10,0,0,0,0,0,0,19,19,0,0,0,0,0,0,0,0,22,19,0,0,0,0,0,0,10,10,0,0,0,0,0,0,0,0,7,10,0,0,0,0,0,0,19,19],[4,21,0,0,0,0,0,0,20,25,0,0,0,0,0,0,0,0,25,8,0,0,0,0,0,0,9,4,0,0,0,0,0,0,0,0,12,3,0,0,0,0,0,0,0,17,0,0,0,0,0,0,0,0,12,3,0,0,0,0,0,0,0,17] >;
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | ··· | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| order | 1 | 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 | 28 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | D14 | 2+ (1+4) | 2- (1+4) | D4⋊6D14 | D7×C4○D4 | D4.10D14 |
| kernel | C42.137D14 | C4×Dic14 | C42⋊2D7 | C23.11D14 | C22⋊Dic14 | C23.D14 | Dic7⋊4D4 | D14.D4 | Dic7.D4 | C23.18D14 | Dic7⋊D4 | Dic7⋊Q8 | D14⋊3Q8 | C7×C4.4D4 | C4.4D4 | Dic7 | C42 | C22⋊C4 | C2×D4 | C2×Q8 | C14 | C14 | C2 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 3 | 12 | 3 | 3 | 1 | 1 | 6 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{137}D_{14} % in TeX
G:=Group("C4^2.137D14"); // GroupNames label
G:=SmallGroup(448,1122);
// by ID
G=gap.SmallGroup(448,1122);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,387,100,1123,346,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a*b^2,c*b*c^-1=a^2*b,d*b*d^-1=a^2*b^-1,d*c*d^-1=c^-1>;
// generators/relations
×
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ℤ
𝔽
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