metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.144D14, C14.922- (1+4), C14.1282+ (1+4), C28⋊2Q8⋊31C2, (D4×Dic7)⋊32C2, (Q8×Dic7)⋊21C2, C4.4D4⋊15D7, D14⋊3Q8⋊33C2, (C2×D4).177D14, C28⋊2D4.13C2, C42⋊D7⋊21C2, (C2×C28).82C23, (C2×Q8).140D14, C22⋊C4.37D14, C28.127(C4○D4), C4.39(D4⋊2D7), (C2×C14).226C24, (C4×C28).189C22, C2.52(D4⋊8D14), C23.48(C22×D7), D14⋊C4.111C22, Dic7.D4⋊42C2, C22⋊Dic14⋊42C2, (D4×C14).159C22, C23.D14⋊42C2, C22.D28⋊27C2, Dic7⋊C4.49C22, C4⋊Dic7.236C22, (C22×C14).56C23, (Q8×C14).130C22, (C22×D7).98C23, C22.247(C23×D7), C23.D7.59C22, C7⋊9(C22.36C24), (C2×Dic14).38C22, (C4×Dic7).136C22, (C2×Dic7).116C23, C2.53(D4.10D14), (C22×Dic7).146C22, C14.94(C2×C4○D4), (C7×C4.4D4)⋊18C2, C2.58(C2×D4⋊2D7), (C2×C4×D7).122C22, (C2×C4).199(C22×D7), (C2×C7⋊D4).64C22, (C7×C22⋊C4).68C22, SmallGroup(448,1135)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 940 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 [×4], C22⋊C4 [×8], C4⋊C4 [×10], C22×C4 [×3], C2×D4, C2×D4 [×2], C2×Q8, C2×Q8 [×2], 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, C4.4D4 [×2], C42⋊2C2 [×2], C4⋊Q8, Dic14 [×2], C4×D7 [×2], C2×Dic7 [×3], C2×Dic7 [×4], C2×Dic7 [×2], C7⋊D4 [×2], C2×C28 [×3], C2×C28 [×2], C7×D4 [×2], C7×Q8 [×2], C22×D7, C22×C14 [×2], C22.36C24, C4×Dic7, C4×Dic7 [×2], Dic7⋊C4 [×2], Dic7⋊C4 [×2], C4⋊Dic7 [×2], C4⋊Dic7 [×4], D14⋊C4 [×2], D14⋊C4 [×2], 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, C28⋊2Q8, C42⋊D7, C22⋊Dic14 [×2], C23.D14 [×2], Dic7.D4 [×2], C22.D28 [×2], D4×Dic7, C28⋊2D4, Q8×Dic7, D14⋊3Q8, C7×C4.4D4, C42.144D14
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, D4⋊2D7 [×2], C23×D7, C2×D4⋊2D7, D4⋊8D14, D4.10D14, C42.144D14
Generators and relations
G = < a,b,c,d | a4=b4=c14=1, d2=b2, ab=ba, cac-1=dad-1=a-1, cbc-1=a2b-1, dbd-1=b-1, dcd-1=b2c-1 >
►On 224 points
Generators in S224
(1 130 8 137)(2 138 9 131)(3 132 10 139)(4 140 11 133)(5 134 12 127)(6 128 13 135)(7 136 14 129)(15 204 35 197)(16 198 29 205)(17 206 30 199)(18 200 31 207)(19 208 32 201)(20 202 33 209)(21 210 34 203)(22 58 40 65)(23 66 41 59)(24 60 42 67)(25 68 36 61)(26 62 37 69)(27 70 38 63)(28 64 39 57)(43 160 51 167)(44 168 52 161)(45 162 53 155)(46 156 54 163)(47 164 55 157)(48 158 56 165)(49 166 50 159)(71 148 111 222)(72 223 112 149)(73 150 99 224)(74 211 100 151)(75 152 101 212)(76 213 102 153)(77 154 103 214)(78 215 104 141)(79 142 105 216)(80 217 106 143)(81 144 107 218)(82 219 108 145)(83 146 109 220)(84 221 110 147)(85 114 182 185)(86 186 169 115)(87 116 170 187)(88 188 171 117)(89 118 172 189)(90 190 173 119)(91 120 174 191)(92 192 175 121)(93 122 176 193)(94 194 177 123)(95 124 178 195)(96 196 179 125)(97 126 180 183)(98 184 181 113)
(1 147 38 214)(2 141 39 222)(3 149 40 216)(4 143 41 224)(5 151 42 218)(6 145 36 212)(7 153 37 220)(8 221 27 154)(9 215 28 148)(10 223 22 142)(11 217 23 150)(12 211 24 144)(13 219 25 152)(14 213 26 146)(15 180 53 90)(16 174 54 98)(17 182 55 92)(18 176 56 86)(19 170 50 94)(20 178 51 88)(21 172 52 96)(29 91 46 181)(30 85 47 175)(31 93 48 169)(32 87 49 177)(33 95 43 171)(34 89 44 179)(35 97 45 173)(57 71 138 78)(58 105 139 112)(59 73 140 80)(60 107 127 100)(61 75 128 82)(62 109 129 102)(63 77 130 84)(64 111 131 104)(65 79 132 72)(66 99 133 106)(67 81 134 74)(68 101 135 108)(69 83 136 76)(70 103 137 110)(113 205 120 156)(114 164 121 199)(115 207 122 158)(116 166 123 201)(117 209 124 160)(118 168 125 203)(119 197 126 162)(155 190 204 183)(157 192 206 185)(159 194 208 187)(161 196 210 189)(163 184 198 191)(165 186 200 193)(167 188 202 195)
(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)
(1 121 38 114)(2 113 39 120)(3 119 40 126)(4 125 41 118)(5 117 42 124)(6 123 36 116)(7 115 37 122)(8 192 27 185)(9 184 28 191)(10 190 22 183)(11 196 23 189)(12 188 24 195)(13 194 25 187)(14 186 26 193)(15 112 53 105)(16 104 54 111)(17 110 55 103)(18 102 56 109)(19 108 50 101)(20 100 51 107)(21 106 52 99)(29 78 46 71)(30 84 47 77)(31 76 48 83)(32 82 49 75)(33 74 43 81)(34 80 44 73)(35 72 45 79)(57 91 138 181)(58 180 139 90)(59 89 140 179)(60 178 127 88)(61 87 128 177)(62 176 129 86)(63 85 130 175)(64 174 131 98)(65 97 132 173)(66 172 133 96)(67 95 134 171)(68 170 135 94)(69 93 136 169)(70 182 137 92)(141 156 222 205)(142 204 223 155)(143 168 224 203)(144 202 211 167)(145 166 212 201)(146 200 213 165)(147 164 214 199)(148 198 215 163)(149 162 216 197)(150 210 217 161)(151 160 218 209)(152 208 219 159)(153 158 220 207)(154 206 221 157)
G:=sub<Sym(224)| (1,130,8,137)(2,138,9,131)(3,132,10,139)(4,140,11,133)(5,134,12,127)(6,128,13,135)(7,136,14,129)(15,204,35,197)(16,198,29,205)(17,206,30,199)(18,200,31,207)(19,208,32,201)(20,202,33,209)(21,210,34,203)(22,58,40,65)(23,66,41,59)(24,60,42,67)(25,68,36,61)(26,62,37,69)(27,70,38,63)(28,64,39,57)(43,160,51,167)(44,168,52,161)(45,162,53,155)(46,156,54,163)(47,164,55,157)(48,158,56,165)(49,166,50,159)(71,148,111,222)(72,223,112,149)(73,150,99,224)(74,211,100,151)(75,152,101,212)(76,213,102,153)(77,154,103,214)(78,215,104,141)(79,142,105,216)(80,217,106,143)(81,144,107,218)(82,219,108,145)(83,146,109,220)(84,221,110,147)(85,114,182,185)(86,186,169,115)(87,116,170,187)(88,188,171,117)(89,118,172,189)(90,190,173,119)(91,120,174,191)(92,192,175,121)(93,122,176,193)(94,194,177,123)(95,124,178,195)(96,196,179,125)(97,126,180,183)(98,184,181,113), (1,147,38,214)(2,141,39,222)(3,149,40,216)(4,143,41,224)(5,151,42,218)(6,145,36,212)(7,153,37,220)(8,221,27,154)(9,215,28,148)(10,223,22,142)(11,217,23,150)(12,211,24,144)(13,219,25,152)(14,213,26,146)(15,180,53,90)(16,174,54,98)(17,182,55,92)(18,176,56,86)(19,170,50,94)(20,178,51,88)(21,172,52,96)(29,91,46,181)(30,85,47,175)(31,93,48,169)(32,87,49,177)(33,95,43,171)(34,89,44,179)(35,97,45,173)(57,71,138,78)(58,105,139,112)(59,73,140,80)(60,107,127,100)(61,75,128,82)(62,109,129,102)(63,77,130,84)(64,111,131,104)(65,79,132,72)(66,99,133,106)(67,81,134,74)(68,101,135,108)(69,83,136,76)(70,103,137,110)(113,205,120,156)(114,164,121,199)(115,207,122,158)(116,166,123,201)(117,209,124,160)(118,168,125,203)(119,197,126,162)(155,190,204,183)(157,192,206,185)(159,194,208,187)(161,196,210,189)(163,184,198,191)(165,186,200,193)(167,188,202,195), (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), (1,121,38,114)(2,113,39,120)(3,119,40,126)(4,125,41,118)(5,117,42,124)(6,123,36,116)(7,115,37,122)(8,192,27,185)(9,184,28,191)(10,190,22,183)(11,196,23,189)(12,188,24,195)(13,194,25,187)(14,186,26,193)(15,112,53,105)(16,104,54,111)(17,110,55,103)(18,102,56,109)(19,108,50,101)(20,100,51,107)(21,106,52,99)(29,78,46,71)(30,84,47,77)(31,76,48,83)(32,82,49,75)(33,74,43,81)(34,80,44,73)(35,72,45,79)(57,91,138,181)(58,180,139,90)(59,89,140,179)(60,178,127,88)(61,87,128,177)(62,176,129,86)(63,85,130,175)(64,174,131,98)(65,97,132,173)(66,172,133,96)(67,95,134,171)(68,170,135,94)(69,93,136,169)(70,182,137,92)(141,156,222,205)(142,204,223,155)(143,168,224,203)(144,202,211,167)(145,166,212,201)(146,200,213,165)(147,164,214,199)(148,198,215,163)(149,162,216,197)(150,210,217,161)(151,160,218,209)(152,208,219,159)(153,158,220,207)(154,206,221,157)>;
G:=Group( (1,130,8,137)(2,138,9,131)(3,132,10,139)(4,140,11,133)(5,134,12,127)(6,128,13,135)(7,136,14,129)(15,204,35,197)(16,198,29,205)(17,206,30,199)(18,200,31,207)(19,208,32,201)(20,202,33,209)(21,210,34,203)(22,58,40,65)(23,66,41,59)(24,60,42,67)(25,68,36,61)(26,62,37,69)(27,70,38,63)(28,64,39,57)(43,160,51,167)(44,168,52,161)(45,162,53,155)(46,156,54,163)(47,164,55,157)(48,158,56,165)(49,166,50,159)(71,148,111,222)(72,223,112,149)(73,150,99,224)(74,211,100,151)(75,152,101,212)(76,213,102,153)(77,154,103,214)(78,215,104,141)(79,142,105,216)(80,217,106,143)(81,144,107,218)(82,219,108,145)(83,146,109,220)(84,221,110,147)(85,114,182,185)(86,186,169,115)(87,116,170,187)(88,188,171,117)(89,118,172,189)(90,190,173,119)(91,120,174,191)(92,192,175,121)(93,122,176,193)(94,194,177,123)(95,124,178,195)(96,196,179,125)(97,126,180,183)(98,184,181,113), (1,147,38,214)(2,141,39,222)(3,149,40,216)(4,143,41,224)(5,151,42,218)(6,145,36,212)(7,153,37,220)(8,221,27,154)(9,215,28,148)(10,223,22,142)(11,217,23,150)(12,211,24,144)(13,219,25,152)(14,213,26,146)(15,180,53,90)(16,174,54,98)(17,182,55,92)(18,176,56,86)(19,170,50,94)(20,178,51,88)(21,172,52,96)(29,91,46,181)(30,85,47,175)(31,93,48,169)(32,87,49,177)(33,95,43,171)(34,89,44,179)(35,97,45,173)(57,71,138,78)(58,105,139,112)(59,73,140,80)(60,107,127,100)(61,75,128,82)(62,109,129,102)(63,77,130,84)(64,111,131,104)(65,79,132,72)(66,99,133,106)(67,81,134,74)(68,101,135,108)(69,83,136,76)(70,103,137,110)(113,205,120,156)(114,164,121,199)(115,207,122,158)(116,166,123,201)(117,209,124,160)(118,168,125,203)(119,197,126,162)(155,190,204,183)(157,192,206,185)(159,194,208,187)(161,196,210,189)(163,184,198,191)(165,186,200,193)(167,188,202,195), (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), (1,121,38,114)(2,113,39,120)(3,119,40,126)(4,125,41,118)(5,117,42,124)(6,123,36,116)(7,115,37,122)(8,192,27,185)(9,184,28,191)(10,190,22,183)(11,196,23,189)(12,188,24,195)(13,194,25,187)(14,186,26,193)(15,112,53,105)(16,104,54,111)(17,110,55,103)(18,102,56,109)(19,108,50,101)(20,100,51,107)(21,106,52,99)(29,78,46,71)(30,84,47,77)(31,76,48,83)(32,82,49,75)(33,74,43,81)(34,80,44,73)(35,72,45,79)(57,91,138,181)(58,180,139,90)(59,89,140,179)(60,178,127,88)(61,87,128,177)(62,176,129,86)(63,85,130,175)(64,174,131,98)(65,97,132,173)(66,172,133,96)(67,95,134,171)(68,170,135,94)(69,93,136,169)(70,182,137,92)(141,156,222,205)(142,204,223,155)(143,168,224,203)(144,202,211,167)(145,166,212,201)(146,200,213,165)(147,164,214,199)(148,198,215,163)(149,162,216,197)(150,210,217,161)(151,160,218,209)(152,208,219,159)(153,158,220,207)(154,206,221,157) );
G=PermutationGroup([(1,130,8,137),(2,138,9,131),(3,132,10,139),(4,140,11,133),(5,134,12,127),(6,128,13,135),(7,136,14,129),(15,204,35,197),(16,198,29,205),(17,206,30,199),(18,200,31,207),(19,208,32,201),(20,202,33,209),(21,210,34,203),(22,58,40,65),(23,66,41,59),(24,60,42,67),(25,68,36,61),(26,62,37,69),(27,70,38,63),(28,64,39,57),(43,160,51,167),(44,168,52,161),(45,162,53,155),(46,156,54,163),(47,164,55,157),(48,158,56,165),(49,166,50,159),(71,148,111,222),(72,223,112,149),(73,150,99,224),(74,211,100,151),(75,152,101,212),(76,213,102,153),(77,154,103,214),(78,215,104,141),(79,142,105,216),(80,217,106,143),(81,144,107,218),(82,219,108,145),(83,146,109,220),(84,221,110,147),(85,114,182,185),(86,186,169,115),(87,116,170,187),(88,188,171,117),(89,118,172,189),(90,190,173,119),(91,120,174,191),(92,192,175,121),(93,122,176,193),(94,194,177,123),(95,124,178,195),(96,196,179,125),(97,126,180,183),(98,184,181,113)], [(1,147,38,214),(2,141,39,222),(3,149,40,216),(4,143,41,224),(5,151,42,218),(6,145,36,212),(7,153,37,220),(8,221,27,154),(9,215,28,148),(10,223,22,142),(11,217,23,150),(12,211,24,144),(13,219,25,152),(14,213,26,146),(15,180,53,90),(16,174,54,98),(17,182,55,92),(18,176,56,86),(19,170,50,94),(20,178,51,88),(21,172,52,96),(29,91,46,181),(30,85,47,175),(31,93,48,169),(32,87,49,177),(33,95,43,171),(34,89,44,179),(35,97,45,173),(57,71,138,78),(58,105,139,112),(59,73,140,80),(60,107,127,100),(61,75,128,82),(62,109,129,102),(63,77,130,84),(64,111,131,104),(65,79,132,72),(66,99,133,106),(67,81,134,74),(68,101,135,108),(69,83,136,76),(70,103,137,110),(113,205,120,156),(114,164,121,199),(115,207,122,158),(116,166,123,201),(117,209,124,160),(118,168,125,203),(119,197,126,162),(155,190,204,183),(157,192,206,185),(159,194,208,187),(161,196,210,189),(163,184,198,191),(165,186,200,193),(167,188,202,195)], [(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)], [(1,121,38,114),(2,113,39,120),(3,119,40,126),(4,125,41,118),(5,117,42,124),(6,123,36,116),(7,115,37,122),(8,192,27,185),(9,184,28,191),(10,190,22,183),(11,196,23,189),(12,188,24,195),(13,194,25,187),(14,186,26,193),(15,112,53,105),(16,104,54,111),(17,110,55,103),(18,102,56,109),(19,108,50,101),(20,100,51,107),(21,106,52,99),(29,78,46,71),(30,84,47,77),(31,76,48,83),(32,82,49,75),(33,74,43,81),(34,80,44,73),(35,72,45,79),(57,91,138,181),(58,180,139,90),(59,89,140,179),(60,178,127,88),(61,87,128,177),(62,176,129,86),(63,85,130,175),(64,174,131,98),(65,97,132,173),(66,172,133,96),(67,95,134,171),(68,170,135,94),(69,93,136,169),(70,182,137,92),(141,156,222,205),(142,204,223,155),(143,168,224,203),(144,202,211,167),(145,166,212,201),(146,200,213,165),(147,164,214,199),(148,198,215,163),(149,162,216,197),(150,210,217,161),(151,160,218,209),(152,208,219,159),(153,158,220,207),(154,206,221,157)])
Matrix representation ►G ⊆ GL8(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 24 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 24 |
| 0 | 0 | 0 | 0 | 12 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 | 0 | 28 |
| 28 | 28 | 0 | 0 | 0 | 0 | 0 | 0 |
| 2 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 10 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 | 0 | 28 |
| 17 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 24 | 12 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 20 | 6 | 0 | 0 | 0 | 0 |
| 0 | 0 | 6 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 | 0 | 2 |
| 0 | 0 | 0 | 0 | 17 | 0 | 2 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12 |
| 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
G:=sub<GL(8,GF(29))| [28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,12,0,0,0,0,0,0,1,0,12,0,0,0,0,24,0,28,0,0,0,0,0,0,24,0,28],[28,2,0,0,0,0,0,0,28,1,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0,1,28,0,0,0,0,0,0,0,0,1,3,0,0,0,0,0,0,10,2,0,0,0,0,0,0,0,0,1,0,12,0,0,0,0,0,0,1,0,12,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28],[17,24,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,20,6,0,0,0,0,0,0,6,9,0,0,0,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,0,0,0,0,0,0,2,0,12,0,0,0,0,2,0,12,0] >;
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 | 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 | D7 | C4○D4 | D14 | D14 | D14 | D14 | 2+ (1+4) | 2- (1+4) | D4⋊2D7 | D4⋊8D14 | D4.10D14 |
| kernel | C42.144D14 | C28⋊2Q8 | C42⋊D7 | C22⋊Dic14 | C23.D14 | Dic7.D4 | C22.D28 | D4×Dic7 | C28⋊2D4 | Q8×Dic7 | D14⋊3Q8 | C7×C4.4D4 | C4.4D4 | C28 | C42 | C22⋊C4 | C2×D4 | C2×Q8 | C14 | C14 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 2 | 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._{144}D_{14} % in TeX
G:=Group("C4^2.144D14"); // GroupNames label
G:=SmallGroup(448,1135);
// by ID
G=gap.SmallGroup(448,1135);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,100,675,570,409,18822]);
// 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,c*b*c^-1=a^2*b^-1,d*b*d^-1=b^-1,d*c*d^-1=b^2*c^-1>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀