metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.135D14, C14.672- (1+4), (C4×Q8)⋊17D7, (Q8×C28)⋊19C2, C4⋊C4.302D14, C28⋊2Q8⋊29C2, (C4×D28).23C2, D14⋊3Q8⋊11C2, (C4×Dic14)⋊41C2, C4.69(C4○D28), (C2×Q8).183D14, C28.122(C4○D4), (C4×C28).180C22, (C2×C14).128C24, (C2×C28).591C23, D14⋊C4.56C22, C4.50(Q8⋊2D7), C4.D28.11C2, (C2×D28).219C22, C4⋊Dic7.400C22, (Q8×C14).228C22, (C22×D7).50C23, C22.149(C23×D7), Dic7⋊C4.157C22, C7⋊4(C22.50C24), (C4×Dic7).210C22, (C2×Dic7).218C23, C2.25(D4.10D14), (C2×Dic14).243C22, C4⋊C4⋊7D7⋊18C2, C4⋊C4⋊D7⋊11C2, C2.67(C2×C4○D28), (C2×C4×D7).78C22, C14.113(C2×C4○D4), C2.13(C2×Q8⋊2D7), (C7×C4⋊C4).356C22, (C2×C4).172(C22×D7), SmallGroup(448,1037)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 900 in 212 conjugacy classes, 99 normal (29 characteristic)
C1, C2 [×3], C2 [×2], C4 [×4], C4 [×11], C22, C22 [×6], C7, C2×C4 [×3], C2×C4 [×4], C2×C4 [×10], D4 [×2], Q8 [×6], C23 [×2], D7 [×2], C14 [×3], C42, C42 [×2], C42 [×4], C22⋊C4 [×10], C4⋊C4, C4⋊C4 [×2], C4⋊C4 [×9], C22×C4 [×2], C2×D4, C2×Q8, C2×Q8 [×2], Dic7 [×6], C28 [×4], C28 [×5], D14 [×6], C2×C14, C42⋊C2 [×2], C4×D4, C4×Q8, C4×Q8 [×2], C22⋊Q8 [×2], C4.4D4 [×2], C42⋊2C2 [×4], C4⋊Q8, Dic14 [×4], C4×D7 [×4], D28 [×2], C2×Dic7 [×6], C2×C28 [×3], C2×C28 [×4], C7×Q8 [×2], C22×D7 [×2], C22.50C24, C4×Dic7 [×4], Dic7⋊C4 [×4], C4⋊Dic7, C4⋊Dic7 [×4], D14⋊C4 [×10], C4×C28, C4×C28 [×2], C7×C4⋊C4, C7×C4⋊C4 [×2], C2×Dic14 [×2], C2×C4×D7 [×2], C2×D28, Q8×C14, C4×Dic14 [×2], C28⋊2Q8, C4×D28, C4.D28 [×2], C4⋊C4⋊7D7 [×2], C4⋊C4⋊D7 [×4], D14⋊3Q8 [×2], Q8×C28, C42.135D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×4], C24, D14 [×7], C2×C4○D4 [×2], 2- (1+4), C22×D7 [×7], C22.50C24, C4○D28 [×2], Q8⋊2D7 [×2], C23×D7, C2×C4○D28, C2×Q8⋊2D7, D4.10D14, C42.135D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=d2=a2b2, ab=ba, ac=ca, dad-1=a-1, cbc-1=a2b-1, bd=db, dcd-1=c13 >
►On 224 points
Generators in S224
(1 142 89 214)(2 143 90 215)(3 144 91 216)(4 145 92 217)(5 146 93 218)(6 147 94 219)(7 148 95 220)(8 149 96 221)(9 150 97 222)(10 151 98 223)(11 152 99 224)(12 153 100 197)(13 154 101 198)(14 155 102 199)(15 156 103 200)(16 157 104 201)(17 158 105 202)(18 159 106 203)(19 160 107 204)(20 161 108 205)(21 162 109 206)(22 163 110 207)(23 164 111 208)(24 165 112 209)(25 166 85 210)(26 167 86 211)(27 168 87 212)(28 141 88 213)(29 186 134 76)(30 187 135 77)(31 188 136 78)(32 189 137 79)(33 190 138 80)(34 191 139 81)(35 192 140 82)(36 193 113 83)(37 194 114 84)(38 195 115 57)(39 196 116 58)(40 169 117 59)(41 170 118 60)(42 171 119 61)(43 172 120 62)(44 173 121 63)(45 174 122 64)(46 175 123 65)(47 176 124 66)(48 177 125 67)(49 178 126 68)(50 179 127 69)(51 180 128 70)(52 181 129 71)(53 182 130 72)(54 183 131 73)(55 184 132 74)(56 185 133 75)
(1 125 103 34)(2 140 104 49)(3 127 105 36)(4 114 106 51)(5 129 107 38)(6 116 108 53)(7 131 109 40)(8 118 110 55)(9 133 111 42)(10 120 112 29)(11 135 85 44)(12 122 86 31)(13 137 87 46)(14 124 88 33)(15 139 89 48)(16 126 90 35)(17 113 91 50)(18 128 92 37)(19 115 93 52)(20 130 94 39)(21 117 95 54)(22 132 96 41)(23 119 97 56)(24 134 98 43)(25 121 99 30)(26 136 100 45)(27 123 101 32)(28 138 102 47)(57 218 181 160)(58 205 182 147)(59 220 183 162)(60 207 184 149)(61 222 185 164)(62 209 186 151)(63 224 187 166)(64 211 188 153)(65 198 189 168)(66 213 190 155)(67 200 191 142)(68 215 192 157)(69 202 193 144)(70 217 194 159)(71 204 195 146)(72 219 196 161)(73 206 169 148)(74 221 170 163)(75 208 171 150)(76 223 172 165)(77 210 173 152)(78 197 174 167)(79 212 175 154)(80 199 176 141)(81 214 177 156)(82 201 178 143)(83 216 179 158)(84 203 180 145)
(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)
(1 199 15 213)(2 212 16 198)(3 197 17 211)(4 210 18 224)(5 223 19 209)(6 208 20 222)(7 221 21 207)(8 206 22 220)(9 219 23 205)(10 204 24 218)(11 217 25 203)(12 202 26 216)(13 215 27 201)(14 200 28 214)(29 71 43 57)(30 84 44 70)(31 69 45 83)(32 82 46 68)(33 67 47 81)(34 80 48 66)(35 65 49 79)(36 78 50 64)(37 63 51 77)(38 76 52 62)(39 61 53 75)(40 74 54 60)(41 59 55 73)(42 72 56 58)(85 159 99 145)(86 144 100 158)(87 157 101 143)(88 142 102 156)(89 155 103 141)(90 168 104 154)(91 153 105 167)(92 166 106 152)(93 151 107 165)(94 164 108 150)(95 149 109 163)(96 162 110 148)(97 147 111 161)(98 160 112 146)(113 188 127 174)(114 173 128 187)(115 186 129 172)(116 171 130 185)(117 184 131 170)(118 169 132 183)(119 182 133 196)(120 195 134 181)(121 180 135 194)(122 193 136 179)(123 178 137 192)(124 191 138 177)(125 176 139 190)(126 189 140 175)
G:=sub<Sym(224)| (1,142,89,214)(2,143,90,215)(3,144,91,216)(4,145,92,217)(5,146,93,218)(6,147,94,219)(7,148,95,220)(8,149,96,221)(9,150,97,222)(10,151,98,223)(11,152,99,224)(12,153,100,197)(13,154,101,198)(14,155,102,199)(15,156,103,200)(16,157,104,201)(17,158,105,202)(18,159,106,203)(19,160,107,204)(20,161,108,205)(21,162,109,206)(22,163,110,207)(23,164,111,208)(24,165,112,209)(25,166,85,210)(26,167,86,211)(27,168,87,212)(28,141,88,213)(29,186,134,76)(30,187,135,77)(31,188,136,78)(32,189,137,79)(33,190,138,80)(34,191,139,81)(35,192,140,82)(36,193,113,83)(37,194,114,84)(38,195,115,57)(39,196,116,58)(40,169,117,59)(41,170,118,60)(42,171,119,61)(43,172,120,62)(44,173,121,63)(45,174,122,64)(46,175,123,65)(47,176,124,66)(48,177,125,67)(49,178,126,68)(50,179,127,69)(51,180,128,70)(52,181,129,71)(53,182,130,72)(54,183,131,73)(55,184,132,74)(56,185,133,75), (1,125,103,34)(2,140,104,49)(3,127,105,36)(4,114,106,51)(5,129,107,38)(6,116,108,53)(7,131,109,40)(8,118,110,55)(9,133,111,42)(10,120,112,29)(11,135,85,44)(12,122,86,31)(13,137,87,46)(14,124,88,33)(15,139,89,48)(16,126,90,35)(17,113,91,50)(18,128,92,37)(19,115,93,52)(20,130,94,39)(21,117,95,54)(22,132,96,41)(23,119,97,56)(24,134,98,43)(25,121,99,30)(26,136,100,45)(27,123,101,32)(28,138,102,47)(57,218,181,160)(58,205,182,147)(59,220,183,162)(60,207,184,149)(61,222,185,164)(62,209,186,151)(63,224,187,166)(64,211,188,153)(65,198,189,168)(66,213,190,155)(67,200,191,142)(68,215,192,157)(69,202,193,144)(70,217,194,159)(71,204,195,146)(72,219,196,161)(73,206,169,148)(74,221,170,163)(75,208,171,150)(76,223,172,165)(77,210,173,152)(78,197,174,167)(79,212,175,154)(80,199,176,141)(81,214,177,156)(82,201,178,143)(83,216,179,158)(84,203,180,145), (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), (1,199,15,213)(2,212,16,198)(3,197,17,211)(4,210,18,224)(5,223,19,209)(6,208,20,222)(7,221,21,207)(8,206,22,220)(9,219,23,205)(10,204,24,218)(11,217,25,203)(12,202,26,216)(13,215,27,201)(14,200,28,214)(29,71,43,57)(30,84,44,70)(31,69,45,83)(32,82,46,68)(33,67,47,81)(34,80,48,66)(35,65,49,79)(36,78,50,64)(37,63,51,77)(38,76,52,62)(39,61,53,75)(40,74,54,60)(41,59,55,73)(42,72,56,58)(85,159,99,145)(86,144,100,158)(87,157,101,143)(88,142,102,156)(89,155,103,141)(90,168,104,154)(91,153,105,167)(92,166,106,152)(93,151,107,165)(94,164,108,150)(95,149,109,163)(96,162,110,148)(97,147,111,161)(98,160,112,146)(113,188,127,174)(114,173,128,187)(115,186,129,172)(116,171,130,185)(117,184,131,170)(118,169,132,183)(119,182,133,196)(120,195,134,181)(121,180,135,194)(122,193,136,179)(123,178,137,192)(124,191,138,177)(125,176,139,190)(126,189,140,175)>;
G:=Group( (1,142,89,214)(2,143,90,215)(3,144,91,216)(4,145,92,217)(5,146,93,218)(6,147,94,219)(7,148,95,220)(8,149,96,221)(9,150,97,222)(10,151,98,223)(11,152,99,224)(12,153,100,197)(13,154,101,198)(14,155,102,199)(15,156,103,200)(16,157,104,201)(17,158,105,202)(18,159,106,203)(19,160,107,204)(20,161,108,205)(21,162,109,206)(22,163,110,207)(23,164,111,208)(24,165,112,209)(25,166,85,210)(26,167,86,211)(27,168,87,212)(28,141,88,213)(29,186,134,76)(30,187,135,77)(31,188,136,78)(32,189,137,79)(33,190,138,80)(34,191,139,81)(35,192,140,82)(36,193,113,83)(37,194,114,84)(38,195,115,57)(39,196,116,58)(40,169,117,59)(41,170,118,60)(42,171,119,61)(43,172,120,62)(44,173,121,63)(45,174,122,64)(46,175,123,65)(47,176,124,66)(48,177,125,67)(49,178,126,68)(50,179,127,69)(51,180,128,70)(52,181,129,71)(53,182,130,72)(54,183,131,73)(55,184,132,74)(56,185,133,75), (1,125,103,34)(2,140,104,49)(3,127,105,36)(4,114,106,51)(5,129,107,38)(6,116,108,53)(7,131,109,40)(8,118,110,55)(9,133,111,42)(10,120,112,29)(11,135,85,44)(12,122,86,31)(13,137,87,46)(14,124,88,33)(15,139,89,48)(16,126,90,35)(17,113,91,50)(18,128,92,37)(19,115,93,52)(20,130,94,39)(21,117,95,54)(22,132,96,41)(23,119,97,56)(24,134,98,43)(25,121,99,30)(26,136,100,45)(27,123,101,32)(28,138,102,47)(57,218,181,160)(58,205,182,147)(59,220,183,162)(60,207,184,149)(61,222,185,164)(62,209,186,151)(63,224,187,166)(64,211,188,153)(65,198,189,168)(66,213,190,155)(67,200,191,142)(68,215,192,157)(69,202,193,144)(70,217,194,159)(71,204,195,146)(72,219,196,161)(73,206,169,148)(74,221,170,163)(75,208,171,150)(76,223,172,165)(77,210,173,152)(78,197,174,167)(79,212,175,154)(80,199,176,141)(81,214,177,156)(82,201,178,143)(83,216,179,158)(84,203,180,145), (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), (1,199,15,213)(2,212,16,198)(3,197,17,211)(4,210,18,224)(5,223,19,209)(6,208,20,222)(7,221,21,207)(8,206,22,220)(9,219,23,205)(10,204,24,218)(11,217,25,203)(12,202,26,216)(13,215,27,201)(14,200,28,214)(29,71,43,57)(30,84,44,70)(31,69,45,83)(32,82,46,68)(33,67,47,81)(34,80,48,66)(35,65,49,79)(36,78,50,64)(37,63,51,77)(38,76,52,62)(39,61,53,75)(40,74,54,60)(41,59,55,73)(42,72,56,58)(85,159,99,145)(86,144,100,158)(87,157,101,143)(88,142,102,156)(89,155,103,141)(90,168,104,154)(91,153,105,167)(92,166,106,152)(93,151,107,165)(94,164,108,150)(95,149,109,163)(96,162,110,148)(97,147,111,161)(98,160,112,146)(113,188,127,174)(114,173,128,187)(115,186,129,172)(116,171,130,185)(117,184,131,170)(118,169,132,183)(119,182,133,196)(120,195,134,181)(121,180,135,194)(122,193,136,179)(123,178,137,192)(124,191,138,177)(125,176,139,190)(126,189,140,175) );
G=PermutationGroup([(1,142,89,214),(2,143,90,215),(3,144,91,216),(4,145,92,217),(5,146,93,218),(6,147,94,219),(7,148,95,220),(8,149,96,221),(9,150,97,222),(10,151,98,223),(11,152,99,224),(12,153,100,197),(13,154,101,198),(14,155,102,199),(15,156,103,200),(16,157,104,201),(17,158,105,202),(18,159,106,203),(19,160,107,204),(20,161,108,205),(21,162,109,206),(22,163,110,207),(23,164,111,208),(24,165,112,209),(25,166,85,210),(26,167,86,211),(27,168,87,212),(28,141,88,213),(29,186,134,76),(30,187,135,77),(31,188,136,78),(32,189,137,79),(33,190,138,80),(34,191,139,81),(35,192,140,82),(36,193,113,83),(37,194,114,84),(38,195,115,57),(39,196,116,58),(40,169,117,59),(41,170,118,60),(42,171,119,61),(43,172,120,62),(44,173,121,63),(45,174,122,64),(46,175,123,65),(47,176,124,66),(48,177,125,67),(49,178,126,68),(50,179,127,69),(51,180,128,70),(52,181,129,71),(53,182,130,72),(54,183,131,73),(55,184,132,74),(56,185,133,75)], [(1,125,103,34),(2,140,104,49),(3,127,105,36),(4,114,106,51),(5,129,107,38),(6,116,108,53),(7,131,109,40),(8,118,110,55),(9,133,111,42),(10,120,112,29),(11,135,85,44),(12,122,86,31),(13,137,87,46),(14,124,88,33),(15,139,89,48),(16,126,90,35),(17,113,91,50),(18,128,92,37),(19,115,93,52),(20,130,94,39),(21,117,95,54),(22,132,96,41),(23,119,97,56),(24,134,98,43),(25,121,99,30),(26,136,100,45),(27,123,101,32),(28,138,102,47),(57,218,181,160),(58,205,182,147),(59,220,183,162),(60,207,184,149),(61,222,185,164),(62,209,186,151),(63,224,187,166),(64,211,188,153),(65,198,189,168),(66,213,190,155),(67,200,191,142),(68,215,192,157),(69,202,193,144),(70,217,194,159),(71,204,195,146),(72,219,196,161),(73,206,169,148),(74,221,170,163),(75,208,171,150),(76,223,172,165),(77,210,173,152),(78,197,174,167),(79,212,175,154),(80,199,176,141),(81,214,177,156),(82,201,178,143),(83,216,179,158),(84,203,180,145)], [(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)], [(1,199,15,213),(2,212,16,198),(3,197,17,211),(4,210,18,224),(5,223,19,209),(6,208,20,222),(7,221,21,207),(8,206,22,220),(9,219,23,205),(10,204,24,218),(11,217,25,203),(12,202,26,216),(13,215,27,201),(14,200,28,214),(29,71,43,57),(30,84,44,70),(31,69,45,83),(32,82,46,68),(33,67,47,81),(34,80,48,66),(35,65,49,79),(36,78,50,64),(37,63,51,77),(38,76,52,62),(39,61,53,75),(40,74,54,60),(41,59,55,73),(42,72,56,58),(85,159,99,145),(86,144,100,158),(87,157,101,143),(88,142,102,156),(89,155,103,141),(90,168,104,154),(91,153,105,167),(92,166,106,152),(93,151,107,165),(94,164,108,150),(95,149,109,163),(96,162,110,148),(97,147,111,161),(98,160,112,146),(113,188,127,174),(114,173,128,187),(115,186,129,172),(116,171,130,185),(117,184,131,170),(118,169,132,183),(119,182,133,196),(120,195,134,181),(121,180,135,194),(122,193,136,179),(123,178,137,192),(124,191,138,177),(125,176,139,190),(126,189,140,175)])
Matrix representation ►G ⊆ GL4(𝔽29) generated by
| 13 | 5 | 0 | 0 |
| 24 | 16 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 17 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 |
| 0 | 0 | 28 | 26 |
| 0 | 0 | 20 | 1 |
| 4 | 4 | 0 | 0 |
| 25 | 18 | 0 | 0 |
| 0 | 0 | 17 | 0 |
| 0 | 0 | 8 | 12 |
| 3 | 26 | 0 | 0 |
| 22 | 26 | 0 | 0 |
| 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 17 |
G:=sub<GL(4,GF(29))| [13,24,0,0,5,16,0,0,0,0,1,0,0,0,0,1],[17,0,0,0,0,17,0,0,0,0,28,20,0,0,26,1],[4,25,0,0,4,18,0,0,0,0,17,8,0,0,0,12],[3,22,0,0,26,26,0,0,0,0,17,0,0,0,0,17] >;
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 4Q | 4R | 4S | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 2 | ··· | 2 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 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 | D7 | C4○D4 | D14 | D14 | D14 | C4○D28 | 2- (1+4) | Q8⋊2D7 | D4.10D14 |
| kernel | C42.135D14 | C4×Dic14 | C28⋊2Q8 | C4×D28 | C4.D28 | C4⋊C4⋊7D7 | C4⋊C4⋊D7 | D14⋊3Q8 | Q8×C28 | C4×Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | C4 | C14 | C4 | C2 |
| # reps | 1 | 2 | 1 | 1 | 2 | 2 | 4 | 2 | 1 | 3 | 8 | 9 | 9 | 3 | 24 | 1 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{135}D_{14} % in TeX
G:=Group("C4^2.135D14"); // GroupNames label
G:=SmallGroup(448,1037);
// by ID
G=gap.SmallGroup(448,1037);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,232,100,675,185,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^2*b^2,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,c*b*c^-1=a^2*b^-1,b*d=d*b,d*c*d^-1=c^13>;
// generators/relations
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