metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.141D14, C14.902- (1+4), C4.33(D4×D7), (C4×D7).12D4, C28.62(C2×D4), C4.4D4⋊9D7, C28⋊2Q8⋊30C2, D14.46(C2×D4), (C2×D4).172D14, C42⋊D7⋊20C2, (C2×C28).80C23, (C2×Q8).136D14, C22⋊C4.35D14, Dic7.51(C2×D4), C14.89(C22×D4), Dic7⋊Q8⋊24C2, D14.D4⋊41C2, C28.17D4⋊24C2, (C2×C14).219C24, (C4×C28).185C22, C4⋊Dic7.51C22, C23.41(C22×D7), D14⋊C4.110C22, C22⋊Dic14⋊40C2, (D4×C14).154C22, (C22×C14).49C23, (Q8×C14).126C22, C22.240(C23×D7), C23.D7.54C22, Dic7⋊C4.120C22, C7⋊4(C23.38C23), (C2×Dic7).114C23, (C4×Dic7).133C22, (C22×D7).214C23, C2.51(D4.10D14), (C2×Dic14).177C22, (C22×Dic7).142C22, (C2×Q8×D7)⋊10C2, C2.62(C2×D4×D7), (C2×D4⋊2D7).9C2, (C7×C4.4D4)⋊11C2, (C2×C4×D7).120C22, (C2×C4).194(C22×D7), (C2×C7⋊D4).59C22, (C7×C22⋊C4).64C22, SmallGroup(448,1128)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1196 in 270 conjugacy classes, 103 normal (29 characteristic)
C1, C2, C2 [×2], C2 [×4], C4 [×2], C4 [×12], C22, C22 [×10], C7, C2×C4, C2×C4 [×4], C2×C4 [×19], D4 [×6], Q8 [×10], C23 [×2], C23, D7 [×2], C14, C14 [×2], C14 [×2], C42, C42, C22⋊C4 [×4], C22⋊C4 [×6], C4⋊C4 [×10], C22×C4 [×5], C2×D4, C2×D4 [×2], C2×Q8, C2×Q8 [×8], C4○D4 [×4], Dic7 [×2], Dic7 [×6], C28 [×2], C28 [×4], D14 [×2], D14 [×2], C2×C14, C2×C14 [×6], C42⋊C2, C22⋊Q8 [×4], C22.D4 [×4], C4.4D4, C4.4D4, C4⋊Q8 [×2], C22×Q8, C2×C4○D4, Dic14 [×8], C4×D7 [×4], C4×D7 [×4], C2×Dic7, C2×Dic7 [×6], C2×Dic7 [×4], C7⋊D4 [×4], C2×C28, C2×C28 [×4], C7×D4 [×2], C7×Q8 [×2], C22×D7, C22×C14 [×2], C23.38C23, C4×Dic7, Dic7⋊C4 [×6], C4⋊Dic7 [×4], D14⋊C4 [×2], C23.D7 [×4], C4×C28, C7×C22⋊C4 [×4], C2×Dic14 [×2], C2×Dic14 [×2], C2×C4×D7, C2×C4×D7 [×2], D4⋊2D7 [×4], Q8×D7 [×4], C22×Dic7 [×2], C2×C7⋊D4 [×2], D4×C14, Q8×C14, C28⋊2Q8, C42⋊D7, C22⋊Dic14 [×4], D14.D4 [×4], C28.17D4, Dic7⋊Q8, C7×C4.4D4, C2×D4⋊2D7, C2×Q8×D7, C42.141D14
Quotients:
C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D7, C2×D4 [×6], C24, D14 [×7], C22×D4, 2- (1+4) [×2], C22×D7 [×7], C23.38C23, D4×D7 [×2], C23×D7, C2×D4×D7, D4.10D14 [×2], C42.141D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=d2=a2, ab=ba, cac-1=dad-1=a-1, cbc-1=a2b-1, dbd-1=b-1, dcd-1=c13 >
►On 224 points
Generators in S224
(1 117 15 131)(2 132 16 118)(3 119 17 133)(4 134 18 120)(5 121 19 135)(6 136 20 122)(7 123 21 137)(8 138 22 124)(9 125 23 139)(10 140 24 126)(11 127 25 113)(12 114 26 128)(13 129 27 115)(14 116 28 130)(29 144 43 158)(30 159 44 145)(31 146 45 160)(32 161 46 147)(33 148 47 162)(34 163 48 149)(35 150 49 164)(36 165 50 151)(37 152 51 166)(38 167 52 153)(39 154 53 168)(40 141 54 155)(41 156 55 142)(42 143 56 157)(57 176 71 190)(58 191 72 177)(59 178 73 192)(60 193 74 179)(61 180 75 194)(62 195 76 181)(63 182 77 196)(64 169 78 183)(65 184 79 170)(66 171 80 185)(67 186 81 172)(68 173 82 187)(69 188 83 174)(70 175 84 189)(85 201 99 215)(86 216 100 202)(87 203 101 217)(88 218 102 204)(89 205 103 219)(90 220 104 206)(91 207 105 221)(92 222 106 208)(93 209 107 223)(94 224 108 210)(95 211 109 197)(96 198 110 212)(97 213 111 199)(98 200 112 214)
(1 64 223 153)(2 168 224 79)(3 66 197 155)(4 142 198 81)(5 68 199 157)(6 144 200 83)(7 70 201 159)(8 146 202 57)(9 72 203 161)(10 148 204 59)(11 74 205 163)(12 150 206 61)(13 76 207 165)(14 152 208 63)(15 78 209 167)(16 154 210 65)(17 80 211 141)(18 156 212 67)(19 82 213 143)(20 158 214 69)(21 84 215 145)(22 160 216 71)(23 58 217 147)(24 162 218 73)(25 60 219 149)(26 164 220 75)(27 62 221 151)(28 166 222 77)(29 98 188 122)(30 137 189 85)(31 100 190 124)(32 139 191 87)(33 102 192 126)(34 113 193 89)(35 104 194 128)(36 115 195 91)(37 106 196 130)(38 117 169 93)(39 108 170 132)(40 119 171 95)(41 110 172 134)(42 121 173 97)(43 112 174 136)(44 123 175 99)(45 86 176 138)(46 125 177 101)(47 88 178 140)(48 127 179 103)(49 90 180 114)(50 129 181 105)(51 92 182 116)(52 131 183 107)(53 94 184 118)(54 133 185 109)(55 96 186 120)(56 135 187 111)
(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 14 15 28)(2 27 16 13)(3 12 17 26)(4 25 18 11)(5 10 19 24)(6 23 20 9)(7 8 21 22)(29 32 43 46)(30 45 44 31)(33 56 47 42)(34 41 48 55)(35 54 49 40)(36 39 50 53)(37 52 51 38)(57 84 71 70)(58 69 72 83)(59 82 73 68)(60 67 74 81)(61 80 75 66)(62 65 76 79)(63 78 77 64)(85 86 99 100)(87 112 101 98)(88 97 102 111)(89 110 103 96)(90 95 104 109)(91 108 105 94)(92 93 106 107)(113 134 127 120)(114 119 128 133)(115 132 129 118)(116 117 130 131)(121 126 135 140)(122 139 136 125)(123 124 137 138)(141 164 155 150)(142 149 156 163)(143 162 157 148)(144 147 158 161)(145 160 159 146)(151 154 165 168)(152 167 166 153)(169 196 183 182)(170 181 184 195)(171 194 185 180)(172 179 186 193)(173 192 187 178)(174 177 188 191)(175 190 189 176)(197 206 211 220)(198 219 212 205)(199 204 213 218)(200 217 214 203)(201 202 215 216)(207 224 221 210)(208 209 222 223)
G:=sub<Sym(224)| (1,117,15,131)(2,132,16,118)(3,119,17,133)(4,134,18,120)(5,121,19,135)(6,136,20,122)(7,123,21,137)(8,138,22,124)(9,125,23,139)(10,140,24,126)(11,127,25,113)(12,114,26,128)(13,129,27,115)(14,116,28,130)(29,144,43,158)(30,159,44,145)(31,146,45,160)(32,161,46,147)(33,148,47,162)(34,163,48,149)(35,150,49,164)(36,165,50,151)(37,152,51,166)(38,167,52,153)(39,154,53,168)(40,141,54,155)(41,156,55,142)(42,143,56,157)(57,176,71,190)(58,191,72,177)(59,178,73,192)(60,193,74,179)(61,180,75,194)(62,195,76,181)(63,182,77,196)(64,169,78,183)(65,184,79,170)(66,171,80,185)(67,186,81,172)(68,173,82,187)(69,188,83,174)(70,175,84,189)(85,201,99,215)(86,216,100,202)(87,203,101,217)(88,218,102,204)(89,205,103,219)(90,220,104,206)(91,207,105,221)(92,222,106,208)(93,209,107,223)(94,224,108,210)(95,211,109,197)(96,198,110,212)(97,213,111,199)(98,200,112,214), (1,64,223,153)(2,168,224,79)(3,66,197,155)(4,142,198,81)(5,68,199,157)(6,144,200,83)(7,70,201,159)(8,146,202,57)(9,72,203,161)(10,148,204,59)(11,74,205,163)(12,150,206,61)(13,76,207,165)(14,152,208,63)(15,78,209,167)(16,154,210,65)(17,80,211,141)(18,156,212,67)(19,82,213,143)(20,158,214,69)(21,84,215,145)(22,160,216,71)(23,58,217,147)(24,162,218,73)(25,60,219,149)(26,164,220,75)(27,62,221,151)(28,166,222,77)(29,98,188,122)(30,137,189,85)(31,100,190,124)(32,139,191,87)(33,102,192,126)(34,113,193,89)(35,104,194,128)(36,115,195,91)(37,106,196,130)(38,117,169,93)(39,108,170,132)(40,119,171,95)(41,110,172,134)(42,121,173,97)(43,112,174,136)(44,123,175,99)(45,86,176,138)(46,125,177,101)(47,88,178,140)(48,127,179,103)(49,90,180,114)(50,129,181,105)(51,92,182,116)(52,131,183,107)(53,94,184,118)(54,133,185,109)(55,96,186,120)(56,135,187,111), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,32,43,46)(30,45,44,31)(33,56,47,42)(34,41,48,55)(35,54,49,40)(36,39,50,53)(37,52,51,38)(57,84,71,70)(58,69,72,83)(59,82,73,68)(60,67,74,81)(61,80,75,66)(62,65,76,79)(63,78,77,64)(85,86,99,100)(87,112,101,98)(88,97,102,111)(89,110,103,96)(90,95,104,109)(91,108,105,94)(92,93,106,107)(113,134,127,120)(114,119,128,133)(115,132,129,118)(116,117,130,131)(121,126,135,140)(122,139,136,125)(123,124,137,138)(141,164,155,150)(142,149,156,163)(143,162,157,148)(144,147,158,161)(145,160,159,146)(151,154,165,168)(152,167,166,153)(169,196,183,182)(170,181,184,195)(171,194,185,180)(172,179,186,193)(173,192,187,178)(174,177,188,191)(175,190,189,176)(197,206,211,220)(198,219,212,205)(199,204,213,218)(200,217,214,203)(201,202,215,216)(207,224,221,210)(208,209,222,223)>;
G:=Group( (1,117,15,131)(2,132,16,118)(3,119,17,133)(4,134,18,120)(5,121,19,135)(6,136,20,122)(7,123,21,137)(8,138,22,124)(9,125,23,139)(10,140,24,126)(11,127,25,113)(12,114,26,128)(13,129,27,115)(14,116,28,130)(29,144,43,158)(30,159,44,145)(31,146,45,160)(32,161,46,147)(33,148,47,162)(34,163,48,149)(35,150,49,164)(36,165,50,151)(37,152,51,166)(38,167,52,153)(39,154,53,168)(40,141,54,155)(41,156,55,142)(42,143,56,157)(57,176,71,190)(58,191,72,177)(59,178,73,192)(60,193,74,179)(61,180,75,194)(62,195,76,181)(63,182,77,196)(64,169,78,183)(65,184,79,170)(66,171,80,185)(67,186,81,172)(68,173,82,187)(69,188,83,174)(70,175,84,189)(85,201,99,215)(86,216,100,202)(87,203,101,217)(88,218,102,204)(89,205,103,219)(90,220,104,206)(91,207,105,221)(92,222,106,208)(93,209,107,223)(94,224,108,210)(95,211,109,197)(96,198,110,212)(97,213,111,199)(98,200,112,214), (1,64,223,153)(2,168,224,79)(3,66,197,155)(4,142,198,81)(5,68,199,157)(6,144,200,83)(7,70,201,159)(8,146,202,57)(9,72,203,161)(10,148,204,59)(11,74,205,163)(12,150,206,61)(13,76,207,165)(14,152,208,63)(15,78,209,167)(16,154,210,65)(17,80,211,141)(18,156,212,67)(19,82,213,143)(20,158,214,69)(21,84,215,145)(22,160,216,71)(23,58,217,147)(24,162,218,73)(25,60,219,149)(26,164,220,75)(27,62,221,151)(28,166,222,77)(29,98,188,122)(30,137,189,85)(31,100,190,124)(32,139,191,87)(33,102,192,126)(34,113,193,89)(35,104,194,128)(36,115,195,91)(37,106,196,130)(38,117,169,93)(39,108,170,132)(40,119,171,95)(41,110,172,134)(42,121,173,97)(43,112,174,136)(44,123,175,99)(45,86,176,138)(46,125,177,101)(47,88,178,140)(48,127,179,103)(49,90,180,114)(50,129,181,105)(51,92,182,116)(52,131,183,107)(53,94,184,118)(54,133,185,109)(55,96,186,120)(56,135,187,111), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,32,43,46)(30,45,44,31)(33,56,47,42)(34,41,48,55)(35,54,49,40)(36,39,50,53)(37,52,51,38)(57,84,71,70)(58,69,72,83)(59,82,73,68)(60,67,74,81)(61,80,75,66)(62,65,76,79)(63,78,77,64)(85,86,99,100)(87,112,101,98)(88,97,102,111)(89,110,103,96)(90,95,104,109)(91,108,105,94)(92,93,106,107)(113,134,127,120)(114,119,128,133)(115,132,129,118)(116,117,130,131)(121,126,135,140)(122,139,136,125)(123,124,137,138)(141,164,155,150)(142,149,156,163)(143,162,157,148)(144,147,158,161)(145,160,159,146)(151,154,165,168)(152,167,166,153)(169,196,183,182)(170,181,184,195)(171,194,185,180)(172,179,186,193)(173,192,187,178)(174,177,188,191)(175,190,189,176)(197,206,211,220)(198,219,212,205)(199,204,213,218)(200,217,214,203)(201,202,215,216)(207,224,221,210)(208,209,222,223) );
G=PermutationGroup([(1,117,15,131),(2,132,16,118),(3,119,17,133),(4,134,18,120),(5,121,19,135),(6,136,20,122),(7,123,21,137),(8,138,22,124),(9,125,23,139),(10,140,24,126),(11,127,25,113),(12,114,26,128),(13,129,27,115),(14,116,28,130),(29,144,43,158),(30,159,44,145),(31,146,45,160),(32,161,46,147),(33,148,47,162),(34,163,48,149),(35,150,49,164),(36,165,50,151),(37,152,51,166),(38,167,52,153),(39,154,53,168),(40,141,54,155),(41,156,55,142),(42,143,56,157),(57,176,71,190),(58,191,72,177),(59,178,73,192),(60,193,74,179),(61,180,75,194),(62,195,76,181),(63,182,77,196),(64,169,78,183),(65,184,79,170),(66,171,80,185),(67,186,81,172),(68,173,82,187),(69,188,83,174),(70,175,84,189),(85,201,99,215),(86,216,100,202),(87,203,101,217),(88,218,102,204),(89,205,103,219),(90,220,104,206),(91,207,105,221),(92,222,106,208),(93,209,107,223),(94,224,108,210),(95,211,109,197),(96,198,110,212),(97,213,111,199),(98,200,112,214)], [(1,64,223,153),(2,168,224,79),(3,66,197,155),(4,142,198,81),(5,68,199,157),(6,144,200,83),(7,70,201,159),(8,146,202,57),(9,72,203,161),(10,148,204,59),(11,74,205,163),(12,150,206,61),(13,76,207,165),(14,152,208,63),(15,78,209,167),(16,154,210,65),(17,80,211,141),(18,156,212,67),(19,82,213,143),(20,158,214,69),(21,84,215,145),(22,160,216,71),(23,58,217,147),(24,162,218,73),(25,60,219,149),(26,164,220,75),(27,62,221,151),(28,166,222,77),(29,98,188,122),(30,137,189,85),(31,100,190,124),(32,139,191,87),(33,102,192,126),(34,113,193,89),(35,104,194,128),(36,115,195,91),(37,106,196,130),(38,117,169,93),(39,108,170,132),(40,119,171,95),(41,110,172,134),(42,121,173,97),(43,112,174,136),(44,123,175,99),(45,86,176,138),(46,125,177,101),(47,88,178,140),(48,127,179,103),(49,90,180,114),(50,129,181,105),(51,92,182,116),(52,131,183,107),(53,94,184,118),(54,133,185,109),(55,96,186,120),(56,135,187,111)], [(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)], [(1,14,15,28),(2,27,16,13),(3,12,17,26),(4,25,18,11),(5,10,19,24),(6,23,20,9),(7,8,21,22),(29,32,43,46),(30,45,44,31),(33,56,47,42),(34,41,48,55),(35,54,49,40),(36,39,50,53),(37,52,51,38),(57,84,71,70),(58,69,72,83),(59,82,73,68),(60,67,74,81),(61,80,75,66),(62,65,76,79),(63,78,77,64),(85,86,99,100),(87,112,101,98),(88,97,102,111),(89,110,103,96),(90,95,104,109),(91,108,105,94),(92,93,106,107),(113,134,127,120),(114,119,128,133),(115,132,129,118),(116,117,130,131),(121,126,135,140),(122,139,136,125),(123,124,137,138),(141,164,155,150),(142,149,156,163),(143,162,157,148),(144,147,158,161),(145,160,159,146),(151,154,165,168),(152,167,166,153),(169,196,183,182),(170,181,184,195),(171,194,185,180),(172,179,186,193),(173,192,187,178),(174,177,188,191),(175,190,189,176),(197,206,211,220),(198,219,212,205),(199,204,213,218),(200,217,214,203),(201,202,215,216),(207,224,221,210),(208,209,222,223)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 21 | 24 |
| 0 | 0 | 0 | 0 | 13 | 8 |
| 0 | 0 | 21 | 24 | 0 | 0 |
| 0 | 0 | 13 | 8 | 0 | 0 |
| 11 | 7 | 0 | 0 | 0 | 0 |
| 24 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 23 | 25 | 0 | 0 | 0 | 0 |
| 16 | 6 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 10 | 0 | 0 |
| 0 | 0 | 3 | 26 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 19 |
| 0 | 0 | 0 | 0 | 26 | 3 |
| 6 | 4 | 0 | 0 | 0 | 0 |
| 13 | 23 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 10 | 0 | 0 |
| 0 | 0 | 28 | 26 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 10 |
| 0 | 0 | 0 | 0 | 28 | 26 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,21,13,0,0,0,0,24,8,0,0,21,13,0,0,0,0,24,8,0,0],[11,24,0,0,0,0,7,18,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,1,0,0],[23,16,0,0,0,0,25,6,0,0,0,0,0,0,0,3,0,0,0,0,10,26,0,0,0,0,0,0,0,26,0,0,0,0,19,3],[6,13,0,0,0,0,4,23,0,0,0,0,0,0,3,28,0,0,0,0,10,26,0,0,0,0,0,0,3,28,0,0,0,0,10,26] >;
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4N | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 2 | 2 | 4 | 4 | 4 | 4 | 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 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | D14 | D14 | D14 | D14 | 2- (1+4) | D4×D7 | D4.10D14 |
| kernel | C42.141D14 | C28⋊2Q8 | C42⋊D7 | C22⋊Dic14 | D14.D4 | C28.17D4 | Dic7⋊Q8 | C7×C4.4D4 | C2×D4⋊2D7 | C2×Q8×D7 | C4×D7 | C4.4D4 | C42 | C22⋊C4 | C2×D4 | C2×Q8 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 4 | 4 | 1 | 1 | 1 | 1 | 1 | 4 | 3 | 3 | 12 | 3 | 3 | 2 | 6 | 12 |
In GAP, Magma, Sage, TeX
C_4^2._{141}D_{14} % in TeX
G:=Group("C4^2.141D14"); // GroupNames label
G:=SmallGroup(448,1128);
// by ID
G=gap.SmallGroup(448,1128);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,100,675,297,192,18822]);
// 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,c*b*c^-1=a^2*b^-1,d*b*d^-1=b^-1,d*c*d^-1=c^13>;
// generators/relations
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