metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.232D14, (C4×D7)⋊6Q8, C28⋊Q8⋊48C2, (C4×Q8)⋊11D7, C4.59(Q8×D7), (Q8×C28)⋊13C2, D14.1(C2×Q8), C4⋊C4.297D14, C28.117(C2×Q8), Dic7.2(C2×Q8), (D7×C42).6C2, (C4×Dic14)⋊39C2, C4.47(C4○D28), Dic7.Q8⋊46C2, D14⋊Q8.5C2, (C2×Q8).177D14, C42⋊D7.4C2, Dic7⋊Q8⋊33C2, C28.117(C4○D4), C14.30(C22×Q8), (C4×C28).174C22, (C2×C28).499C23, (C2×C14).122C24, D14⋊3Q8.14C2, D14⋊2Q8.14C2, Dic7.4(C4○D4), D14⋊C4.102C22, C4⋊Dic7.307C22, (Q8×C14).222C22, C22.143(C23×D7), Dic7⋊C4.155C22, C7⋊3(C23.37C23), (C2×Dic7).216C23, (C4×Dic7).253C22, (C22×D7).179C23, (C2×Dic14).291C22, C2.13(C2×Q8×D7), C2.30(D7×C4○D4), C14.54(C2×C4○D4), C2.61(C2×C4○D28), (C2×C4×D7).295C22, (C7×C4⋊C4).350C22, (C2×C4).584(C22×D7), SmallGroup(448,1031)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 868 in 222 conjugacy classes, 109 normal (43 characteristic)
C1, C2 [×3], C2 [×2], C4 [×4], C4 [×14], C22, C22 [×4], C7, C2×C4 [×3], C2×C4 [×4], C2×C4 [×15], Q8 [×8], C23, D7 [×2], C14 [×3], C42, C42 [×2], C42 [×5], C22⋊C4 [×4], C4⋊C4, C4⋊C4 [×2], C4⋊C4 [×13], C22×C4 [×3], C2×Q8, C2×Q8 [×3], Dic7 [×4], Dic7 [×5], C28 [×4], C28 [×5], D14 [×2], D14 [×2], C2×C14, C2×C42, C42⋊C2 [×2], C4×Q8, C4×Q8 [×3], C22⋊Q8 [×4], C42.C2 [×2], C4⋊Q8 [×2], Dic14 [×6], C4×D7 [×4], C4×D7 [×4], C2×Dic7 [×3], C2×Dic7 [×4], C2×C28 [×3], C2×C28 [×4], C7×Q8 [×2], C22×D7, C23.37C23, C4×Dic7 [×3], C4×Dic7 [×2], Dic7⋊C4 [×10], C4⋊Dic7, C4⋊Dic7 [×2], D14⋊C4 [×4], C4×C28, C4×C28 [×2], C7×C4⋊C4, C7×C4⋊C4 [×2], C2×Dic14, C2×Dic14 [×2], C2×C4×D7 [×3], Q8×C14, C4×Dic14, C4×Dic14 [×2], D7×C42, C42⋊D7 [×2], C28⋊Q8, Dic7.Q8 [×2], D14⋊Q8 [×2], D14⋊2Q8, Dic7⋊Q8, D14⋊3Q8, Q8×C28, C42.232D14
Quotients:
C1, C2 [×15], C22 [×35], Q8 [×4], C23 [×15], D7, C2×Q8 [×6], C4○D4 [×4], C24, D14 [×7], C22×Q8, C2×C4○D4 [×2], C22×D7 [×7], C23.37C23, C4○D28 [×2], Q8×D7 [×2], C23×D7, C2×C4○D28, C2×Q8×D7, D7×C4○D4, C42.232D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=a2, d2=a2b2, ab=ba, cac-1=dad-1=a-1, bc=cb, bd=db, dcd-1=b2c13 >
►On 224 points
Generators in S224
(1 32 15 46)(2 47 16 33)(3 34 17 48)(4 49 18 35)(5 36 19 50)(6 51 20 37)(7 38 21 52)(8 53 22 39)(9 40 23 54)(10 55 24 41)(11 42 25 56)(12 29 26 43)(13 44 27 30)(14 31 28 45)(57 222 71 208)(58 209 72 223)(59 224 73 210)(60 211 74 197)(61 198 75 212)(62 213 76 199)(63 200 77 214)(64 215 78 201)(65 202 79 216)(66 217 80 203)(67 204 81 218)(68 219 82 205)(69 206 83 220)(70 221 84 207)(85 159 99 145)(86 146 100 160)(87 161 101 147)(88 148 102 162)(89 163 103 149)(90 150 104 164)(91 165 105 151)(92 152 106 166)(93 167 107 153)(94 154 108 168)(95 141 109 155)(96 156 110 142)(97 143 111 157)(98 158 112 144)(113 172 127 186)(114 187 128 173)(115 174 129 188)(116 189 130 175)(117 176 131 190)(118 191 132 177)(119 178 133 192)(120 193 134 179)(121 180 135 194)(122 195 136 181)(123 182 137 196)(124 169 138 183)(125 184 139 170)(126 171 140 185)
(1 220 155 137)(2 221 156 138)(3 222 157 139)(4 223 158 140)(5 224 159 113)(6 197 160 114)(7 198 161 115)(8 199 162 116)(9 200 163 117)(10 201 164 118)(11 202 165 119)(12 203 166 120)(13 204 167 121)(14 205 168 122)(15 206 141 123)(16 207 142 124)(17 208 143 125)(18 209 144 126)(19 210 145 127)(20 211 146 128)(21 212 147 129)(22 213 148 130)(23 214 149 131)(24 215 150 132)(25 216 151 133)(26 217 152 134)(27 218 153 135)(28 219 154 136)(29 66 92 193)(30 67 93 194)(31 68 94 195)(32 69 95 196)(33 70 96 169)(34 71 97 170)(35 72 98 171)(36 73 99 172)(37 74 100 173)(38 75 101 174)(39 76 102 175)(40 77 103 176)(41 78 104 177)(42 79 105 178)(43 80 106 179)(44 81 107 180)(45 82 108 181)(46 83 109 182)(47 84 110 183)(48 57 111 184)(49 58 112 185)(50 59 85 186)(51 60 86 187)(52 61 87 188)(53 62 88 189)(54 63 89 190)(55 64 90 191)(56 65 91 192)
(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 14 141 154)(2 153 142 13)(3 12 143 152)(4 151 144 11)(5 10 145 150)(6 149 146 9)(7 8 147 148)(15 28 155 168)(16 167 156 27)(17 26 157 166)(18 165 158 25)(19 24 159 164)(20 163 160 23)(21 22 161 162)(29 97 106 48)(30 47 107 96)(31 95 108 46)(32 45 109 94)(33 93 110 44)(34 43 111 92)(35 91 112 42)(36 41 85 90)(37 89 86 40)(38 39 87 88)(49 105 98 56)(50 55 99 104)(51 103 100 54)(52 53 101 102)(57 66 170 179)(58 178 171 65)(59 64 172 177)(60 176 173 63)(61 62 174 175)(67 84 180 169)(68 196 181 83)(69 82 182 195)(70 194 183 81)(71 80 184 193)(72 192 185 79)(73 78 186 191)(74 190 187 77)(75 76 188 189)(113 118 210 215)(114 214 211 117)(115 116 212 213)(119 140 216 209)(120 208 217 139)(121 138 218 207)(122 206 219 137)(123 136 220 205)(124 204 221 135)(125 134 222 203)(126 202 223 133)(127 132 224 201)(128 200 197 131)(129 130 198 199)
G:=sub<Sym(224)| (1,32,15,46)(2,47,16,33)(3,34,17,48)(4,49,18,35)(5,36,19,50)(6,51,20,37)(7,38,21,52)(8,53,22,39)(9,40,23,54)(10,55,24,41)(11,42,25,56)(12,29,26,43)(13,44,27,30)(14,31,28,45)(57,222,71,208)(58,209,72,223)(59,224,73,210)(60,211,74,197)(61,198,75,212)(62,213,76,199)(63,200,77,214)(64,215,78,201)(65,202,79,216)(66,217,80,203)(67,204,81,218)(68,219,82,205)(69,206,83,220)(70,221,84,207)(85,159,99,145)(86,146,100,160)(87,161,101,147)(88,148,102,162)(89,163,103,149)(90,150,104,164)(91,165,105,151)(92,152,106,166)(93,167,107,153)(94,154,108,168)(95,141,109,155)(96,156,110,142)(97,143,111,157)(98,158,112,144)(113,172,127,186)(114,187,128,173)(115,174,129,188)(116,189,130,175)(117,176,131,190)(118,191,132,177)(119,178,133,192)(120,193,134,179)(121,180,135,194)(122,195,136,181)(123,182,137,196)(124,169,138,183)(125,184,139,170)(126,171,140,185), (1,220,155,137)(2,221,156,138)(3,222,157,139)(4,223,158,140)(5,224,159,113)(6,197,160,114)(7,198,161,115)(8,199,162,116)(9,200,163,117)(10,201,164,118)(11,202,165,119)(12,203,166,120)(13,204,167,121)(14,205,168,122)(15,206,141,123)(16,207,142,124)(17,208,143,125)(18,209,144,126)(19,210,145,127)(20,211,146,128)(21,212,147,129)(22,213,148,130)(23,214,149,131)(24,215,150,132)(25,216,151,133)(26,217,152,134)(27,218,153,135)(28,219,154,136)(29,66,92,193)(30,67,93,194)(31,68,94,195)(32,69,95,196)(33,70,96,169)(34,71,97,170)(35,72,98,171)(36,73,99,172)(37,74,100,173)(38,75,101,174)(39,76,102,175)(40,77,103,176)(41,78,104,177)(42,79,105,178)(43,80,106,179)(44,81,107,180)(45,82,108,181)(46,83,109,182)(47,84,110,183)(48,57,111,184)(49,58,112,185)(50,59,85,186)(51,60,86,187)(52,61,87,188)(53,62,88,189)(54,63,89,190)(55,64,90,191)(56,65,91,192), (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), (1,14,141,154)(2,153,142,13)(3,12,143,152)(4,151,144,11)(5,10,145,150)(6,149,146,9)(7,8,147,148)(15,28,155,168)(16,167,156,27)(17,26,157,166)(18,165,158,25)(19,24,159,164)(20,163,160,23)(21,22,161,162)(29,97,106,48)(30,47,107,96)(31,95,108,46)(32,45,109,94)(33,93,110,44)(34,43,111,92)(35,91,112,42)(36,41,85,90)(37,89,86,40)(38,39,87,88)(49,105,98,56)(50,55,99,104)(51,103,100,54)(52,53,101,102)(57,66,170,179)(58,178,171,65)(59,64,172,177)(60,176,173,63)(61,62,174,175)(67,84,180,169)(68,196,181,83)(69,82,182,195)(70,194,183,81)(71,80,184,193)(72,192,185,79)(73,78,186,191)(74,190,187,77)(75,76,188,189)(113,118,210,215)(114,214,211,117)(115,116,212,213)(119,140,216,209)(120,208,217,139)(121,138,218,207)(122,206,219,137)(123,136,220,205)(124,204,221,135)(125,134,222,203)(126,202,223,133)(127,132,224,201)(128,200,197,131)(129,130,198,199)>;
G:=Group( (1,32,15,46)(2,47,16,33)(3,34,17,48)(4,49,18,35)(5,36,19,50)(6,51,20,37)(7,38,21,52)(8,53,22,39)(9,40,23,54)(10,55,24,41)(11,42,25,56)(12,29,26,43)(13,44,27,30)(14,31,28,45)(57,222,71,208)(58,209,72,223)(59,224,73,210)(60,211,74,197)(61,198,75,212)(62,213,76,199)(63,200,77,214)(64,215,78,201)(65,202,79,216)(66,217,80,203)(67,204,81,218)(68,219,82,205)(69,206,83,220)(70,221,84,207)(85,159,99,145)(86,146,100,160)(87,161,101,147)(88,148,102,162)(89,163,103,149)(90,150,104,164)(91,165,105,151)(92,152,106,166)(93,167,107,153)(94,154,108,168)(95,141,109,155)(96,156,110,142)(97,143,111,157)(98,158,112,144)(113,172,127,186)(114,187,128,173)(115,174,129,188)(116,189,130,175)(117,176,131,190)(118,191,132,177)(119,178,133,192)(120,193,134,179)(121,180,135,194)(122,195,136,181)(123,182,137,196)(124,169,138,183)(125,184,139,170)(126,171,140,185), (1,220,155,137)(2,221,156,138)(3,222,157,139)(4,223,158,140)(5,224,159,113)(6,197,160,114)(7,198,161,115)(8,199,162,116)(9,200,163,117)(10,201,164,118)(11,202,165,119)(12,203,166,120)(13,204,167,121)(14,205,168,122)(15,206,141,123)(16,207,142,124)(17,208,143,125)(18,209,144,126)(19,210,145,127)(20,211,146,128)(21,212,147,129)(22,213,148,130)(23,214,149,131)(24,215,150,132)(25,216,151,133)(26,217,152,134)(27,218,153,135)(28,219,154,136)(29,66,92,193)(30,67,93,194)(31,68,94,195)(32,69,95,196)(33,70,96,169)(34,71,97,170)(35,72,98,171)(36,73,99,172)(37,74,100,173)(38,75,101,174)(39,76,102,175)(40,77,103,176)(41,78,104,177)(42,79,105,178)(43,80,106,179)(44,81,107,180)(45,82,108,181)(46,83,109,182)(47,84,110,183)(48,57,111,184)(49,58,112,185)(50,59,85,186)(51,60,86,187)(52,61,87,188)(53,62,88,189)(54,63,89,190)(55,64,90,191)(56,65,91,192), (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), (1,14,141,154)(2,153,142,13)(3,12,143,152)(4,151,144,11)(5,10,145,150)(6,149,146,9)(7,8,147,148)(15,28,155,168)(16,167,156,27)(17,26,157,166)(18,165,158,25)(19,24,159,164)(20,163,160,23)(21,22,161,162)(29,97,106,48)(30,47,107,96)(31,95,108,46)(32,45,109,94)(33,93,110,44)(34,43,111,92)(35,91,112,42)(36,41,85,90)(37,89,86,40)(38,39,87,88)(49,105,98,56)(50,55,99,104)(51,103,100,54)(52,53,101,102)(57,66,170,179)(58,178,171,65)(59,64,172,177)(60,176,173,63)(61,62,174,175)(67,84,180,169)(68,196,181,83)(69,82,182,195)(70,194,183,81)(71,80,184,193)(72,192,185,79)(73,78,186,191)(74,190,187,77)(75,76,188,189)(113,118,210,215)(114,214,211,117)(115,116,212,213)(119,140,216,209)(120,208,217,139)(121,138,218,207)(122,206,219,137)(123,136,220,205)(124,204,221,135)(125,134,222,203)(126,202,223,133)(127,132,224,201)(128,200,197,131)(129,130,198,199) );
G=PermutationGroup([(1,32,15,46),(2,47,16,33),(3,34,17,48),(4,49,18,35),(5,36,19,50),(6,51,20,37),(7,38,21,52),(8,53,22,39),(9,40,23,54),(10,55,24,41),(11,42,25,56),(12,29,26,43),(13,44,27,30),(14,31,28,45),(57,222,71,208),(58,209,72,223),(59,224,73,210),(60,211,74,197),(61,198,75,212),(62,213,76,199),(63,200,77,214),(64,215,78,201),(65,202,79,216),(66,217,80,203),(67,204,81,218),(68,219,82,205),(69,206,83,220),(70,221,84,207),(85,159,99,145),(86,146,100,160),(87,161,101,147),(88,148,102,162),(89,163,103,149),(90,150,104,164),(91,165,105,151),(92,152,106,166),(93,167,107,153),(94,154,108,168),(95,141,109,155),(96,156,110,142),(97,143,111,157),(98,158,112,144),(113,172,127,186),(114,187,128,173),(115,174,129,188),(116,189,130,175),(117,176,131,190),(118,191,132,177),(119,178,133,192),(120,193,134,179),(121,180,135,194),(122,195,136,181),(123,182,137,196),(124,169,138,183),(125,184,139,170),(126,171,140,185)], [(1,220,155,137),(2,221,156,138),(3,222,157,139),(4,223,158,140),(5,224,159,113),(6,197,160,114),(7,198,161,115),(8,199,162,116),(9,200,163,117),(10,201,164,118),(11,202,165,119),(12,203,166,120),(13,204,167,121),(14,205,168,122),(15,206,141,123),(16,207,142,124),(17,208,143,125),(18,209,144,126),(19,210,145,127),(20,211,146,128),(21,212,147,129),(22,213,148,130),(23,214,149,131),(24,215,150,132),(25,216,151,133),(26,217,152,134),(27,218,153,135),(28,219,154,136),(29,66,92,193),(30,67,93,194),(31,68,94,195),(32,69,95,196),(33,70,96,169),(34,71,97,170),(35,72,98,171),(36,73,99,172),(37,74,100,173),(38,75,101,174),(39,76,102,175),(40,77,103,176),(41,78,104,177),(42,79,105,178),(43,80,106,179),(44,81,107,180),(45,82,108,181),(46,83,109,182),(47,84,110,183),(48,57,111,184),(49,58,112,185),(50,59,85,186),(51,60,86,187),(52,61,87,188),(53,62,88,189),(54,63,89,190),(55,64,90,191),(56,65,91,192)], [(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)], [(1,14,141,154),(2,153,142,13),(3,12,143,152),(4,151,144,11),(5,10,145,150),(6,149,146,9),(7,8,147,148),(15,28,155,168),(16,167,156,27),(17,26,157,166),(18,165,158,25),(19,24,159,164),(20,163,160,23),(21,22,161,162),(29,97,106,48),(30,47,107,96),(31,95,108,46),(32,45,109,94),(33,93,110,44),(34,43,111,92),(35,91,112,42),(36,41,85,90),(37,89,86,40),(38,39,87,88),(49,105,98,56),(50,55,99,104),(51,103,100,54),(52,53,101,102),(57,66,170,179),(58,178,171,65),(59,64,172,177),(60,176,173,63),(61,62,174,175),(67,84,180,169),(68,196,181,83),(69,82,182,195),(70,194,183,81),(71,80,184,193),(72,192,185,79),(73,78,186,191),(74,190,187,77),(75,76,188,189),(113,118,210,215),(114,214,211,117),(115,116,212,213),(119,140,216,209),(120,208,217,139),(121,138,218,207),(122,206,219,137),(123,136,220,205),(124,204,221,135),(125,134,222,203),(126,202,223,133),(127,132,224,201),(128,200,197,131),(129,130,198,199)])
Matrix representation ►G ⊆ GL4(𝔽29) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 12 |
| 12 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 |
| 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 12 |
| 7 | 22 | 0 | 0 |
| 7 | 26 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 28 | 0 |
| 7 | 22 | 0 | 0 |
| 3 | 22 | 0 | 0 |
| 0 | 0 | 0 | 28 |
| 0 | 0 | 28 | 0 |
G:=sub<GL(4,GF(29))| [1,0,0,0,0,1,0,0,0,0,17,0,0,0,0,12],[12,0,0,0,0,12,0,0,0,0,12,0,0,0,0,12],[7,7,0,0,22,26,0,0,0,0,0,28,0,0,1,0],[7,3,0,0,22,22,0,0,0,0,0,28,0,0,28,0] >;
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | ··· | 4R | 4S | 4T | 4U | 4V | 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 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | - | + | + | + | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | Q8 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | C4○D28 | Q8×D7 | D7×C4○D4 |
| kernel | C42.232D14 | C4×Dic14 | D7×C42 | C42⋊D7 | C28⋊Q8 | Dic7.Q8 | D14⋊Q8 | D14⋊2Q8 | Dic7⋊Q8 | D14⋊3Q8 | Q8×C28 | C4×D7 | C4×Q8 | Dic7 | C28 | C42 | C4⋊C4 | C2×Q8 | C4 | C4 | C2 |
| # reps | 1 | 3 | 1 | 2 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 4 | 3 | 4 | 4 | 9 | 9 | 3 | 24 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{232}D_{14} % in TeX
G:=Group("C4^2.232D14"); // GroupNames label
G:=SmallGroup(448,1031);
// by ID
G=gap.SmallGroup(448,1031);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,100,675,570,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=a^2,d^2=a^2*b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,b*c=c*b,b*d=d*b,d*c*d^-1=b^2*c^13>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀