metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.150D14, C14.282- (1+4), C14.1322+ (1+4), (C4×D28)⋊47C2, C42.C2⋊6D7, C4⋊C4.207D14, C42⋊2D7⋊9C2, D28⋊C4⋊36C2, D14⋊2Q8⋊37C2, D14⋊Q8⋊35C2, C28⋊1D4.12C2, Dic7.Q8⋊33C2, D14.11(C4○D4), D14.5D4⋊34C2, (C2×C14).236C24, (C2×C28).188C23, (C4×C28).196C22, D14⋊C4.10C22, C2.57(D4⋊8D14), (C2×D28).164C22, Dic7⋊C4.52C22, C4⋊Dic7.314C22, C22.257(C23×D7), C7⋊8(C22.33C24), (C4×Dic7).143C22, (C2×Dic7).258C23, (C22×D7).102C23, C2.29(Q8.10D14), (C2×Dic14).180C22, (D7×C4⋊C4)⋊36C2, C2.87(D7×C4○D4), C4⋊C4⋊D7⋊34C2, (C7×C42.C2)⋊9C2, C14.198(C2×C4○D4), (C2×C4×D7).126C22, (C2×C4).80(C22×D7), (C7×C4⋊C4).191C22, SmallGroup(448,1145)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1084 in 218 conjugacy classes, 93 normal (91 characteristic)
C1, C2 [×3], C2 [×4], C4 [×12], C22, C22 [×10], C7, C2×C4 [×7], C2×C4 [×11], D4 [×5], Q8, C23 [×3], D7 [×4], C14 [×3], C42, C42, C22⋊C4 [×10], C4⋊C4 [×6], C4⋊C4 [×8], C22×C4 [×5], C2×D4 [×3], C2×Q8, Dic7 [×5], C28 [×7], D14 [×2], D14 [×8], C2×C14, C2×C4⋊C4, C4×D4 [×2], C4⋊D4, C22⋊Q8 [×3], C22.D4 [×4], C42.C2, C42.C2, C42⋊2C2 [×2], Dic14, C4×D7 [×6], D28 [×5], C2×Dic7 [×5], C2×C28 [×7], C22×D7 [×3], C22.33C24, C4×Dic7, Dic7⋊C4 [×6], C4⋊Dic7 [×2], D14⋊C4 [×10], C4×C28, C7×C4⋊C4 [×6], C2×Dic14, C2×C4×D7 [×5], C2×D28 [×3], C4×D28, C42⋊2D7, Dic7.Q8, D7×C4⋊C4, D28⋊C4, D14.5D4 [×4], C28⋊1D4, D14⋊Q8 [×2], D14⋊2Q8, C4⋊C4⋊D7, C7×C42.C2, C42.150D14
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], C22.33C24, C23×D7, Q8.10D14, D7×C4○D4, D4⋊8D14, C42.150D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=d2=a2b2, ab=ba, cac-1=dad-1=a-1b2, cbc-1=b-1, dbd-1=a2b, dcd-1=c13 >
►On 224 points
Generators in S224
(1 180 45 201)(2 195 46 216)(3 182 47 203)(4 169 48 218)(5 184 49 205)(6 171 50 220)(7 186 51 207)(8 173 52 222)(9 188 53 209)(10 175 54 224)(11 190 55 211)(12 177 56 198)(13 192 29 213)(14 179 30 200)(15 194 31 215)(16 181 32 202)(17 196 33 217)(18 183 34 204)(19 170 35 219)(20 185 36 206)(21 172 37 221)(22 187 38 208)(23 174 39 223)(24 189 40 210)(25 176 41 197)(26 191 42 212)(27 178 43 199)(28 193 44 214)(57 112 142 129)(58 99 143 116)(59 86 144 131)(60 101 145 118)(61 88 146 133)(62 103 147 120)(63 90 148 135)(64 105 149 122)(65 92 150 137)(66 107 151 124)(67 94 152 139)(68 109 153 126)(69 96 154 113)(70 111 155 128)(71 98 156 115)(72 85 157 130)(73 100 158 117)(74 87 159 132)(75 102 160 119)(76 89 161 134)(77 104 162 121)(78 91 163 136)(79 106 164 123)(80 93 165 138)(81 108 166 125)(82 95 167 140)(83 110 168 127)(84 97 141 114)
(1 157 31 58)(2 59 32 158)(3 159 33 60)(4 61 34 160)(5 161 35 62)(6 63 36 162)(7 163 37 64)(8 65 38 164)(9 165 39 66)(10 67 40 166)(11 167 41 68)(12 69 42 168)(13 141 43 70)(14 71 44 142)(15 143 45 72)(16 73 46 144)(17 145 47 74)(18 75 48 146)(19 147 49 76)(20 77 50 148)(21 149 51 78)(22 79 52 150)(23 151 53 80)(24 81 54 152)(25 153 55 82)(26 83 56 154)(27 155 29 84)(28 57 30 156)(85 194 116 201)(86 202 117 195)(87 196 118 203)(88 204 119 169)(89 170 120 205)(90 206 121 171)(91 172 122 207)(92 208 123 173)(93 174 124 209)(94 210 125 175)(95 176 126 211)(96 212 127 177)(97 178 128 213)(98 214 129 179)(99 180 130 215)(100 216 131 181)(101 182 132 217)(102 218 133 183)(103 184 134 219)(104 220 135 185)(105 186 136 221)(106 222 137 187)(107 188 138 223)(108 224 139 189)(109 190 140 197)(110 198 113 191)(111 192 114 199)(112 200 115 193)
(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 15 28)(2 27 16 13)(3 12 17 26)(4 25 18 11)(5 10 19 24)(6 23 20 9)(7 8 21 22)(29 46 43 32)(30 31 44 45)(33 42 47 56)(34 55 48 41)(35 40 49 54)(36 53 50 39)(37 38 51 52)(57 72 71 58)(59 70 73 84)(60 83 74 69)(61 68 75 82)(62 81 76 67)(63 66 77 80)(64 79 78 65)(85 112 99 98)(86 97 100 111)(87 110 101 96)(88 95 102 109)(89 108 103 94)(90 93 104 107)(91 106 105 92)(113 132 127 118)(114 117 128 131)(115 130 129 116)(119 126 133 140)(120 139 134 125)(121 124 135 138)(122 137 136 123)(141 144 155 158)(142 157 156 143)(145 168 159 154)(146 153 160 167)(147 166 161 152)(148 151 162 165)(149 164 163 150)(169 190 183 176)(170 175 184 189)(171 188 185 174)(172 173 186 187)(177 182 191 196)(178 195 192 181)(179 180 193 194)(197 218 211 204)(198 203 212 217)(199 216 213 202)(200 201 214 215)(205 210 219 224)(206 223 220 209)(207 208 221 222)
G:=sub<Sym(224)| (1,180,45,201)(2,195,46,216)(3,182,47,203)(4,169,48,218)(5,184,49,205)(6,171,50,220)(7,186,51,207)(8,173,52,222)(9,188,53,209)(10,175,54,224)(11,190,55,211)(12,177,56,198)(13,192,29,213)(14,179,30,200)(15,194,31,215)(16,181,32,202)(17,196,33,217)(18,183,34,204)(19,170,35,219)(20,185,36,206)(21,172,37,221)(22,187,38,208)(23,174,39,223)(24,189,40,210)(25,176,41,197)(26,191,42,212)(27,178,43,199)(28,193,44,214)(57,112,142,129)(58,99,143,116)(59,86,144,131)(60,101,145,118)(61,88,146,133)(62,103,147,120)(63,90,148,135)(64,105,149,122)(65,92,150,137)(66,107,151,124)(67,94,152,139)(68,109,153,126)(69,96,154,113)(70,111,155,128)(71,98,156,115)(72,85,157,130)(73,100,158,117)(74,87,159,132)(75,102,160,119)(76,89,161,134)(77,104,162,121)(78,91,163,136)(79,106,164,123)(80,93,165,138)(81,108,166,125)(82,95,167,140)(83,110,168,127)(84,97,141,114), (1,157,31,58)(2,59,32,158)(3,159,33,60)(4,61,34,160)(5,161,35,62)(6,63,36,162)(7,163,37,64)(8,65,38,164)(9,165,39,66)(10,67,40,166)(11,167,41,68)(12,69,42,168)(13,141,43,70)(14,71,44,142)(15,143,45,72)(16,73,46,144)(17,145,47,74)(18,75,48,146)(19,147,49,76)(20,77,50,148)(21,149,51,78)(22,79,52,150)(23,151,53,80)(24,81,54,152)(25,153,55,82)(26,83,56,154)(27,155,29,84)(28,57,30,156)(85,194,116,201)(86,202,117,195)(87,196,118,203)(88,204,119,169)(89,170,120,205)(90,206,121,171)(91,172,122,207)(92,208,123,173)(93,174,124,209)(94,210,125,175)(95,176,126,211)(96,212,127,177)(97,178,128,213)(98,214,129,179)(99,180,130,215)(100,216,131,181)(101,182,132,217)(102,218,133,183)(103,184,134,219)(104,220,135,185)(105,186,136,221)(106,222,137,187)(107,188,138,223)(108,224,139,189)(109,190,140,197)(110,198,113,191)(111,192,114,199)(112,200,115,193), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,46,43,32)(30,31,44,45)(33,42,47,56)(34,55,48,41)(35,40,49,54)(36,53,50,39)(37,38,51,52)(57,72,71,58)(59,70,73,84)(60,83,74,69)(61,68,75,82)(62,81,76,67)(63,66,77,80)(64,79,78,65)(85,112,99,98)(86,97,100,111)(87,110,101,96)(88,95,102,109)(89,108,103,94)(90,93,104,107)(91,106,105,92)(113,132,127,118)(114,117,128,131)(115,130,129,116)(119,126,133,140)(120,139,134,125)(121,124,135,138)(122,137,136,123)(141,144,155,158)(142,157,156,143)(145,168,159,154)(146,153,160,167)(147,166,161,152)(148,151,162,165)(149,164,163,150)(169,190,183,176)(170,175,184,189)(171,188,185,174)(172,173,186,187)(177,182,191,196)(178,195,192,181)(179,180,193,194)(197,218,211,204)(198,203,212,217)(199,216,213,202)(200,201,214,215)(205,210,219,224)(206,223,220,209)(207,208,221,222)>;
G:=Group( (1,180,45,201)(2,195,46,216)(3,182,47,203)(4,169,48,218)(5,184,49,205)(6,171,50,220)(7,186,51,207)(8,173,52,222)(9,188,53,209)(10,175,54,224)(11,190,55,211)(12,177,56,198)(13,192,29,213)(14,179,30,200)(15,194,31,215)(16,181,32,202)(17,196,33,217)(18,183,34,204)(19,170,35,219)(20,185,36,206)(21,172,37,221)(22,187,38,208)(23,174,39,223)(24,189,40,210)(25,176,41,197)(26,191,42,212)(27,178,43,199)(28,193,44,214)(57,112,142,129)(58,99,143,116)(59,86,144,131)(60,101,145,118)(61,88,146,133)(62,103,147,120)(63,90,148,135)(64,105,149,122)(65,92,150,137)(66,107,151,124)(67,94,152,139)(68,109,153,126)(69,96,154,113)(70,111,155,128)(71,98,156,115)(72,85,157,130)(73,100,158,117)(74,87,159,132)(75,102,160,119)(76,89,161,134)(77,104,162,121)(78,91,163,136)(79,106,164,123)(80,93,165,138)(81,108,166,125)(82,95,167,140)(83,110,168,127)(84,97,141,114), (1,157,31,58)(2,59,32,158)(3,159,33,60)(4,61,34,160)(5,161,35,62)(6,63,36,162)(7,163,37,64)(8,65,38,164)(9,165,39,66)(10,67,40,166)(11,167,41,68)(12,69,42,168)(13,141,43,70)(14,71,44,142)(15,143,45,72)(16,73,46,144)(17,145,47,74)(18,75,48,146)(19,147,49,76)(20,77,50,148)(21,149,51,78)(22,79,52,150)(23,151,53,80)(24,81,54,152)(25,153,55,82)(26,83,56,154)(27,155,29,84)(28,57,30,156)(85,194,116,201)(86,202,117,195)(87,196,118,203)(88,204,119,169)(89,170,120,205)(90,206,121,171)(91,172,122,207)(92,208,123,173)(93,174,124,209)(94,210,125,175)(95,176,126,211)(96,212,127,177)(97,178,128,213)(98,214,129,179)(99,180,130,215)(100,216,131,181)(101,182,132,217)(102,218,133,183)(103,184,134,219)(104,220,135,185)(105,186,136,221)(106,222,137,187)(107,188,138,223)(108,224,139,189)(109,190,140,197)(110,198,113,191)(111,192,114,199)(112,200,115,193), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,46,43,32)(30,31,44,45)(33,42,47,56)(34,55,48,41)(35,40,49,54)(36,53,50,39)(37,38,51,52)(57,72,71,58)(59,70,73,84)(60,83,74,69)(61,68,75,82)(62,81,76,67)(63,66,77,80)(64,79,78,65)(85,112,99,98)(86,97,100,111)(87,110,101,96)(88,95,102,109)(89,108,103,94)(90,93,104,107)(91,106,105,92)(113,132,127,118)(114,117,128,131)(115,130,129,116)(119,126,133,140)(120,139,134,125)(121,124,135,138)(122,137,136,123)(141,144,155,158)(142,157,156,143)(145,168,159,154)(146,153,160,167)(147,166,161,152)(148,151,162,165)(149,164,163,150)(169,190,183,176)(170,175,184,189)(171,188,185,174)(172,173,186,187)(177,182,191,196)(178,195,192,181)(179,180,193,194)(197,218,211,204)(198,203,212,217)(199,216,213,202)(200,201,214,215)(205,210,219,224)(206,223,220,209)(207,208,221,222) );
G=PermutationGroup([(1,180,45,201),(2,195,46,216),(3,182,47,203),(4,169,48,218),(5,184,49,205),(6,171,50,220),(7,186,51,207),(8,173,52,222),(9,188,53,209),(10,175,54,224),(11,190,55,211),(12,177,56,198),(13,192,29,213),(14,179,30,200),(15,194,31,215),(16,181,32,202),(17,196,33,217),(18,183,34,204),(19,170,35,219),(20,185,36,206),(21,172,37,221),(22,187,38,208),(23,174,39,223),(24,189,40,210),(25,176,41,197),(26,191,42,212),(27,178,43,199),(28,193,44,214),(57,112,142,129),(58,99,143,116),(59,86,144,131),(60,101,145,118),(61,88,146,133),(62,103,147,120),(63,90,148,135),(64,105,149,122),(65,92,150,137),(66,107,151,124),(67,94,152,139),(68,109,153,126),(69,96,154,113),(70,111,155,128),(71,98,156,115),(72,85,157,130),(73,100,158,117),(74,87,159,132),(75,102,160,119),(76,89,161,134),(77,104,162,121),(78,91,163,136),(79,106,164,123),(80,93,165,138),(81,108,166,125),(82,95,167,140),(83,110,168,127),(84,97,141,114)], [(1,157,31,58),(2,59,32,158),(3,159,33,60),(4,61,34,160),(5,161,35,62),(6,63,36,162),(7,163,37,64),(8,65,38,164),(9,165,39,66),(10,67,40,166),(11,167,41,68),(12,69,42,168),(13,141,43,70),(14,71,44,142),(15,143,45,72),(16,73,46,144),(17,145,47,74),(18,75,48,146),(19,147,49,76),(20,77,50,148),(21,149,51,78),(22,79,52,150),(23,151,53,80),(24,81,54,152),(25,153,55,82),(26,83,56,154),(27,155,29,84),(28,57,30,156),(85,194,116,201),(86,202,117,195),(87,196,118,203),(88,204,119,169),(89,170,120,205),(90,206,121,171),(91,172,122,207),(92,208,123,173),(93,174,124,209),(94,210,125,175),(95,176,126,211),(96,212,127,177),(97,178,128,213),(98,214,129,179),(99,180,130,215),(100,216,131,181),(101,182,132,217),(102,218,133,183),(103,184,134,219),(104,220,135,185),(105,186,136,221),(106,222,137,187),(107,188,138,223),(108,224,139,189),(109,190,140,197),(110,198,113,191),(111,192,114,199),(112,200,115,193)], [(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)], [(1,14,15,28),(2,27,16,13),(3,12,17,26),(4,25,18,11),(5,10,19,24),(6,23,20,9),(7,8,21,22),(29,46,43,32),(30,31,44,45),(33,42,47,56),(34,55,48,41),(35,40,49,54),(36,53,50,39),(37,38,51,52),(57,72,71,58),(59,70,73,84),(60,83,74,69),(61,68,75,82),(62,81,76,67),(63,66,77,80),(64,79,78,65),(85,112,99,98),(86,97,100,111),(87,110,101,96),(88,95,102,109),(89,108,103,94),(90,93,104,107),(91,106,105,92),(113,132,127,118),(114,117,128,131),(115,130,129,116),(119,126,133,140),(120,139,134,125),(121,124,135,138),(122,137,136,123),(141,144,155,158),(142,157,156,143),(145,168,159,154),(146,153,160,167),(147,166,161,152),(148,151,162,165),(149,164,163,150),(169,190,183,176),(170,175,184,189),(171,188,185,174),(172,173,186,187),(177,182,191,196),(178,195,192,181),(179,180,193,194),(197,218,211,204),(198,203,212,217),(199,216,213,202),(200,201,214,215),(205,210,219,224),(206,223,220,209),(207,208,221,222)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 18 | 22 | 1 |
| 0 | 0 | 27 | 8 | 16 | 0 |
| 0 | 0 | 0 | 11 | 2 | 11 |
| 0 | 0 | 2 | 19 | 18 | 27 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 4 | 8 |
| 0 | 0 | 0 | 1 | 3 | 2 |
| 0 | 0 | 22 | 28 | 28 | 0 |
| 0 | 0 | 25 | 15 | 0 | 28 |
| 9 | 6 | 0 | 0 | 0 | 0 |
| 6 | 20 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 20 | 0 | 0 |
| 0 | 0 | 1 | 17 | 0 | 0 |
| 0 | 0 | 27 | 17 | 7 | 9 |
| 0 | 0 | 2 | 1 | 20 | 9 |
| 20 | 23 | 0 | 0 | 0 | 0 |
| 23 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 26 | 7 | 0 | 0 |
| 0 | 0 | 11 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 0 | 0 | 0 | 0 | 12 | 0 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,0,12,0,0,0,0,0,0,21,27,0,2,0,0,18,8,11,19,0,0,22,16,2,18,0,0,1,0,11,27],[0,28,0,0,0,0,1,0,0,0,0,0,0,0,1,0,22,25,0,0,0,1,28,15,0,0,4,3,28,0,0,0,8,2,0,28],[9,6,0,0,0,0,6,20,0,0,0,0,0,0,25,1,27,2,0,0,20,17,17,1,0,0,0,0,7,20,0,0,0,0,9,9],[20,23,0,0,0,0,23,9,0,0,0,0,0,0,26,11,0,0,0,0,7,3,0,0,0,0,0,0,0,12,0,0,0,0,12,0] >;
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 28 | 28 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 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 | 2+ (1+4) | 2- (1+4) | Q8.10D14 | D7×C4○D4 | D4⋊8D14 |
| kernel | C42.150D14 | C4×D28 | C42⋊2D7 | Dic7.Q8 | D7×C4⋊C4 | D28⋊C4 | D14.5D4 | C28⋊1D4 | D14⋊Q8 | D14⋊2Q8 | C4⋊C4⋊D7 | C7×C42.C2 | C42.C2 | D14 | C42 | C4⋊C4 | C14 | C14 | C2 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 4 | 1 | 2 | 1 | 1 | 1 | 3 | 4 | 3 | 18 | 1 | 1 | 6 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{150}D_{14} % in TeX
G:=Group("C4^2.150D14"); // GroupNames label
G:=SmallGroup(448,1145);
// by ID
G=gap.SmallGroup(448,1145);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,268,675,570,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^2*b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1*b^2,c*b*c^-1=b^-1,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations
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