metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.157D14, C14.312- (1+4), C14.1352+ (1+4), C28⋊Q8⋊38C2, C4⋊C4.114D14, C42.C2⋊13D7, D14⋊Q8⋊37C2, D14⋊2Q8⋊39C2, C28.6Q8⋊30C2, (C2×C14).243C24, (C2×C28).190C23, (C4×C28).224C22, D14⋊C4.43C22, D14.5D4.4C2, C4.D28.12C2, (C2×D28).36C22, C2.60(D4⋊8D14), Dic7⋊C4.86C22, C4⋊Dic7.245C22, C22.264(C23×D7), C7⋊4(C22.57C24), (C4×Dic7).148C22, (C2×Dic7).125C23, (C2×Dic14).41C22, (C22×D7).108C23, C2.61(D4.10D14), C2.32(Q8.10D14), C4⋊C4⋊D7⋊38C2, (C7×C42.C2)⋊16C2, (C2×C4×D7).133C22, (C7×C4⋊C4).198C22, (C2×C4).207(C22×D7), SmallGroup(448,1152)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 924 in 196 conjugacy classes, 91 normal (31 characteristic)
C1, C2 [×3], C2 [×2], C4 [×13], C22, C22 [×6], C7, C2×C4 [×3], C2×C4 [×4], C2×C4 [×8], D4, Q8 [×3], C23 [×2], D7 [×2], C14 [×3], C42, C42 [×2], C22⋊C4 [×10], C4⋊C4 [×2], C4⋊C4 [×4], C4⋊C4 [×10], C22×C4 [×2], C2×D4, C2×Q8 [×3], Dic7 [×6], C28 [×7], D14 [×6], C2×C14, C22⋊Q8 [×4], C22.D4 [×2], C4.4D4, C42.C2, C42.C2, C42⋊2C2 [×4], C4⋊Q8 [×2], Dic14 [×3], C4×D7 [×2], D28, C2×Dic7 [×6], C2×C28 [×3], C2×C28 [×4], C22×D7 [×2], C22.57C24, C4×Dic7 [×2], Dic7⋊C4 [×6], C4⋊Dic7 [×2], C4⋊Dic7 [×2], D14⋊C4 [×10], C4×C28, C7×C4⋊C4 [×2], C7×C4⋊C4 [×4], C2×Dic14, C2×Dic14 [×2], C2×C4×D7 [×2], C2×D28, C28.6Q8, C4.D28, C28⋊Q8 [×2], D14.5D4 [×2], D14⋊Q8 [×2], D14⋊2Q8 [×2], C4⋊C4⋊D7 [×4], C7×C42.C2, C42.157D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C24, D14 [×7], 2+ (1+4), 2- (1+4) [×2], C22×D7 [×7], C22.57C24, C23×D7, Q8.10D14, D4⋊8D14, D4.10D14, C42.157D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=d2=a2b2, ab=ba, cac-1=a-1b2, dad-1=a-1, cbc-1=b-1, dbd-1=a2b-1, dcd-1=c13 >
►On 224 points
Generators in S224
(1 30 61 107)(2 45 62 94)(3 32 63 109)(4 47 64 96)(5 34 65 111)(6 49 66 98)(7 36 67 85)(8 51 68 100)(9 38 69 87)(10 53 70 102)(11 40 71 89)(12 55 72 104)(13 42 73 91)(14 29 74 106)(15 44 75 93)(16 31 76 108)(17 46 77 95)(18 33 78 110)(19 48 79 97)(20 35 80 112)(21 50 81 99)(22 37 82 86)(23 52 83 101)(24 39 84 88)(25 54 57 103)(26 41 58 90)(27 56 59 105)(28 43 60 92)(113 188 167 207)(114 175 168 222)(115 190 141 209)(116 177 142 224)(117 192 143 211)(118 179 144 198)(119 194 145 213)(120 181 146 200)(121 196 147 215)(122 183 148 202)(123 170 149 217)(124 185 150 204)(125 172 151 219)(126 187 152 206)(127 174 153 221)(128 189 154 208)(129 176 155 223)(130 191 156 210)(131 178 157 197)(132 193 158 212)(133 180 159 199)(134 195 160 214)(135 182 161 201)(136 169 162 216)(137 184 163 203)(138 171 164 218)(139 186 165 205)(140 173 166 220)
(1 168 75 128)(2 129 76 141)(3 142 77 130)(4 131 78 143)(5 144 79 132)(6 133 80 145)(7 146 81 134)(8 135 82 147)(9 148 83 136)(10 137 84 149)(11 150 57 138)(12 139 58 151)(13 152 59 140)(14 113 60 153)(15 154 61 114)(16 115 62 155)(17 156 63 116)(18 117 64 157)(19 158 65 118)(20 119 66 159)(21 160 67 120)(22 121 68 161)(23 162 69 122)(24 123 70 163)(25 164 71 124)(26 125 72 165)(27 166 73 126)(28 127 74 167)(29 188 92 221)(30 222 93 189)(31 190 94 223)(32 224 95 191)(33 192 96 197)(34 198 97 193)(35 194 98 199)(36 200 99 195)(37 196 100 201)(38 202 101 169)(39 170 102 203)(40 204 103 171)(41 172 104 205)(42 206 105 173)(43 174 106 207)(44 208 107 175)(45 176 108 209)(46 210 109 177)(47 178 110 211)(48 212 111 179)(49 180 112 213)(50 214 85 181)(51 182 86 215)(52 216 87 183)(53 184 88 217)(54 218 89 185)(55 186 90 219)(56 220 91 187)
(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)
(1 221 15 207)(2 206 16 220)(3 219 17 205)(4 204 18 218)(5 217 19 203)(6 202 20 216)(7 215 21 201)(8 200 22 214)(9 213 23 199)(10 198 24 212)(11 211 25 197)(12 224 26 210)(13 209 27 223)(14 222 28 208)(29 168 43 154)(30 153 44 167)(31 166 45 152)(32 151 46 165)(33 164 47 150)(34 149 48 163)(35 162 49 148)(36 147 50 161)(37 160 51 146)(38 145 52 159)(39 158 53 144)(40 143 54 157)(41 156 55 142)(42 141 56 155)(57 178 71 192)(58 191 72 177)(59 176 73 190)(60 189 74 175)(61 174 75 188)(62 187 76 173)(63 172 77 186)(64 185 78 171)(65 170 79 184)(66 183 80 169)(67 196 81 182)(68 181 82 195)(69 194 83 180)(70 179 84 193)(85 121 99 135)(86 134 100 120)(87 119 101 133)(88 132 102 118)(89 117 103 131)(90 130 104 116)(91 115 105 129)(92 128 106 114)(93 113 107 127)(94 126 108 140)(95 139 109 125)(96 124 110 138)(97 137 111 123)(98 122 112 136)
G:=sub<Sym(224)| (1,30,61,107)(2,45,62,94)(3,32,63,109)(4,47,64,96)(5,34,65,111)(6,49,66,98)(7,36,67,85)(8,51,68,100)(9,38,69,87)(10,53,70,102)(11,40,71,89)(12,55,72,104)(13,42,73,91)(14,29,74,106)(15,44,75,93)(16,31,76,108)(17,46,77,95)(18,33,78,110)(19,48,79,97)(20,35,80,112)(21,50,81,99)(22,37,82,86)(23,52,83,101)(24,39,84,88)(25,54,57,103)(26,41,58,90)(27,56,59,105)(28,43,60,92)(113,188,167,207)(114,175,168,222)(115,190,141,209)(116,177,142,224)(117,192,143,211)(118,179,144,198)(119,194,145,213)(120,181,146,200)(121,196,147,215)(122,183,148,202)(123,170,149,217)(124,185,150,204)(125,172,151,219)(126,187,152,206)(127,174,153,221)(128,189,154,208)(129,176,155,223)(130,191,156,210)(131,178,157,197)(132,193,158,212)(133,180,159,199)(134,195,160,214)(135,182,161,201)(136,169,162,216)(137,184,163,203)(138,171,164,218)(139,186,165,205)(140,173,166,220), (1,168,75,128)(2,129,76,141)(3,142,77,130)(4,131,78,143)(5,144,79,132)(6,133,80,145)(7,146,81,134)(8,135,82,147)(9,148,83,136)(10,137,84,149)(11,150,57,138)(12,139,58,151)(13,152,59,140)(14,113,60,153)(15,154,61,114)(16,115,62,155)(17,156,63,116)(18,117,64,157)(19,158,65,118)(20,119,66,159)(21,160,67,120)(22,121,68,161)(23,162,69,122)(24,123,70,163)(25,164,71,124)(26,125,72,165)(27,166,73,126)(28,127,74,167)(29,188,92,221)(30,222,93,189)(31,190,94,223)(32,224,95,191)(33,192,96,197)(34,198,97,193)(35,194,98,199)(36,200,99,195)(37,196,100,201)(38,202,101,169)(39,170,102,203)(40,204,103,171)(41,172,104,205)(42,206,105,173)(43,174,106,207)(44,208,107,175)(45,176,108,209)(46,210,109,177)(47,178,110,211)(48,212,111,179)(49,180,112,213)(50,214,85,181)(51,182,86,215)(52,216,87,183)(53,184,88,217)(54,218,89,185)(55,186,90,219)(56,220,91,187), (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), (1,221,15,207)(2,206,16,220)(3,219,17,205)(4,204,18,218)(5,217,19,203)(6,202,20,216)(7,215,21,201)(8,200,22,214)(9,213,23,199)(10,198,24,212)(11,211,25,197)(12,224,26,210)(13,209,27,223)(14,222,28,208)(29,168,43,154)(30,153,44,167)(31,166,45,152)(32,151,46,165)(33,164,47,150)(34,149,48,163)(35,162,49,148)(36,147,50,161)(37,160,51,146)(38,145,52,159)(39,158,53,144)(40,143,54,157)(41,156,55,142)(42,141,56,155)(57,178,71,192)(58,191,72,177)(59,176,73,190)(60,189,74,175)(61,174,75,188)(62,187,76,173)(63,172,77,186)(64,185,78,171)(65,170,79,184)(66,183,80,169)(67,196,81,182)(68,181,82,195)(69,194,83,180)(70,179,84,193)(85,121,99,135)(86,134,100,120)(87,119,101,133)(88,132,102,118)(89,117,103,131)(90,130,104,116)(91,115,105,129)(92,128,106,114)(93,113,107,127)(94,126,108,140)(95,139,109,125)(96,124,110,138)(97,137,111,123)(98,122,112,136)>;
G:=Group( (1,30,61,107)(2,45,62,94)(3,32,63,109)(4,47,64,96)(5,34,65,111)(6,49,66,98)(7,36,67,85)(8,51,68,100)(9,38,69,87)(10,53,70,102)(11,40,71,89)(12,55,72,104)(13,42,73,91)(14,29,74,106)(15,44,75,93)(16,31,76,108)(17,46,77,95)(18,33,78,110)(19,48,79,97)(20,35,80,112)(21,50,81,99)(22,37,82,86)(23,52,83,101)(24,39,84,88)(25,54,57,103)(26,41,58,90)(27,56,59,105)(28,43,60,92)(113,188,167,207)(114,175,168,222)(115,190,141,209)(116,177,142,224)(117,192,143,211)(118,179,144,198)(119,194,145,213)(120,181,146,200)(121,196,147,215)(122,183,148,202)(123,170,149,217)(124,185,150,204)(125,172,151,219)(126,187,152,206)(127,174,153,221)(128,189,154,208)(129,176,155,223)(130,191,156,210)(131,178,157,197)(132,193,158,212)(133,180,159,199)(134,195,160,214)(135,182,161,201)(136,169,162,216)(137,184,163,203)(138,171,164,218)(139,186,165,205)(140,173,166,220), (1,168,75,128)(2,129,76,141)(3,142,77,130)(4,131,78,143)(5,144,79,132)(6,133,80,145)(7,146,81,134)(8,135,82,147)(9,148,83,136)(10,137,84,149)(11,150,57,138)(12,139,58,151)(13,152,59,140)(14,113,60,153)(15,154,61,114)(16,115,62,155)(17,156,63,116)(18,117,64,157)(19,158,65,118)(20,119,66,159)(21,160,67,120)(22,121,68,161)(23,162,69,122)(24,123,70,163)(25,164,71,124)(26,125,72,165)(27,166,73,126)(28,127,74,167)(29,188,92,221)(30,222,93,189)(31,190,94,223)(32,224,95,191)(33,192,96,197)(34,198,97,193)(35,194,98,199)(36,200,99,195)(37,196,100,201)(38,202,101,169)(39,170,102,203)(40,204,103,171)(41,172,104,205)(42,206,105,173)(43,174,106,207)(44,208,107,175)(45,176,108,209)(46,210,109,177)(47,178,110,211)(48,212,111,179)(49,180,112,213)(50,214,85,181)(51,182,86,215)(52,216,87,183)(53,184,88,217)(54,218,89,185)(55,186,90,219)(56,220,91,187), (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), (1,221,15,207)(2,206,16,220)(3,219,17,205)(4,204,18,218)(5,217,19,203)(6,202,20,216)(7,215,21,201)(8,200,22,214)(9,213,23,199)(10,198,24,212)(11,211,25,197)(12,224,26,210)(13,209,27,223)(14,222,28,208)(29,168,43,154)(30,153,44,167)(31,166,45,152)(32,151,46,165)(33,164,47,150)(34,149,48,163)(35,162,49,148)(36,147,50,161)(37,160,51,146)(38,145,52,159)(39,158,53,144)(40,143,54,157)(41,156,55,142)(42,141,56,155)(57,178,71,192)(58,191,72,177)(59,176,73,190)(60,189,74,175)(61,174,75,188)(62,187,76,173)(63,172,77,186)(64,185,78,171)(65,170,79,184)(66,183,80,169)(67,196,81,182)(68,181,82,195)(69,194,83,180)(70,179,84,193)(85,121,99,135)(86,134,100,120)(87,119,101,133)(88,132,102,118)(89,117,103,131)(90,130,104,116)(91,115,105,129)(92,128,106,114)(93,113,107,127)(94,126,108,140)(95,139,109,125)(96,124,110,138)(97,137,111,123)(98,122,112,136) );
G=PermutationGroup([(1,30,61,107),(2,45,62,94),(3,32,63,109),(4,47,64,96),(5,34,65,111),(6,49,66,98),(7,36,67,85),(8,51,68,100),(9,38,69,87),(10,53,70,102),(11,40,71,89),(12,55,72,104),(13,42,73,91),(14,29,74,106),(15,44,75,93),(16,31,76,108),(17,46,77,95),(18,33,78,110),(19,48,79,97),(20,35,80,112),(21,50,81,99),(22,37,82,86),(23,52,83,101),(24,39,84,88),(25,54,57,103),(26,41,58,90),(27,56,59,105),(28,43,60,92),(113,188,167,207),(114,175,168,222),(115,190,141,209),(116,177,142,224),(117,192,143,211),(118,179,144,198),(119,194,145,213),(120,181,146,200),(121,196,147,215),(122,183,148,202),(123,170,149,217),(124,185,150,204),(125,172,151,219),(126,187,152,206),(127,174,153,221),(128,189,154,208),(129,176,155,223),(130,191,156,210),(131,178,157,197),(132,193,158,212),(133,180,159,199),(134,195,160,214),(135,182,161,201),(136,169,162,216),(137,184,163,203),(138,171,164,218),(139,186,165,205),(140,173,166,220)], [(1,168,75,128),(2,129,76,141),(3,142,77,130),(4,131,78,143),(5,144,79,132),(6,133,80,145),(7,146,81,134),(8,135,82,147),(9,148,83,136),(10,137,84,149),(11,150,57,138),(12,139,58,151),(13,152,59,140),(14,113,60,153),(15,154,61,114),(16,115,62,155),(17,156,63,116),(18,117,64,157),(19,158,65,118),(20,119,66,159),(21,160,67,120),(22,121,68,161),(23,162,69,122),(24,123,70,163),(25,164,71,124),(26,125,72,165),(27,166,73,126),(28,127,74,167),(29,188,92,221),(30,222,93,189),(31,190,94,223),(32,224,95,191),(33,192,96,197),(34,198,97,193),(35,194,98,199),(36,200,99,195),(37,196,100,201),(38,202,101,169),(39,170,102,203),(40,204,103,171),(41,172,104,205),(42,206,105,173),(43,174,106,207),(44,208,107,175),(45,176,108,209),(46,210,109,177),(47,178,110,211),(48,212,111,179),(49,180,112,213),(50,214,85,181),(51,182,86,215),(52,216,87,183),(53,184,88,217),(54,218,89,185),(55,186,90,219),(56,220,91,187)], [(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)], [(1,221,15,207),(2,206,16,220),(3,219,17,205),(4,204,18,218),(5,217,19,203),(6,202,20,216),(7,215,21,201),(8,200,22,214),(9,213,23,199),(10,198,24,212),(11,211,25,197),(12,224,26,210),(13,209,27,223),(14,222,28,208),(29,168,43,154),(30,153,44,167),(31,166,45,152),(32,151,46,165),(33,164,47,150),(34,149,48,163),(35,162,49,148),(36,147,50,161),(37,160,51,146),(38,145,52,159),(39,158,53,144),(40,143,54,157),(41,156,55,142),(42,141,56,155),(57,178,71,192),(58,191,72,177),(59,176,73,190),(60,189,74,175),(61,174,75,188),(62,187,76,173),(63,172,77,186),(64,185,78,171),(65,170,79,184),(66,183,80,169),(67,196,81,182),(68,181,82,195),(69,194,83,180),(70,179,84,193),(85,121,99,135),(86,134,100,120),(87,119,101,133),(88,132,102,118),(89,117,103,131),(90,130,104,116),(91,115,105,129),(92,128,106,114),(93,113,107,127),(94,126,108,140),(95,139,109,125),(96,124,110,138),(97,137,111,123),(98,122,112,136)])
Matrix representation ►G ⊆ GL8(𝔽29)
| 0 | 0 | 21 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 8 | 0 | 0 | 0 | 0 |
| 8 | 11 | 0 | 0 | 0 | 0 | 0 | 0 |
| 2 | 21 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 24 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 8 | 24 |
| 0 | 0 | 0 | 0 | 0 | 0 | 13 | 21 |
| 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 | 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 |
| 20 | 16 | 15 | 12 | 0 | 0 | 0 | 0 |
| 24 | 2 | 18 | 16 | 0 | 0 | 0 | 0 |
| 15 | 12 | 9 | 13 | 0 | 0 | 0 | 0 |
| 18 | 16 | 5 | 27 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 23 | 19 | 14 |
| 0 | 0 | 0 | 0 | 4 | 12 | 10 | 0 |
| 0 | 0 | 0 | 0 | 19 | 14 | 21 | 6 |
| 0 | 0 | 0 | 0 | 10 | 0 | 25 | 17 |
| 21 | 10 | 23 | 22 | 0 | 0 | 0 | 0 |
| 23 | 8 | 10 | 6 | 0 | 0 | 0 | 0 |
| 23 | 22 | 8 | 19 | 0 | 0 | 0 | 0 |
| 10 | 6 | 6 | 21 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 3 | 2 | 0 |
| 0 | 0 | 0 | 0 | 11 | 28 | 18 | 27 |
| 0 | 0 | 0 | 0 | 27 | 0 | 1 | 3 |
| 0 | 0 | 0 | 0 | 11 | 2 | 11 | 28 |
G:=sub<GL(8,GF(29))| [0,0,8,2,0,0,0,0,0,0,11,21,0,0,0,0,21,27,0,0,0,0,0,0,18,8,0,0,0,0,0,0,0,0,0,0,8,13,0,0,0,0,0,0,24,21,0,0,0,0,0,0,0,0,8,13,0,0,0,0,0,0,24,21],[0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0],[20,24,15,18,0,0,0,0,16,2,12,16,0,0,0,0,15,18,9,5,0,0,0,0,12,16,13,27,0,0,0,0,0,0,0,0,8,4,19,10,0,0,0,0,23,12,14,0,0,0,0,0,19,10,21,25,0,0,0,0,14,0,6,17],[21,23,23,10,0,0,0,0,10,8,22,6,0,0,0,0,23,10,8,6,0,0,0,0,22,6,19,21,0,0,0,0,0,0,0,0,1,11,27,11,0,0,0,0,3,28,0,2,0,0,0,0,2,18,1,11,0,0,0,0,0,27,3,28] >;
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4G | 4H | ··· | 4M | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| 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 | 28 | 28 | 4 | ··· | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | D14 | D14 | 2+ (1+4) | 2- (1+4) | Q8.10D14 | D4⋊8D14 | D4.10D14 |
| kernel | C42.157D14 | C28.6Q8 | C4.D28 | C28⋊Q8 | D14.5D4 | D14⋊Q8 | D14⋊2Q8 | C4⋊C4⋊D7 | C7×C42.C2 | C42.C2 | C42 | C4⋊C4 | C14 | C14 | C2 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 1 | 3 | 3 | 18 | 1 | 2 | 6 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{157}D_{14} % in TeX
G:=Group("C4^2.157D14"); // GroupNames label
G:=SmallGroup(448,1152);
// by ID
G=gap.SmallGroup(448,1152);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,758,219,268,1571,570,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^2*b^2,a*b=b*a,c*a*c^-1=a^-1*b^2,d*a*d^-1=a^-1,c*b*c^-1=b^-1,d*b*d^-1=a^2*b^-1,d*c*d^-1=c^13>;
// generators/relations
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