metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.229D14, (C4×D4)⋊19D7, (D4×C28)⋊21C2, (D7×C42)⋊5C2, C4⋊C4.285D14, D14⋊2Q8⋊48C2, D14.2(C4○D4), (C4×Dic14)⋊33C2, (C2×D4).218D14, C4.44(C4○D28), C28⋊2D4.14C2, C4.Dic14⋊46C2, D14.D4⋊54C2, C28.310(C4○D4), C28.17D4⋊32C2, (C2×C14).101C24, (C4×C28).156C22, (C2×C28).161C23, D14⋊C4.99C22, C22⋊C4.114D14, (C22×C4).212D14, C4.137(D4⋊2D7), C23.98(C22×D7), (D4×C14).261C22, C23.21D14⋊8C2, C23.D14⋊50C2, C4⋊Dic7.300C22, C22.126(C23×D7), Dic7⋊C4.112C22, (C22×C28).110C22, (C22×C14).171C23, C7⋊4(C23.36C23), (C2×Dic7).208C23, (C4×Dic7).293C22, (C22×D7).174C23, C23.D7.106C22, (C2×Dic14).288C22, (C4×C7⋊D4)⋊5C2, C2.24(D7×C4○D4), C2.50(C2×C4○D28), C14.141(C2×C4○D4), C2.23(C2×D4⋊2D7), (C2×C4×D7).293C22, (C7×C4⋊C4).330C22, (C2×C4).161(C22×D7), (C2×C7⋊D4).115C22, (C7×C22⋊C4).125C22, SmallGroup(448,1010)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 916 in 234 conjugacy classes, 101 normal (43 characteristic)
C1, C2 [×3], C2 [×4], C4 [×4], C4 [×10], C22, C22 [×10], C7, C2×C4 [×3], C2×C4 [×2], C2×C4 [×17], D4 [×6], Q8 [×2], C23 [×2], C23, D7 [×2], C14 [×3], C14 [×2], C42, C42 [×5], C22⋊C4 [×2], C22⋊C4 [×8], C4⋊C4, C4⋊C4 [×9], C22×C4 [×2], C22×C4 [×3], C2×D4, C2×D4 [×2], C2×Q8, Dic7 [×7], C28 [×4], C28 [×3], D14 [×2], D14 [×2], C2×C14, C2×C14 [×6], C2×C42, C42⋊C2 [×2], C4×D4, C4×D4 [×2], C4×Q8, C4⋊D4, C22⋊Q8, C22.D4 [×2], C4.4D4, C42.C2, C42⋊2C2 [×2], Dic14 [×2], C4×D7 [×6], C2×Dic7 [×3], C2×Dic7 [×4], C7⋊D4 [×4], C2×C28 [×3], C2×C28 [×2], C2×C28 [×4], C7×D4 [×2], C22×D7, C22×C14 [×2], C23.36C23, C4×Dic7 [×3], C4×Dic7 [×2], Dic7⋊C4 [×4], C4⋊Dic7, C4⋊Dic7 [×4], D14⋊C4 [×2], C23.D7 [×6], C4×C28, C7×C22⋊C4 [×2], C7×C4⋊C4, C2×Dic14, C2×C4×D7 [×3], C2×C7⋊D4 [×2], C22×C28 [×2], D4×C14, C4×Dic14, D7×C42, C23.D14 [×2], D14.D4 [×2], C4.Dic14, D14⋊2Q8, C23.21D14 [×2], C4×C7⋊D4 [×2], C28.17D4, C28⋊2D4, D4×C28, C42.229D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×6], C24, D14 [×7], C2×C4○D4 [×3], C22×D7 [×7], C23.36C23, C4○D28 [×2], D4⋊2D7 [×2], C23×D7, C2×C4○D28, C2×D4⋊2D7, D7×C4○D4, C42.229D14
Generators and relations
G = < a,b,c,d | a4=b4=c14=1, d2=a2, ab=ba, cac-1=dad-1=a-1b2, bc=cb, bd=db, dcd-1=a2c-1 >
►On 224 points
Generators in S224
(1 155 102 221)(2 154 103 76)(3 157 104 223)(4 142 105 78)(5 159 106 211)(6 144 107 80)(7 161 108 213)(8 146 109 82)(9 163 110 215)(10 148 111 84)(11 165 112 217)(12 150 99 72)(13 167 100 219)(14 152 101 74)(15 36 115 171)(16 97 116 60)(17 38 117 173)(18 85 118 62)(19 40 119 175)(20 87 120 64)(21 42 121 177)(22 89 122 66)(23 30 123 179)(24 91 124 68)(25 32 125 181)(26 93 126 70)(27 34 113 169)(28 95 114 58)(29 206 178 184)(31 208 180 186)(33 210 182 188)(35 198 170 190)(37 200 172 192)(39 202 174 194)(41 204 176 196)(43 151 129 73)(44 168 130 220)(45 153 131 75)(46 156 132 222)(47 141 133 77)(48 158 134 224)(49 143 135 79)(50 160 136 212)(51 145 137 81)(52 162 138 214)(53 147 139 83)(54 164 140 216)(55 149 127 71)(56 166 128 218)(57 189 94 197)(59 191 96 199)(61 193 98 201)(63 195 86 203)(65 183 88 205)(67 185 90 207)(69 187 92 209)
(1 64 131 41)(2 65 132 42)(3 66 133 29)(4 67 134 30)(5 68 135 31)(6 69 136 32)(7 70 137 33)(8 57 138 34)(9 58 139 35)(10 59 140 36)(11 60 127 37)(12 61 128 38)(13 62 129 39)(14 63 130 40)(15 84 199 164)(16 71 200 165)(17 72 201 166)(18 73 202 167)(19 74 203 168)(20 75 204 155)(21 76 205 156)(22 77 206 157)(23 78 207 158)(24 79 208 159)(25 80 209 160)(26 81 210 161)(27 82 197 162)(28 83 198 163)(43 174 100 85)(44 175 101 86)(45 176 102 87)(46 177 103 88)(47 178 104 89)(48 179 105 90)(49 180 106 91)(50 181 107 92)(51 182 108 93)(52 169 109 94)(53 170 110 95)(54 171 111 96)(55 172 112 97)(56 173 99 98)(113 146 189 214)(114 147 190 215)(115 148 191 216)(116 149 192 217)(117 150 193 218)(118 151 194 219)(119 152 195 220)(120 153 196 221)(121 154 183 222)(122 141 184 223)(123 142 185 224)(124 143 186 211)(125 144 187 212)(126 145 188 213)
(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 14 102 101)(2 100 103 13)(3 12 104 99)(4 112 105 11)(5 10 106 111)(6 110 107 9)(7 8 108 109)(15 124 115 24)(16 23 116 123)(17 122 117 22)(18 21 118 121)(19 120 119 20)(25 114 125 28)(26 27 126 113)(29 38 178 173)(30 172 179 37)(31 36 180 171)(32 170 181 35)(33 34 182 169)(39 42 174 177)(40 176 175 41)(43 46 129 132)(44 131 130 45)(47 56 133 128)(48 127 134 55)(49 54 135 140)(50 139 136 53)(51 52 137 138)(57 93 94 70)(58 69 95 92)(59 91 96 68)(60 67 97 90)(61 89 98 66)(62 65 85 88)(63 87 86 64)(71 78 149 142)(72 141 150 77)(73 76 151 154)(74 153 152 75)(79 84 143 148)(80 147 144 83)(81 82 145 146)(155 168 221 220)(156 219 222 167)(157 166 223 218)(158 217 224 165)(159 164 211 216)(160 215 212 163)(161 162 213 214)(183 202 205 194)(184 193 206 201)(185 200 207 192)(186 191 208 199)(187 198 209 190)(188 189 210 197)(195 204 203 196)
G:=sub<Sym(224)| (1,155,102,221)(2,154,103,76)(3,157,104,223)(4,142,105,78)(5,159,106,211)(6,144,107,80)(7,161,108,213)(8,146,109,82)(9,163,110,215)(10,148,111,84)(11,165,112,217)(12,150,99,72)(13,167,100,219)(14,152,101,74)(15,36,115,171)(16,97,116,60)(17,38,117,173)(18,85,118,62)(19,40,119,175)(20,87,120,64)(21,42,121,177)(22,89,122,66)(23,30,123,179)(24,91,124,68)(25,32,125,181)(26,93,126,70)(27,34,113,169)(28,95,114,58)(29,206,178,184)(31,208,180,186)(33,210,182,188)(35,198,170,190)(37,200,172,192)(39,202,174,194)(41,204,176,196)(43,151,129,73)(44,168,130,220)(45,153,131,75)(46,156,132,222)(47,141,133,77)(48,158,134,224)(49,143,135,79)(50,160,136,212)(51,145,137,81)(52,162,138,214)(53,147,139,83)(54,164,140,216)(55,149,127,71)(56,166,128,218)(57,189,94,197)(59,191,96,199)(61,193,98,201)(63,195,86,203)(65,183,88,205)(67,185,90,207)(69,187,92,209), (1,64,131,41)(2,65,132,42)(3,66,133,29)(4,67,134,30)(5,68,135,31)(6,69,136,32)(7,70,137,33)(8,57,138,34)(9,58,139,35)(10,59,140,36)(11,60,127,37)(12,61,128,38)(13,62,129,39)(14,63,130,40)(15,84,199,164)(16,71,200,165)(17,72,201,166)(18,73,202,167)(19,74,203,168)(20,75,204,155)(21,76,205,156)(22,77,206,157)(23,78,207,158)(24,79,208,159)(25,80,209,160)(26,81,210,161)(27,82,197,162)(28,83,198,163)(43,174,100,85)(44,175,101,86)(45,176,102,87)(46,177,103,88)(47,178,104,89)(48,179,105,90)(49,180,106,91)(50,181,107,92)(51,182,108,93)(52,169,109,94)(53,170,110,95)(54,171,111,96)(55,172,112,97)(56,173,99,98)(113,146,189,214)(114,147,190,215)(115,148,191,216)(116,149,192,217)(117,150,193,218)(118,151,194,219)(119,152,195,220)(120,153,196,221)(121,154,183,222)(122,141,184,223)(123,142,185,224)(124,143,186,211)(125,144,187,212)(126,145,188,213), (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), (1,14,102,101)(2,100,103,13)(3,12,104,99)(4,112,105,11)(5,10,106,111)(6,110,107,9)(7,8,108,109)(15,124,115,24)(16,23,116,123)(17,122,117,22)(18,21,118,121)(19,120,119,20)(25,114,125,28)(26,27,126,113)(29,38,178,173)(30,172,179,37)(31,36,180,171)(32,170,181,35)(33,34,182,169)(39,42,174,177)(40,176,175,41)(43,46,129,132)(44,131,130,45)(47,56,133,128)(48,127,134,55)(49,54,135,140)(50,139,136,53)(51,52,137,138)(57,93,94,70)(58,69,95,92)(59,91,96,68)(60,67,97,90)(61,89,98,66)(62,65,85,88)(63,87,86,64)(71,78,149,142)(72,141,150,77)(73,76,151,154)(74,153,152,75)(79,84,143,148)(80,147,144,83)(81,82,145,146)(155,168,221,220)(156,219,222,167)(157,166,223,218)(158,217,224,165)(159,164,211,216)(160,215,212,163)(161,162,213,214)(183,202,205,194)(184,193,206,201)(185,200,207,192)(186,191,208,199)(187,198,209,190)(188,189,210,197)(195,204,203,196)>;
G:=Group( (1,155,102,221)(2,154,103,76)(3,157,104,223)(4,142,105,78)(5,159,106,211)(6,144,107,80)(7,161,108,213)(8,146,109,82)(9,163,110,215)(10,148,111,84)(11,165,112,217)(12,150,99,72)(13,167,100,219)(14,152,101,74)(15,36,115,171)(16,97,116,60)(17,38,117,173)(18,85,118,62)(19,40,119,175)(20,87,120,64)(21,42,121,177)(22,89,122,66)(23,30,123,179)(24,91,124,68)(25,32,125,181)(26,93,126,70)(27,34,113,169)(28,95,114,58)(29,206,178,184)(31,208,180,186)(33,210,182,188)(35,198,170,190)(37,200,172,192)(39,202,174,194)(41,204,176,196)(43,151,129,73)(44,168,130,220)(45,153,131,75)(46,156,132,222)(47,141,133,77)(48,158,134,224)(49,143,135,79)(50,160,136,212)(51,145,137,81)(52,162,138,214)(53,147,139,83)(54,164,140,216)(55,149,127,71)(56,166,128,218)(57,189,94,197)(59,191,96,199)(61,193,98,201)(63,195,86,203)(65,183,88,205)(67,185,90,207)(69,187,92,209), (1,64,131,41)(2,65,132,42)(3,66,133,29)(4,67,134,30)(5,68,135,31)(6,69,136,32)(7,70,137,33)(8,57,138,34)(9,58,139,35)(10,59,140,36)(11,60,127,37)(12,61,128,38)(13,62,129,39)(14,63,130,40)(15,84,199,164)(16,71,200,165)(17,72,201,166)(18,73,202,167)(19,74,203,168)(20,75,204,155)(21,76,205,156)(22,77,206,157)(23,78,207,158)(24,79,208,159)(25,80,209,160)(26,81,210,161)(27,82,197,162)(28,83,198,163)(43,174,100,85)(44,175,101,86)(45,176,102,87)(46,177,103,88)(47,178,104,89)(48,179,105,90)(49,180,106,91)(50,181,107,92)(51,182,108,93)(52,169,109,94)(53,170,110,95)(54,171,111,96)(55,172,112,97)(56,173,99,98)(113,146,189,214)(114,147,190,215)(115,148,191,216)(116,149,192,217)(117,150,193,218)(118,151,194,219)(119,152,195,220)(120,153,196,221)(121,154,183,222)(122,141,184,223)(123,142,185,224)(124,143,186,211)(125,144,187,212)(126,145,188,213), (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), (1,14,102,101)(2,100,103,13)(3,12,104,99)(4,112,105,11)(5,10,106,111)(6,110,107,9)(7,8,108,109)(15,124,115,24)(16,23,116,123)(17,122,117,22)(18,21,118,121)(19,120,119,20)(25,114,125,28)(26,27,126,113)(29,38,178,173)(30,172,179,37)(31,36,180,171)(32,170,181,35)(33,34,182,169)(39,42,174,177)(40,176,175,41)(43,46,129,132)(44,131,130,45)(47,56,133,128)(48,127,134,55)(49,54,135,140)(50,139,136,53)(51,52,137,138)(57,93,94,70)(58,69,95,92)(59,91,96,68)(60,67,97,90)(61,89,98,66)(62,65,85,88)(63,87,86,64)(71,78,149,142)(72,141,150,77)(73,76,151,154)(74,153,152,75)(79,84,143,148)(80,147,144,83)(81,82,145,146)(155,168,221,220)(156,219,222,167)(157,166,223,218)(158,217,224,165)(159,164,211,216)(160,215,212,163)(161,162,213,214)(183,202,205,194)(184,193,206,201)(185,200,207,192)(186,191,208,199)(187,198,209,190)(188,189,210,197)(195,204,203,196) );
G=PermutationGroup([(1,155,102,221),(2,154,103,76),(3,157,104,223),(4,142,105,78),(5,159,106,211),(6,144,107,80),(7,161,108,213),(8,146,109,82),(9,163,110,215),(10,148,111,84),(11,165,112,217),(12,150,99,72),(13,167,100,219),(14,152,101,74),(15,36,115,171),(16,97,116,60),(17,38,117,173),(18,85,118,62),(19,40,119,175),(20,87,120,64),(21,42,121,177),(22,89,122,66),(23,30,123,179),(24,91,124,68),(25,32,125,181),(26,93,126,70),(27,34,113,169),(28,95,114,58),(29,206,178,184),(31,208,180,186),(33,210,182,188),(35,198,170,190),(37,200,172,192),(39,202,174,194),(41,204,176,196),(43,151,129,73),(44,168,130,220),(45,153,131,75),(46,156,132,222),(47,141,133,77),(48,158,134,224),(49,143,135,79),(50,160,136,212),(51,145,137,81),(52,162,138,214),(53,147,139,83),(54,164,140,216),(55,149,127,71),(56,166,128,218),(57,189,94,197),(59,191,96,199),(61,193,98,201),(63,195,86,203),(65,183,88,205),(67,185,90,207),(69,187,92,209)], [(1,64,131,41),(2,65,132,42),(3,66,133,29),(4,67,134,30),(5,68,135,31),(6,69,136,32),(7,70,137,33),(8,57,138,34),(9,58,139,35),(10,59,140,36),(11,60,127,37),(12,61,128,38),(13,62,129,39),(14,63,130,40),(15,84,199,164),(16,71,200,165),(17,72,201,166),(18,73,202,167),(19,74,203,168),(20,75,204,155),(21,76,205,156),(22,77,206,157),(23,78,207,158),(24,79,208,159),(25,80,209,160),(26,81,210,161),(27,82,197,162),(28,83,198,163),(43,174,100,85),(44,175,101,86),(45,176,102,87),(46,177,103,88),(47,178,104,89),(48,179,105,90),(49,180,106,91),(50,181,107,92),(51,182,108,93),(52,169,109,94),(53,170,110,95),(54,171,111,96),(55,172,112,97),(56,173,99,98),(113,146,189,214),(114,147,190,215),(115,148,191,216),(116,149,192,217),(117,150,193,218),(118,151,194,219),(119,152,195,220),(120,153,196,221),(121,154,183,222),(122,141,184,223),(123,142,185,224),(124,143,186,211),(125,144,187,212),(126,145,188,213)], [(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)], [(1,14,102,101),(2,100,103,13),(3,12,104,99),(4,112,105,11),(5,10,106,111),(6,110,107,9),(7,8,108,109),(15,124,115,24),(16,23,116,123),(17,122,117,22),(18,21,118,121),(19,120,119,20),(25,114,125,28),(26,27,126,113),(29,38,178,173),(30,172,179,37),(31,36,180,171),(32,170,181,35),(33,34,182,169),(39,42,174,177),(40,176,175,41),(43,46,129,132),(44,131,130,45),(47,56,133,128),(48,127,134,55),(49,54,135,140),(50,139,136,53),(51,52,137,138),(57,93,94,70),(58,69,95,92),(59,91,96,68),(60,67,97,90),(61,89,98,66),(62,65,85,88),(63,87,86,64),(71,78,149,142),(72,141,150,77),(73,76,151,154),(74,153,152,75),(79,84,143,148),(80,147,144,83),(81,82,145,146),(155,168,221,220),(156,219,222,167),(157,166,223,218),(158,217,224,165),(159,164,211,216),(160,215,212,163),(161,162,213,214),(183,202,205,194),(184,193,206,201),(185,200,207,192),(186,191,208,199),(187,198,209,190),(188,189,210,197),(195,204,203,196)])
Matrix representation ►G ⊆ GL4(𝔽29) generated by
| 17 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 |
| 0 | 0 | 12 | 0 |
| 0 | 0 | 23 | 17 |
| 12 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 28 |
| 21 | 8 | 0 | 0 |
| 21 | 19 | 0 | 0 |
| 0 | 0 | 6 | 24 |
| 0 | 0 | 7 | 23 |
| 8 | 21 | 0 | 0 |
| 19 | 21 | 0 | 0 |
| 0 | 0 | 23 | 5 |
| 0 | 0 | 10 | 6 |
G:=sub<GL(4,GF(29))| [17,0,0,0,0,17,0,0,0,0,12,23,0,0,0,17],[12,0,0,0,0,12,0,0,0,0,28,0,0,0,0,28],[21,21,0,0,8,19,0,0,0,0,6,7,0,0,24,23],[8,19,0,0,21,21,0,0,0,0,23,10,0,0,5,6] >;
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | ··· | 4P | 4Q | 4R | 4S | 4T | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 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 | 14 | 14 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | D14 | D14 | C4○D28 | D4⋊2D7 | D7×C4○D4 |
| kernel | C42.229D14 | C4×Dic14 | D7×C42 | C23.D14 | D14.D4 | C4.Dic14 | D14⋊2Q8 | C23.21D14 | C4×C7⋊D4 | C28.17D4 | C28⋊2D4 | D4×C28 | C4×D4 | C28 | D14 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C4 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 3 | 8 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{229}D_{14} % in TeX
G:=Group("C4^2.229D14"); // GroupNames label
G:=SmallGroup(448,1010);
// by ID
G=gap.SmallGroup(448,1010);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,100,1123,794,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1*b^2,b*c=c*b,b*d=d*b,d*c*d^-1=a^2*c^-1>;
// generators/relations
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