metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.125D14, C14.92- (1+4), (C4×Q8)⋊6D7, (Q8×D7)⋊5C4, (Q8×C28)⋊7C2, (Q8×Dic7)⋊8C2, Q8.12(C4×D7), C4⋊C4.323D14, (C4×Dic14)⋊38C2, C28.35(C22×C4), C14.25(C23×C4), (C2×Q8).200D14, C42⋊D7.3C2, Dic7⋊3Q8⋊18C2, (C2×C14).116C24, (C4×C28).168C22, (C2×C28).495C23, Dic14.20(C2×C4), D14.19(C22×C4), C22.35(C23×D7), D14⋊C4.124C22, C4⋊Dic7.366C22, (Q8×C14).216C22, Dic7.11(C22×C4), (C4×Dic7).84C22, C2.4(D4.10D14), Dic7⋊C4.137C22, C2.2(Q8.10D14), C7⋊2(C23.32C23), (C2×Dic7).212C23, (C22×D7).175C23, (C2×Dic14).290C22, C4.35(C2×C4×D7), (C2×Q8×D7).6C2, (C4×D7).9(C2×C4), C2.27(D7×C22×C4), (C7×Q8).16(C2×C4), (C2×C4×D7).69C22, C4⋊C4⋊7D7.10C2, (C7×C4⋊C4).344C22, (C2×C4).288(C22×D7), SmallGroup(448,1025)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 932 in 266 conjugacy classes, 151 normal (22 characteristic)
C1, C2 [×3], C2 [×2], C4 [×6], C4 [×14], C22, C22 [×4], C7, C2×C4, C2×C4 [×6], C2×C4 [×19], Q8 [×4], Q8 [×12], C23, D7 [×2], C14 [×3], C42 [×3], C42 [×9], C22⋊C4 [×4], C4⋊C4 [×3], C4⋊C4 [×9], C22×C4 [×3], C2×Q8, C2×Q8 [×11], Dic7 [×6], Dic7 [×4], C28 [×6], C28 [×4], D14 [×2], D14 [×2], C2×C14, C42⋊C2 [×6], C4×Q8, C4×Q8 [×7], C22×Q8, Dic14 [×12], C4×D7 [×12], C2×Dic7, C2×Dic7 [×6], C2×C28, C2×C28 [×6], C7×Q8 [×4], C22×D7, C23.32C23, C4×Dic7 [×9], Dic7⋊C4 [×6], C4⋊Dic7 [×3], D14⋊C4, D14⋊C4 [×3], C4×C28 [×3], C7×C4⋊C4 [×3], C2×Dic14 [×3], C2×C4×D7 [×3], Q8×D7 [×8], Q8×C14, C4×Dic14 [×3], C42⋊D7 [×3], Dic7⋊3Q8 [×3], C4⋊C4⋊7D7 [×3], Q8×Dic7, Q8×C28, C2×Q8×D7, C42.125D14
Quotients:
C1, C2 [×15], C4 [×8], C22 [×35], C2×C4 [×28], C23 [×15], D7, C22×C4 [×14], C24, D14 [×7], C23×C4, 2- (1+4) [×2], C4×D7 [×4], C22×D7 [×7], C23.32C23, C2×C4×D7 [×6], C23×D7, D7×C22×C4, Q8.10D14, D4.10D14, C42.125D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=d2=a2, ab=ba, cac-1=dad-1=a-1, bc=cb, dbd-1=a2b, dcd-1=c13 >
►On 224 points
Generators in S224
(1 164 15 150)(2 151 16 165)(3 166 17 152)(4 153 18 167)(5 168 19 154)(6 155 20 141)(7 142 21 156)(8 157 22 143)(9 144 23 158)(10 159 24 145)(11 146 25 160)(12 161 26 147)(13 148 27 162)(14 163 28 149)(29 84 43 70)(30 71 44 57)(31 58 45 72)(32 73 46 59)(33 60 47 74)(34 75 48 61)(35 62 49 76)(36 77 50 63)(37 64 51 78)(38 79 52 65)(39 66 53 80)(40 81 54 67)(41 68 55 82)(42 83 56 69)(85 131 99 117)(86 118 100 132)(87 133 101 119)(88 120 102 134)(89 135 103 121)(90 122 104 136)(91 137 105 123)(92 124 106 138)(93 139 107 125)(94 126 108 140)(95 113 109 127)(96 128 110 114)(97 115 111 129)(98 130 112 116)(169 202 183 216)(170 217 184 203)(171 204 185 218)(172 219 186 205)(173 206 187 220)(174 221 188 207)(175 208 189 222)(176 223 190 209)(177 210 191 224)(178 197 192 211)(179 212 193 198)(180 199 194 213)(181 214 195 200)(182 201 196 215)
(1 60 105 205)(2 61 106 206)(3 62 107 207)(4 63 108 208)(5 64 109 209)(6 65 110 210)(7 66 111 211)(8 67 112 212)(9 68 85 213)(10 69 86 214)(11 70 87 215)(12 71 88 216)(13 72 89 217)(14 73 90 218)(15 74 91 219)(16 75 92 220)(17 76 93 221)(18 77 94 222)(19 78 95 223)(20 79 96 224)(21 80 97 197)(22 81 98 198)(23 82 99 199)(24 83 100 200)(25 84 101 201)(26 57 102 202)(27 58 103 203)(28 59 104 204)(29 133 182 146)(30 134 183 147)(31 135 184 148)(32 136 185 149)(33 137 186 150)(34 138 187 151)(35 139 188 152)(36 140 189 153)(37 113 190 154)(38 114 191 155)(39 115 192 156)(40 116 193 157)(41 117 194 158)(42 118 195 159)(43 119 196 160)(44 120 169 161)(45 121 170 162)(46 122 171 163)(47 123 172 164)(48 124 173 165)(49 125 174 166)(50 126 175 167)(51 127 176 168)(52 128 177 141)(53 129 178 142)(54 130 179 143)(55 131 180 144)(56 132 181 145)
(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 90 15 104)(2 103 16 89)(3 88 17 102)(4 101 18 87)(5 86 19 100)(6 99 20 85)(7 112 21 98)(8 97 22 111)(9 110 23 96)(10 95 24 109)(11 108 25 94)(12 93 26 107)(13 106 27 92)(14 91 28 105)(29 189 43 175)(30 174 44 188)(31 187 45 173)(32 172 46 186)(33 185 47 171)(34 170 48 184)(35 183 49 169)(36 196 50 182)(37 181 51 195)(38 194 52 180)(39 179 53 193)(40 192 54 178)(41 177 55 191)(42 190 56 176)(57 221 71 207)(58 206 72 220)(59 219 73 205)(60 204 74 218)(61 217 75 203)(62 202 76 216)(63 215 77 201)(64 200 78 214)(65 213 79 199)(66 198 80 212)(67 211 81 197)(68 224 82 210)(69 209 83 223)(70 222 84 208)(113 159 127 145)(114 144 128 158)(115 157 129 143)(116 142 130 156)(117 155 131 141)(118 168 132 154)(119 153 133 167)(120 166 134 152)(121 151 135 165)(122 164 136 150)(123 149 137 163)(124 162 138 148)(125 147 139 161)(126 160 140 146)
G:=sub<Sym(224)| (1,164,15,150)(2,151,16,165)(3,166,17,152)(4,153,18,167)(5,168,19,154)(6,155,20,141)(7,142,21,156)(8,157,22,143)(9,144,23,158)(10,159,24,145)(11,146,25,160)(12,161,26,147)(13,148,27,162)(14,163,28,149)(29,84,43,70)(30,71,44,57)(31,58,45,72)(32,73,46,59)(33,60,47,74)(34,75,48,61)(35,62,49,76)(36,77,50,63)(37,64,51,78)(38,79,52,65)(39,66,53,80)(40,81,54,67)(41,68,55,82)(42,83,56,69)(85,131,99,117)(86,118,100,132)(87,133,101,119)(88,120,102,134)(89,135,103,121)(90,122,104,136)(91,137,105,123)(92,124,106,138)(93,139,107,125)(94,126,108,140)(95,113,109,127)(96,128,110,114)(97,115,111,129)(98,130,112,116)(169,202,183,216)(170,217,184,203)(171,204,185,218)(172,219,186,205)(173,206,187,220)(174,221,188,207)(175,208,189,222)(176,223,190,209)(177,210,191,224)(178,197,192,211)(179,212,193,198)(180,199,194,213)(181,214,195,200)(182,201,196,215), (1,60,105,205)(2,61,106,206)(3,62,107,207)(4,63,108,208)(5,64,109,209)(6,65,110,210)(7,66,111,211)(8,67,112,212)(9,68,85,213)(10,69,86,214)(11,70,87,215)(12,71,88,216)(13,72,89,217)(14,73,90,218)(15,74,91,219)(16,75,92,220)(17,76,93,221)(18,77,94,222)(19,78,95,223)(20,79,96,224)(21,80,97,197)(22,81,98,198)(23,82,99,199)(24,83,100,200)(25,84,101,201)(26,57,102,202)(27,58,103,203)(28,59,104,204)(29,133,182,146)(30,134,183,147)(31,135,184,148)(32,136,185,149)(33,137,186,150)(34,138,187,151)(35,139,188,152)(36,140,189,153)(37,113,190,154)(38,114,191,155)(39,115,192,156)(40,116,193,157)(41,117,194,158)(42,118,195,159)(43,119,196,160)(44,120,169,161)(45,121,170,162)(46,122,171,163)(47,123,172,164)(48,124,173,165)(49,125,174,166)(50,126,175,167)(51,127,176,168)(52,128,177,141)(53,129,178,142)(54,130,179,143)(55,131,180,144)(56,132,181,145), (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), (1,90,15,104)(2,103,16,89)(3,88,17,102)(4,101,18,87)(5,86,19,100)(6,99,20,85)(7,112,21,98)(8,97,22,111)(9,110,23,96)(10,95,24,109)(11,108,25,94)(12,93,26,107)(13,106,27,92)(14,91,28,105)(29,189,43,175)(30,174,44,188)(31,187,45,173)(32,172,46,186)(33,185,47,171)(34,170,48,184)(35,183,49,169)(36,196,50,182)(37,181,51,195)(38,194,52,180)(39,179,53,193)(40,192,54,178)(41,177,55,191)(42,190,56,176)(57,221,71,207)(58,206,72,220)(59,219,73,205)(60,204,74,218)(61,217,75,203)(62,202,76,216)(63,215,77,201)(64,200,78,214)(65,213,79,199)(66,198,80,212)(67,211,81,197)(68,224,82,210)(69,209,83,223)(70,222,84,208)(113,159,127,145)(114,144,128,158)(115,157,129,143)(116,142,130,156)(117,155,131,141)(118,168,132,154)(119,153,133,167)(120,166,134,152)(121,151,135,165)(122,164,136,150)(123,149,137,163)(124,162,138,148)(125,147,139,161)(126,160,140,146)>;
G:=Group( (1,164,15,150)(2,151,16,165)(3,166,17,152)(4,153,18,167)(5,168,19,154)(6,155,20,141)(7,142,21,156)(8,157,22,143)(9,144,23,158)(10,159,24,145)(11,146,25,160)(12,161,26,147)(13,148,27,162)(14,163,28,149)(29,84,43,70)(30,71,44,57)(31,58,45,72)(32,73,46,59)(33,60,47,74)(34,75,48,61)(35,62,49,76)(36,77,50,63)(37,64,51,78)(38,79,52,65)(39,66,53,80)(40,81,54,67)(41,68,55,82)(42,83,56,69)(85,131,99,117)(86,118,100,132)(87,133,101,119)(88,120,102,134)(89,135,103,121)(90,122,104,136)(91,137,105,123)(92,124,106,138)(93,139,107,125)(94,126,108,140)(95,113,109,127)(96,128,110,114)(97,115,111,129)(98,130,112,116)(169,202,183,216)(170,217,184,203)(171,204,185,218)(172,219,186,205)(173,206,187,220)(174,221,188,207)(175,208,189,222)(176,223,190,209)(177,210,191,224)(178,197,192,211)(179,212,193,198)(180,199,194,213)(181,214,195,200)(182,201,196,215), (1,60,105,205)(2,61,106,206)(3,62,107,207)(4,63,108,208)(5,64,109,209)(6,65,110,210)(7,66,111,211)(8,67,112,212)(9,68,85,213)(10,69,86,214)(11,70,87,215)(12,71,88,216)(13,72,89,217)(14,73,90,218)(15,74,91,219)(16,75,92,220)(17,76,93,221)(18,77,94,222)(19,78,95,223)(20,79,96,224)(21,80,97,197)(22,81,98,198)(23,82,99,199)(24,83,100,200)(25,84,101,201)(26,57,102,202)(27,58,103,203)(28,59,104,204)(29,133,182,146)(30,134,183,147)(31,135,184,148)(32,136,185,149)(33,137,186,150)(34,138,187,151)(35,139,188,152)(36,140,189,153)(37,113,190,154)(38,114,191,155)(39,115,192,156)(40,116,193,157)(41,117,194,158)(42,118,195,159)(43,119,196,160)(44,120,169,161)(45,121,170,162)(46,122,171,163)(47,123,172,164)(48,124,173,165)(49,125,174,166)(50,126,175,167)(51,127,176,168)(52,128,177,141)(53,129,178,142)(54,130,179,143)(55,131,180,144)(56,132,181,145), (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), (1,90,15,104)(2,103,16,89)(3,88,17,102)(4,101,18,87)(5,86,19,100)(6,99,20,85)(7,112,21,98)(8,97,22,111)(9,110,23,96)(10,95,24,109)(11,108,25,94)(12,93,26,107)(13,106,27,92)(14,91,28,105)(29,189,43,175)(30,174,44,188)(31,187,45,173)(32,172,46,186)(33,185,47,171)(34,170,48,184)(35,183,49,169)(36,196,50,182)(37,181,51,195)(38,194,52,180)(39,179,53,193)(40,192,54,178)(41,177,55,191)(42,190,56,176)(57,221,71,207)(58,206,72,220)(59,219,73,205)(60,204,74,218)(61,217,75,203)(62,202,76,216)(63,215,77,201)(64,200,78,214)(65,213,79,199)(66,198,80,212)(67,211,81,197)(68,224,82,210)(69,209,83,223)(70,222,84,208)(113,159,127,145)(114,144,128,158)(115,157,129,143)(116,142,130,156)(117,155,131,141)(118,168,132,154)(119,153,133,167)(120,166,134,152)(121,151,135,165)(122,164,136,150)(123,149,137,163)(124,162,138,148)(125,147,139,161)(126,160,140,146) );
G=PermutationGroup([(1,164,15,150),(2,151,16,165),(3,166,17,152),(4,153,18,167),(5,168,19,154),(6,155,20,141),(7,142,21,156),(8,157,22,143),(9,144,23,158),(10,159,24,145),(11,146,25,160),(12,161,26,147),(13,148,27,162),(14,163,28,149),(29,84,43,70),(30,71,44,57),(31,58,45,72),(32,73,46,59),(33,60,47,74),(34,75,48,61),(35,62,49,76),(36,77,50,63),(37,64,51,78),(38,79,52,65),(39,66,53,80),(40,81,54,67),(41,68,55,82),(42,83,56,69),(85,131,99,117),(86,118,100,132),(87,133,101,119),(88,120,102,134),(89,135,103,121),(90,122,104,136),(91,137,105,123),(92,124,106,138),(93,139,107,125),(94,126,108,140),(95,113,109,127),(96,128,110,114),(97,115,111,129),(98,130,112,116),(169,202,183,216),(170,217,184,203),(171,204,185,218),(172,219,186,205),(173,206,187,220),(174,221,188,207),(175,208,189,222),(176,223,190,209),(177,210,191,224),(178,197,192,211),(179,212,193,198),(180,199,194,213),(181,214,195,200),(182,201,196,215)], [(1,60,105,205),(2,61,106,206),(3,62,107,207),(4,63,108,208),(5,64,109,209),(6,65,110,210),(7,66,111,211),(8,67,112,212),(9,68,85,213),(10,69,86,214),(11,70,87,215),(12,71,88,216),(13,72,89,217),(14,73,90,218),(15,74,91,219),(16,75,92,220),(17,76,93,221),(18,77,94,222),(19,78,95,223),(20,79,96,224),(21,80,97,197),(22,81,98,198),(23,82,99,199),(24,83,100,200),(25,84,101,201),(26,57,102,202),(27,58,103,203),(28,59,104,204),(29,133,182,146),(30,134,183,147),(31,135,184,148),(32,136,185,149),(33,137,186,150),(34,138,187,151),(35,139,188,152),(36,140,189,153),(37,113,190,154),(38,114,191,155),(39,115,192,156),(40,116,193,157),(41,117,194,158),(42,118,195,159),(43,119,196,160),(44,120,169,161),(45,121,170,162),(46,122,171,163),(47,123,172,164),(48,124,173,165),(49,125,174,166),(50,126,175,167),(51,127,176,168),(52,128,177,141),(53,129,178,142),(54,130,179,143),(55,131,180,144),(56,132,181,145)], [(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)], [(1,90,15,104),(2,103,16,89),(3,88,17,102),(4,101,18,87),(5,86,19,100),(6,99,20,85),(7,112,21,98),(8,97,22,111),(9,110,23,96),(10,95,24,109),(11,108,25,94),(12,93,26,107),(13,106,27,92),(14,91,28,105),(29,189,43,175),(30,174,44,188),(31,187,45,173),(32,172,46,186),(33,185,47,171),(34,170,48,184),(35,183,49,169),(36,196,50,182),(37,181,51,195),(38,194,52,180),(39,179,53,193),(40,192,54,178),(41,177,55,191),(42,190,56,176),(57,221,71,207),(58,206,72,220),(59,219,73,205),(60,204,74,218),(61,217,75,203),(62,202,76,216),(63,215,77,201),(64,200,78,214),(65,213,79,199),(66,198,80,212),(67,211,81,197),(68,224,82,210),(69,209,83,223),(70,222,84,208),(113,159,127,145),(114,144,128,158),(115,157,129,143),(116,142,130,156),(117,155,131,141),(118,168,132,154),(119,153,133,167),(120,166,134,152),(121,151,135,165),(122,164,136,150),(123,149,137,163),(124,162,138,148),(125,147,139,161),(126,160,140,146)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 18 | 0 | 0 |
| 0 | 0 | 11 | 27 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 18 |
| 0 | 0 | 0 | 0 | 11 | 27 |
| 2 | 8 | 0 | 0 | 0 | 0 |
| 13 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 21 | 21 |
| 0 | 0 | 0 | 0 | 8 | 26 |
| 0 | 0 | 8 | 8 | 0 | 0 |
| 0 | 0 | 21 | 3 | 0 | 0 |
| 8 | 28 | 0 | 0 | 0 | 0 |
| 5 | 21 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 8 |
| 0 | 0 | 0 | 0 | 3 | 21 |
| 0 | 0 | 21 | 21 | 0 | 0 |
| 0 | 0 | 26 | 8 | 0 | 0 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,12,0,0,0,0,0,0,12,0,0],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,2,11,0,0,0,0,18,27,0,0,0,0,0,0,2,11,0,0,0,0,18,27],[2,13,0,0,0,0,8,9,0,0,0,0,0,0,0,0,8,21,0,0,0,0,8,3,0,0,21,8,0,0,0,0,21,26,0,0],[8,5,0,0,0,0,28,21,0,0,0,0,0,0,0,0,21,26,0,0,0,0,21,8,0,0,8,3,0,0,0,0,8,21,0,0] >;
94 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4N | 4O | ··· | 4AB | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 2 | ··· | 2 | 14 | ··· | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
94 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | D7 | D14 | D14 | D14 | C4×D7 | 2- (1+4) | Q8.10D14 | D4.10D14 |
| kernel | C42.125D14 | C4×Dic14 | C42⋊D7 | Dic7⋊3Q8 | C4⋊C4⋊7D7 | Q8×Dic7 | Q8×C28 | C2×Q8×D7 | Q8×D7 | C4×Q8 | C42 | C4⋊C4 | C2×Q8 | Q8 | C14 | C2 | C2 |
| # reps | 1 | 3 | 3 | 3 | 3 | 1 | 1 | 1 | 16 | 3 | 9 | 9 | 3 | 24 | 2 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{125}D_{14} % in TeX
G:=Group("C4^2.125D14"); // GroupNames label
G:=SmallGroup(448,1025);
// by ID
G=gap.SmallGroup(448,1025);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,387,184,1123,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,b*c=c*b,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations
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