metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.115D14, C14.222+ (1+4), C14.622- (1+4), (C4×D4)⋊23D7, C28⋊Q8⋊16C2, (D4×C28)⋊25C2, C4⋊C4.286D14, D14⋊2Q8⋊16C2, (C4×Dic14)⋊35C2, (C2×D4).222D14, C4.45(C4○D28), C28⋊2D4.10C2, C42⋊D7⋊14C2, C28.112(C4○D4), C28.17D4⋊10C2, C28.48D4⋊12C2, (C2×C14).105C24, (C4×C28).159C22, (C2×C28).163C23, C22⋊C4.117D14, C23.D14⋊9C2, (C22×C4).213D14, C4⋊Dic7.40C22, C2.23(D4⋊6D14), D14⋊C4.123C22, Dic7.D4⋊10C2, (D4×C14).264C22, C23.23D14⋊3C2, (C22×C28).82C22, (C2×Dic7).46C23, (C4×Dic7).77C22, (C22×D7).39C23, C22.130(C23×D7), C23.102(C22×D7), C23.D7.15C22, Dic7⋊C4.135C22, (C22×C14).175C23, C7⋊2(C22.36C24), (C2×Dic14).27C22, C2.19(D4.10D14), C14.47(C2×C4○D4), C2.54(C2×C4○D28), (C2×C4×D7).67C22, (C7×C4⋊C4).333C22, (C2×C4).287(C22×D7), (C2×C7⋊D4).18C22, (C7×C22⋊C4).128C22, SmallGroup(448,1014)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 916 in 216 conjugacy classes, 95 normal (43 characteristic)
C1, C2 [×3], C2 [×3], C4 [×2], C4 [×11], C22, C22 [×9], C7, C2×C4 [×3], C2×C4 [×2], C2×C4 [×11], D4 [×4], Q8 [×4], C23 [×2], C23, D7, C14 [×3], C14 [×2], C42, C42 [×3], C22⋊C4 [×2], C22⋊C4 [×10], C4⋊C4, C4⋊C4 [×9], C22×C4 [×2], C22×C4, C2×D4, C2×D4 [×2], C2×Q8 [×3], Dic7 [×7], C28 [×2], C28 [×4], D14 [×3], C2×C14, C2×C14 [×6], C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8 [×3], C22.D4 [×2], C4.4D4 [×3], C42⋊2C2 [×2], C4⋊Q8, Dic14 [×4], C4×D7 [×2], C2×Dic7 [×3], C2×Dic7 [×4], C7⋊D4 [×2], C2×C28 [×3], C2×C28 [×2], C2×C28 [×2], C7×D4 [×2], C22×D7, C22×C14 [×2], C22.36C24, C4×Dic7, C4×Dic7 [×2], Dic7⋊C4 [×2], Dic7⋊C4 [×4], C4⋊Dic7, C4⋊Dic7 [×2], D14⋊C4 [×2], D14⋊C4 [×2], C23.D7 [×6], C4×C28, C7×C22⋊C4 [×2], C7×C4⋊C4, C2×Dic14, C2×Dic14 [×2], C2×C4×D7, C2×C7⋊D4 [×2], C22×C28 [×2], D4×C14, C4×Dic14, C42⋊D7, C23.D14 [×2], Dic7.D4 [×2], C28⋊Q8, D14⋊2Q8, C28.48D4 [×2], C23.23D14 [×2], C28.17D4, C28⋊2D4, D4×C28, C42.115D14
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, C4○D28 [×2], C23×D7, C2×C4○D28, D4⋊6D14, D4.10D14, C42.115D14
Generators and relations
G = < a,b,c,d | a4=b4=c14=1, d2=b2, ab=ba, cac-1=dad-1=a-1, bc=cb, dbd-1=a2b, dcd-1=b2c-1 >
►On 224 points
Generators in S224
(1 204 10 197)(2 198 11 205)(3 206 12 199)(4 200 13 207)(5 208 14 201)(6 202 8 209)(7 210 9 203)(15 193 22 186)(16 187 23 194)(17 195 24 188)(18 189 25 196)(19 183 26 190)(20 191 27 184)(21 185 28 192)(29 163 36 156)(30 157 37 164)(31 165 38 158)(32 159 39 166)(33 167 40 160)(34 161 41 168)(35 155 42 162)(43 72 53 79)(44 80 54 73)(45 74 55 81)(46 82 56 75)(47 76 50 83)(48 84 51 77)(49 78 52 71)(57 221 127 111)(58 112 128 222)(59 223 129 99)(60 100 130 224)(61 211 131 101)(62 102 132 212)(63 213 133 103)(64 104 134 214)(65 215 135 105)(66 106 136 216)(67 217 137 107)(68 108 138 218)(69 219 139 109)(70 110 140 220)(85 145 126 173)(86 174 113 146)(87 147 114 175)(88 176 115 148)(89 149 116 177)(90 178 117 150)(91 151 118 179)(92 180 119 152)(93 153 120 181)(94 182 121 154)(95 141 122 169)(96 170 123 142)(97 143 124 171)(98 172 125 144)
(1 49 17 31)(2 43 18 32)(3 44 19 33)(4 45 20 34)(5 46 21 35)(6 47 15 29)(7 48 16 30)(8 50 22 36)(9 51 23 37)(10 52 24 38)(11 53 25 39)(12 54 26 40)(13 55 27 41)(14 56 28 42)(57 178 64 171)(58 179 65 172)(59 180 66 173)(60 181 67 174)(61 182 68 175)(62 169 69 176)(63 170 70 177)(71 188 158 197)(72 189 159 198)(73 190 160 199)(74 191 161 200)(75 192 162 201)(76 193 163 202)(77 194 164 203)(78 195 165 204)(79 196 166 205)(80 183 167 206)(81 184 168 207)(82 185 155 208)(83 186 156 209)(84 187 157 210)(85 223 119 106)(86 224 120 107)(87 211 121 108)(88 212 122 109)(89 213 123 110)(90 214 124 111)(91 215 125 112)(92 216 126 99)(93 217 113 100)(94 218 114 101)(95 219 115 102)(96 220 116 103)(97 221 117 104)(98 222 118 105)(127 150 134 143)(128 151 135 144)(129 152 136 145)(130 153 137 146)(131 154 138 147)(132 141 139 148)(133 142 140 149)
(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 58 17 65)(2 64 18 57)(3 70 19 63)(4 62 20 69)(5 68 21 61)(6 60 15 67)(7 66 16 59)(8 130 22 137)(9 136 23 129)(10 128 24 135)(11 134 25 127)(12 140 26 133)(13 132 27 139)(14 138 28 131)(29 146 47 153)(30 152 48 145)(31 144 49 151)(32 150 43 143)(33 142 44 149)(34 148 45 141)(35 154 46 147)(36 174 50 181)(37 180 51 173)(38 172 52 179)(39 178 53 171)(40 170 54 177)(41 176 55 169)(42 182 56 175)(71 118 158 98)(72 97 159 117)(73 116 160 96)(74 95 161 115)(75 114 162 94)(76 93 163 113)(77 126 164 92)(78 91 165 125)(79 124 166 90)(80 89 167 123)(81 122 168 88)(82 87 155 121)(83 120 156 86)(84 85 157 119)(99 210 216 187)(100 186 217 209)(101 208 218 185)(102 184 219 207)(103 206 220 183)(104 196 221 205)(105 204 222 195)(106 194 223 203)(107 202 224 193)(108 192 211 201)(109 200 212 191)(110 190 213 199)(111 198 214 189)(112 188 215 197)
G:=sub<Sym(224)| (1,204,10,197)(2,198,11,205)(3,206,12,199)(4,200,13,207)(5,208,14,201)(6,202,8,209)(7,210,9,203)(15,193,22,186)(16,187,23,194)(17,195,24,188)(18,189,25,196)(19,183,26,190)(20,191,27,184)(21,185,28,192)(29,163,36,156)(30,157,37,164)(31,165,38,158)(32,159,39,166)(33,167,40,160)(34,161,41,168)(35,155,42,162)(43,72,53,79)(44,80,54,73)(45,74,55,81)(46,82,56,75)(47,76,50,83)(48,84,51,77)(49,78,52,71)(57,221,127,111)(58,112,128,222)(59,223,129,99)(60,100,130,224)(61,211,131,101)(62,102,132,212)(63,213,133,103)(64,104,134,214)(65,215,135,105)(66,106,136,216)(67,217,137,107)(68,108,138,218)(69,219,139,109)(70,110,140,220)(85,145,126,173)(86,174,113,146)(87,147,114,175)(88,176,115,148)(89,149,116,177)(90,178,117,150)(91,151,118,179)(92,180,119,152)(93,153,120,181)(94,182,121,154)(95,141,122,169)(96,170,123,142)(97,143,124,171)(98,172,125,144), (1,49,17,31)(2,43,18,32)(3,44,19,33)(4,45,20,34)(5,46,21,35)(6,47,15,29)(7,48,16,30)(8,50,22,36)(9,51,23,37)(10,52,24,38)(11,53,25,39)(12,54,26,40)(13,55,27,41)(14,56,28,42)(57,178,64,171)(58,179,65,172)(59,180,66,173)(60,181,67,174)(61,182,68,175)(62,169,69,176)(63,170,70,177)(71,188,158,197)(72,189,159,198)(73,190,160,199)(74,191,161,200)(75,192,162,201)(76,193,163,202)(77,194,164,203)(78,195,165,204)(79,196,166,205)(80,183,167,206)(81,184,168,207)(82,185,155,208)(83,186,156,209)(84,187,157,210)(85,223,119,106)(86,224,120,107)(87,211,121,108)(88,212,122,109)(89,213,123,110)(90,214,124,111)(91,215,125,112)(92,216,126,99)(93,217,113,100)(94,218,114,101)(95,219,115,102)(96,220,116,103)(97,221,117,104)(98,222,118,105)(127,150,134,143)(128,151,135,144)(129,152,136,145)(130,153,137,146)(131,154,138,147)(132,141,139,148)(133,142,140,149), (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), (1,58,17,65)(2,64,18,57)(3,70,19,63)(4,62,20,69)(5,68,21,61)(6,60,15,67)(7,66,16,59)(8,130,22,137)(9,136,23,129)(10,128,24,135)(11,134,25,127)(12,140,26,133)(13,132,27,139)(14,138,28,131)(29,146,47,153)(30,152,48,145)(31,144,49,151)(32,150,43,143)(33,142,44,149)(34,148,45,141)(35,154,46,147)(36,174,50,181)(37,180,51,173)(38,172,52,179)(39,178,53,171)(40,170,54,177)(41,176,55,169)(42,182,56,175)(71,118,158,98)(72,97,159,117)(73,116,160,96)(74,95,161,115)(75,114,162,94)(76,93,163,113)(77,126,164,92)(78,91,165,125)(79,124,166,90)(80,89,167,123)(81,122,168,88)(82,87,155,121)(83,120,156,86)(84,85,157,119)(99,210,216,187)(100,186,217,209)(101,208,218,185)(102,184,219,207)(103,206,220,183)(104,196,221,205)(105,204,222,195)(106,194,223,203)(107,202,224,193)(108,192,211,201)(109,200,212,191)(110,190,213,199)(111,198,214,189)(112,188,215,197)>;
G:=Group( (1,204,10,197)(2,198,11,205)(3,206,12,199)(4,200,13,207)(5,208,14,201)(6,202,8,209)(7,210,9,203)(15,193,22,186)(16,187,23,194)(17,195,24,188)(18,189,25,196)(19,183,26,190)(20,191,27,184)(21,185,28,192)(29,163,36,156)(30,157,37,164)(31,165,38,158)(32,159,39,166)(33,167,40,160)(34,161,41,168)(35,155,42,162)(43,72,53,79)(44,80,54,73)(45,74,55,81)(46,82,56,75)(47,76,50,83)(48,84,51,77)(49,78,52,71)(57,221,127,111)(58,112,128,222)(59,223,129,99)(60,100,130,224)(61,211,131,101)(62,102,132,212)(63,213,133,103)(64,104,134,214)(65,215,135,105)(66,106,136,216)(67,217,137,107)(68,108,138,218)(69,219,139,109)(70,110,140,220)(85,145,126,173)(86,174,113,146)(87,147,114,175)(88,176,115,148)(89,149,116,177)(90,178,117,150)(91,151,118,179)(92,180,119,152)(93,153,120,181)(94,182,121,154)(95,141,122,169)(96,170,123,142)(97,143,124,171)(98,172,125,144), (1,49,17,31)(2,43,18,32)(3,44,19,33)(4,45,20,34)(5,46,21,35)(6,47,15,29)(7,48,16,30)(8,50,22,36)(9,51,23,37)(10,52,24,38)(11,53,25,39)(12,54,26,40)(13,55,27,41)(14,56,28,42)(57,178,64,171)(58,179,65,172)(59,180,66,173)(60,181,67,174)(61,182,68,175)(62,169,69,176)(63,170,70,177)(71,188,158,197)(72,189,159,198)(73,190,160,199)(74,191,161,200)(75,192,162,201)(76,193,163,202)(77,194,164,203)(78,195,165,204)(79,196,166,205)(80,183,167,206)(81,184,168,207)(82,185,155,208)(83,186,156,209)(84,187,157,210)(85,223,119,106)(86,224,120,107)(87,211,121,108)(88,212,122,109)(89,213,123,110)(90,214,124,111)(91,215,125,112)(92,216,126,99)(93,217,113,100)(94,218,114,101)(95,219,115,102)(96,220,116,103)(97,221,117,104)(98,222,118,105)(127,150,134,143)(128,151,135,144)(129,152,136,145)(130,153,137,146)(131,154,138,147)(132,141,139,148)(133,142,140,149), (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), (1,58,17,65)(2,64,18,57)(3,70,19,63)(4,62,20,69)(5,68,21,61)(6,60,15,67)(7,66,16,59)(8,130,22,137)(9,136,23,129)(10,128,24,135)(11,134,25,127)(12,140,26,133)(13,132,27,139)(14,138,28,131)(29,146,47,153)(30,152,48,145)(31,144,49,151)(32,150,43,143)(33,142,44,149)(34,148,45,141)(35,154,46,147)(36,174,50,181)(37,180,51,173)(38,172,52,179)(39,178,53,171)(40,170,54,177)(41,176,55,169)(42,182,56,175)(71,118,158,98)(72,97,159,117)(73,116,160,96)(74,95,161,115)(75,114,162,94)(76,93,163,113)(77,126,164,92)(78,91,165,125)(79,124,166,90)(80,89,167,123)(81,122,168,88)(82,87,155,121)(83,120,156,86)(84,85,157,119)(99,210,216,187)(100,186,217,209)(101,208,218,185)(102,184,219,207)(103,206,220,183)(104,196,221,205)(105,204,222,195)(106,194,223,203)(107,202,224,193)(108,192,211,201)(109,200,212,191)(110,190,213,199)(111,198,214,189)(112,188,215,197) );
G=PermutationGroup([(1,204,10,197),(2,198,11,205),(3,206,12,199),(4,200,13,207),(5,208,14,201),(6,202,8,209),(7,210,9,203),(15,193,22,186),(16,187,23,194),(17,195,24,188),(18,189,25,196),(19,183,26,190),(20,191,27,184),(21,185,28,192),(29,163,36,156),(30,157,37,164),(31,165,38,158),(32,159,39,166),(33,167,40,160),(34,161,41,168),(35,155,42,162),(43,72,53,79),(44,80,54,73),(45,74,55,81),(46,82,56,75),(47,76,50,83),(48,84,51,77),(49,78,52,71),(57,221,127,111),(58,112,128,222),(59,223,129,99),(60,100,130,224),(61,211,131,101),(62,102,132,212),(63,213,133,103),(64,104,134,214),(65,215,135,105),(66,106,136,216),(67,217,137,107),(68,108,138,218),(69,219,139,109),(70,110,140,220),(85,145,126,173),(86,174,113,146),(87,147,114,175),(88,176,115,148),(89,149,116,177),(90,178,117,150),(91,151,118,179),(92,180,119,152),(93,153,120,181),(94,182,121,154),(95,141,122,169),(96,170,123,142),(97,143,124,171),(98,172,125,144)], [(1,49,17,31),(2,43,18,32),(3,44,19,33),(4,45,20,34),(5,46,21,35),(6,47,15,29),(7,48,16,30),(8,50,22,36),(9,51,23,37),(10,52,24,38),(11,53,25,39),(12,54,26,40),(13,55,27,41),(14,56,28,42),(57,178,64,171),(58,179,65,172),(59,180,66,173),(60,181,67,174),(61,182,68,175),(62,169,69,176),(63,170,70,177),(71,188,158,197),(72,189,159,198),(73,190,160,199),(74,191,161,200),(75,192,162,201),(76,193,163,202),(77,194,164,203),(78,195,165,204),(79,196,166,205),(80,183,167,206),(81,184,168,207),(82,185,155,208),(83,186,156,209),(84,187,157,210),(85,223,119,106),(86,224,120,107),(87,211,121,108),(88,212,122,109),(89,213,123,110),(90,214,124,111),(91,215,125,112),(92,216,126,99),(93,217,113,100),(94,218,114,101),(95,219,115,102),(96,220,116,103),(97,221,117,104),(98,222,118,105),(127,150,134,143),(128,151,135,144),(129,152,136,145),(130,153,137,146),(131,154,138,147),(132,141,139,148),(133,142,140,149)], [(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)], [(1,58,17,65),(2,64,18,57),(3,70,19,63),(4,62,20,69),(5,68,21,61),(6,60,15,67),(7,66,16,59),(8,130,22,137),(9,136,23,129),(10,128,24,135),(11,134,25,127),(12,140,26,133),(13,132,27,139),(14,138,28,131),(29,146,47,153),(30,152,48,145),(31,144,49,151),(32,150,43,143),(33,142,44,149),(34,148,45,141),(35,154,46,147),(36,174,50,181),(37,180,51,173),(38,172,52,179),(39,178,53,171),(40,170,54,177),(41,176,55,169),(42,182,56,175),(71,118,158,98),(72,97,159,117),(73,116,160,96),(74,95,161,115),(75,114,162,94),(76,93,163,113),(77,126,164,92),(78,91,165,125),(79,124,166,90),(80,89,167,123),(81,122,168,88),(82,87,155,121),(83,120,156,86),(84,85,157,119),(99,210,216,187),(100,186,217,209),(101,208,218,185),(102,184,219,207),(103,206,220,183),(104,196,221,205),(105,204,222,195),(106,194,223,203),(107,202,224,193),(108,192,211,201),(109,200,212,191),(110,190,213,199),(111,198,214,189),(112,188,215,197)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 27 | 0 | 0 |
| 0 | 0 | 1 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 27 |
| 0 | 0 | 0 | 0 | 1 | 28 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 23 | 0 | 0 | 0 |
| 0 | 0 | 23 | 6 | 0 | 0 |
| 0 | 0 | 0 | 0 | 5 | 0 |
| 0 | 0 | 0 | 0 | 5 | 24 |
| 14 | 1 | 0 | 0 | 0 | 0 |
| 6 | 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 24 | 0 |
| 0 | 0 | 0 | 0 | 24 | 5 |
| 0 | 0 | 6 | 0 | 0 | 0 |
| 0 | 0 | 6 | 23 | 0 | 0 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,27,28,0,0,0,0,0,0,1,1,0,0,0,0,27,28],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,17,0,0,0,0,0,0,17],[1,1,0,0,0,0,0,28,0,0,0,0,0,0,23,23,0,0,0,0,0,6,0,0,0,0,0,0,5,5,0,0,0,0,0,24],[14,6,0,0,0,0,1,15,0,0,0,0,0,0,0,0,6,6,0,0,0,0,0,23,0,0,24,24,0,0,0,0,0,5,0,0] >;
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | ··· | 4F | 4G | 4H | 4I | ··· | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | D14 | D14 | C4○D28 | 2+ (1+4) | 2- (1+4) | D4⋊6D14 | D4.10D14 |
| kernel | C42.115D14 | C4×Dic14 | C42⋊D7 | C23.D14 | Dic7.D4 | C28⋊Q8 | D14⋊2Q8 | C28.48D4 | C23.23D14 | C28.17D4 | C28⋊2D4 | D4×C28 | C4×D4 | C28 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C4 | C14 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 3 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 1 | 1 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{115}D_{14} % in TeX
G:=Group("C4^2.115D14"); // GroupNames label
G:=SmallGroup(448,1014);
// by ID
G=gap.SmallGroup(448,1014);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,100,675,570,18822]);
// 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^-1,b*c=c*b,d*b*d^-1=a^2*b,d*c*d^-1=b^2*c^-1>;
// generators/relations
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