metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.236D14, (C4×D7)⋊3Q8, C28⋊Q8⋊34C2, C4.38(Q8×D7), D14.3(C2×Q8), C28.49(C2×Q8), C4⋊C4.204D14, C42.C2⋊15D7, (D7×C42).8C2, (C2×C28).86C23, D14⋊Q8.1C2, C28.6Q8⋊22C2, Dic7.16(C2×Q8), Dic7⋊3Q8⋊34C2, C14.41(C22×Q8), (C2×C14).232C24, (C4×C28).192C22, D14⋊C4.38C22, Dic7.12(C4○D4), Dic7⋊C4.50C22, C4⋊Dic7.239C22, C22.253(C23×D7), C7⋊5(C23.37C23), (C4×Dic7).139C22, (C2×Dic7).311C23, (C22×D7).219C23, (C2×Dic14).178C22, C2.24(C2×Q8×D7), C2.84(D7×C4○D4), (C7×C42.C2)⋊5C2, C4⋊C4⋊7D7.11C2, C14.195(C2×C4○D4), (C2×C4×D7).249C22, (C2×C4).77(C22×D7), (C7×C4⋊C4).187C22, SmallGroup(448,1141)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 892 in 222 conjugacy classes, 107 normal (19 characteristic)
C1, C2, C2 [×2], C2 [×2], C4 [×2], C4 [×16], C22, C22 [×4], C7, C2×C4, C2×C4 [×6], C2×C4 [×15], Q8 [×8], C23, D7 [×2], C14, C14 [×2], C42, C42 [×7], C22⋊C4 [×4], C4⋊C4 [×6], C4⋊C4 [×10], C22×C4 [×3], C2×Q8 [×4], Dic7 [×6], Dic7 [×4], C28 [×2], C28 [×6], D14 [×2], D14 [×2], C2×C14, C2×C42, C42⋊C2 [×2], C4×Q8 [×4], C22⋊Q8 [×4], C42.C2, C42.C2, C4⋊Q8 [×2], Dic14 [×8], C4×D7 [×4], C4×D7 [×4], C2×Dic7, C2×Dic7 [×6], C2×C28, C2×C28 [×6], C22×D7, C23.37C23, C4×Dic7, C4×Dic7 [×6], Dic7⋊C4 [×8], C4⋊Dic7 [×2], D14⋊C4 [×4], C4×C28, C7×C4⋊C4 [×6], C2×Dic14 [×4], C2×C4×D7, C2×C4×D7 [×2], C28.6Q8, D7×C42, Dic7⋊3Q8 [×4], C28⋊Q8 [×2], C4⋊C4⋊7D7 [×2], D14⋊Q8 [×4], C7×C42.C2, C42.236D14
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, Q8×D7 [×2], C23×D7, C2×Q8×D7, D7×C4○D4 [×2], C42.236D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=b2, d2=a2b2, ab=ba, cac-1=dad-1=a-1, cbc-1=dbd-1=a2b-1, dcd-1=a2c13 >
►On 224 points
Generators in S224
(1 202 158 69)(2 70 159 203)(3 204 160 71)(4 72 161 205)(5 206 162 73)(6 74 163 207)(7 208 164 75)(8 76 165 209)(9 210 166 77)(10 78 167 211)(11 212 168 79)(12 80 141 213)(13 214 142 81)(14 82 143 215)(15 216 144 83)(16 84 145 217)(17 218 146 57)(18 58 147 219)(19 220 148 59)(20 60 149 221)(21 222 150 61)(22 62 151 223)(23 224 152 63)(24 64 153 197)(25 198 154 65)(26 66 155 199)(27 200 156 67)(28 68 157 201)(29 92 135 185)(30 186 136 93)(31 94 137 187)(32 188 138 95)(33 96 139 189)(34 190 140 97)(35 98 113 191)(36 192 114 99)(37 100 115 193)(38 194 116 101)(39 102 117 195)(40 196 118 103)(41 104 119 169)(42 170 120 105)(43 106 121 171)(44 172 122 107)(45 108 123 173)(46 174 124 109)(47 110 125 175)(48 176 126 111)(49 112 127 177)(50 178 128 85)(51 86 129 179)(52 180 130 87)(53 88 131 181)(54 182 132 89)(55 90 133 183)(56 184 134 91)
(1 132 15 118)(2 41 16 55)(3 134 17 120)(4 43 18 29)(5 136 19 122)(6 45 20 31)(7 138 21 124)(8 47 22 33)(9 140 23 126)(10 49 24 35)(11 114 25 128)(12 51 26 37)(13 116 27 130)(14 53 28 39)(30 148 44 162)(32 150 46 164)(34 152 48 166)(36 154 50 168)(38 156 52 142)(40 158 54 144)(42 160 56 146)(57 170 71 184)(58 92 72 106)(59 172 73 186)(60 94 74 108)(61 174 75 188)(62 96 76 110)(63 176 77 190)(64 98 78 112)(65 178 79 192)(66 100 80 86)(67 180 81 194)(68 102 82 88)(69 182 83 196)(70 104 84 90)(85 212 99 198)(87 214 101 200)(89 216 103 202)(91 218 105 204)(93 220 107 206)(95 222 109 208)(97 224 111 210)(113 167 127 153)(115 141 129 155)(117 143 131 157)(119 145 133 159)(121 147 135 161)(123 149 137 163)(125 151 139 165)(169 217 183 203)(171 219 185 205)(173 221 187 207)(175 223 189 209)(177 197 191 211)(179 199 193 213)(181 201 195 215)
(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 28 144 143)(2 142 145 27)(3 26 146 141)(4 168 147 25)(5 24 148 167)(6 166 149 23)(7 22 150 165)(8 164 151 21)(9 20 152 163)(10 162 153 19)(11 18 154 161)(12 160 155 17)(13 16 156 159)(14 158 157 15)(29 114 121 50)(30 49 122 113)(31 140 123 48)(32 47 124 139)(33 138 125 46)(34 45 126 137)(35 136 127 44)(36 43 128 135)(37 134 129 42)(38 41 130 133)(39 132 131 40)(51 120 115 56)(52 55 116 119)(53 118 117 54)(57 80 204 199)(58 198 205 79)(59 78 206 197)(60 224 207 77)(61 76 208 223)(62 222 209 75)(63 74 210 221)(64 220 211 73)(65 72 212 219)(66 218 213 71)(67 70 214 217)(68 216 215 69)(81 84 200 203)(82 202 201 83)(85 92 192 171)(86 170 193 91)(87 90 194 169)(88 196 195 89)(93 112 172 191)(94 190 173 111)(95 110 174 189)(96 188 175 109)(97 108 176 187)(98 186 177 107)(99 106 178 185)(100 184 179 105)(101 104 180 183)(102 182 181 103)
G:=sub<Sym(224)| (1,202,158,69)(2,70,159,203)(3,204,160,71)(4,72,161,205)(5,206,162,73)(6,74,163,207)(7,208,164,75)(8,76,165,209)(9,210,166,77)(10,78,167,211)(11,212,168,79)(12,80,141,213)(13,214,142,81)(14,82,143,215)(15,216,144,83)(16,84,145,217)(17,218,146,57)(18,58,147,219)(19,220,148,59)(20,60,149,221)(21,222,150,61)(22,62,151,223)(23,224,152,63)(24,64,153,197)(25,198,154,65)(26,66,155,199)(27,200,156,67)(28,68,157,201)(29,92,135,185)(30,186,136,93)(31,94,137,187)(32,188,138,95)(33,96,139,189)(34,190,140,97)(35,98,113,191)(36,192,114,99)(37,100,115,193)(38,194,116,101)(39,102,117,195)(40,196,118,103)(41,104,119,169)(42,170,120,105)(43,106,121,171)(44,172,122,107)(45,108,123,173)(46,174,124,109)(47,110,125,175)(48,176,126,111)(49,112,127,177)(50,178,128,85)(51,86,129,179)(52,180,130,87)(53,88,131,181)(54,182,132,89)(55,90,133,183)(56,184,134,91), (1,132,15,118)(2,41,16,55)(3,134,17,120)(4,43,18,29)(5,136,19,122)(6,45,20,31)(7,138,21,124)(8,47,22,33)(9,140,23,126)(10,49,24,35)(11,114,25,128)(12,51,26,37)(13,116,27,130)(14,53,28,39)(30,148,44,162)(32,150,46,164)(34,152,48,166)(36,154,50,168)(38,156,52,142)(40,158,54,144)(42,160,56,146)(57,170,71,184)(58,92,72,106)(59,172,73,186)(60,94,74,108)(61,174,75,188)(62,96,76,110)(63,176,77,190)(64,98,78,112)(65,178,79,192)(66,100,80,86)(67,180,81,194)(68,102,82,88)(69,182,83,196)(70,104,84,90)(85,212,99,198)(87,214,101,200)(89,216,103,202)(91,218,105,204)(93,220,107,206)(95,222,109,208)(97,224,111,210)(113,167,127,153)(115,141,129,155)(117,143,131,157)(119,145,133,159)(121,147,135,161)(123,149,137,163)(125,151,139,165)(169,217,183,203)(171,219,185,205)(173,221,187,207)(175,223,189,209)(177,197,191,211)(179,199,193,213)(181,201,195,215), (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), (1,28,144,143)(2,142,145,27)(3,26,146,141)(4,168,147,25)(5,24,148,167)(6,166,149,23)(7,22,150,165)(8,164,151,21)(9,20,152,163)(10,162,153,19)(11,18,154,161)(12,160,155,17)(13,16,156,159)(14,158,157,15)(29,114,121,50)(30,49,122,113)(31,140,123,48)(32,47,124,139)(33,138,125,46)(34,45,126,137)(35,136,127,44)(36,43,128,135)(37,134,129,42)(38,41,130,133)(39,132,131,40)(51,120,115,56)(52,55,116,119)(53,118,117,54)(57,80,204,199)(58,198,205,79)(59,78,206,197)(60,224,207,77)(61,76,208,223)(62,222,209,75)(63,74,210,221)(64,220,211,73)(65,72,212,219)(66,218,213,71)(67,70,214,217)(68,216,215,69)(81,84,200,203)(82,202,201,83)(85,92,192,171)(86,170,193,91)(87,90,194,169)(88,196,195,89)(93,112,172,191)(94,190,173,111)(95,110,174,189)(96,188,175,109)(97,108,176,187)(98,186,177,107)(99,106,178,185)(100,184,179,105)(101,104,180,183)(102,182,181,103)>;
G:=Group( (1,202,158,69)(2,70,159,203)(3,204,160,71)(4,72,161,205)(5,206,162,73)(6,74,163,207)(7,208,164,75)(8,76,165,209)(9,210,166,77)(10,78,167,211)(11,212,168,79)(12,80,141,213)(13,214,142,81)(14,82,143,215)(15,216,144,83)(16,84,145,217)(17,218,146,57)(18,58,147,219)(19,220,148,59)(20,60,149,221)(21,222,150,61)(22,62,151,223)(23,224,152,63)(24,64,153,197)(25,198,154,65)(26,66,155,199)(27,200,156,67)(28,68,157,201)(29,92,135,185)(30,186,136,93)(31,94,137,187)(32,188,138,95)(33,96,139,189)(34,190,140,97)(35,98,113,191)(36,192,114,99)(37,100,115,193)(38,194,116,101)(39,102,117,195)(40,196,118,103)(41,104,119,169)(42,170,120,105)(43,106,121,171)(44,172,122,107)(45,108,123,173)(46,174,124,109)(47,110,125,175)(48,176,126,111)(49,112,127,177)(50,178,128,85)(51,86,129,179)(52,180,130,87)(53,88,131,181)(54,182,132,89)(55,90,133,183)(56,184,134,91), (1,132,15,118)(2,41,16,55)(3,134,17,120)(4,43,18,29)(5,136,19,122)(6,45,20,31)(7,138,21,124)(8,47,22,33)(9,140,23,126)(10,49,24,35)(11,114,25,128)(12,51,26,37)(13,116,27,130)(14,53,28,39)(30,148,44,162)(32,150,46,164)(34,152,48,166)(36,154,50,168)(38,156,52,142)(40,158,54,144)(42,160,56,146)(57,170,71,184)(58,92,72,106)(59,172,73,186)(60,94,74,108)(61,174,75,188)(62,96,76,110)(63,176,77,190)(64,98,78,112)(65,178,79,192)(66,100,80,86)(67,180,81,194)(68,102,82,88)(69,182,83,196)(70,104,84,90)(85,212,99,198)(87,214,101,200)(89,216,103,202)(91,218,105,204)(93,220,107,206)(95,222,109,208)(97,224,111,210)(113,167,127,153)(115,141,129,155)(117,143,131,157)(119,145,133,159)(121,147,135,161)(123,149,137,163)(125,151,139,165)(169,217,183,203)(171,219,185,205)(173,221,187,207)(175,223,189,209)(177,197,191,211)(179,199,193,213)(181,201,195,215), (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), (1,28,144,143)(2,142,145,27)(3,26,146,141)(4,168,147,25)(5,24,148,167)(6,166,149,23)(7,22,150,165)(8,164,151,21)(9,20,152,163)(10,162,153,19)(11,18,154,161)(12,160,155,17)(13,16,156,159)(14,158,157,15)(29,114,121,50)(30,49,122,113)(31,140,123,48)(32,47,124,139)(33,138,125,46)(34,45,126,137)(35,136,127,44)(36,43,128,135)(37,134,129,42)(38,41,130,133)(39,132,131,40)(51,120,115,56)(52,55,116,119)(53,118,117,54)(57,80,204,199)(58,198,205,79)(59,78,206,197)(60,224,207,77)(61,76,208,223)(62,222,209,75)(63,74,210,221)(64,220,211,73)(65,72,212,219)(66,218,213,71)(67,70,214,217)(68,216,215,69)(81,84,200,203)(82,202,201,83)(85,92,192,171)(86,170,193,91)(87,90,194,169)(88,196,195,89)(93,112,172,191)(94,190,173,111)(95,110,174,189)(96,188,175,109)(97,108,176,187)(98,186,177,107)(99,106,178,185)(100,184,179,105)(101,104,180,183)(102,182,181,103) );
G=PermutationGroup([(1,202,158,69),(2,70,159,203),(3,204,160,71),(4,72,161,205),(5,206,162,73),(6,74,163,207),(7,208,164,75),(8,76,165,209),(9,210,166,77),(10,78,167,211),(11,212,168,79),(12,80,141,213),(13,214,142,81),(14,82,143,215),(15,216,144,83),(16,84,145,217),(17,218,146,57),(18,58,147,219),(19,220,148,59),(20,60,149,221),(21,222,150,61),(22,62,151,223),(23,224,152,63),(24,64,153,197),(25,198,154,65),(26,66,155,199),(27,200,156,67),(28,68,157,201),(29,92,135,185),(30,186,136,93),(31,94,137,187),(32,188,138,95),(33,96,139,189),(34,190,140,97),(35,98,113,191),(36,192,114,99),(37,100,115,193),(38,194,116,101),(39,102,117,195),(40,196,118,103),(41,104,119,169),(42,170,120,105),(43,106,121,171),(44,172,122,107),(45,108,123,173),(46,174,124,109),(47,110,125,175),(48,176,126,111),(49,112,127,177),(50,178,128,85),(51,86,129,179),(52,180,130,87),(53,88,131,181),(54,182,132,89),(55,90,133,183),(56,184,134,91)], [(1,132,15,118),(2,41,16,55),(3,134,17,120),(4,43,18,29),(5,136,19,122),(6,45,20,31),(7,138,21,124),(8,47,22,33),(9,140,23,126),(10,49,24,35),(11,114,25,128),(12,51,26,37),(13,116,27,130),(14,53,28,39),(30,148,44,162),(32,150,46,164),(34,152,48,166),(36,154,50,168),(38,156,52,142),(40,158,54,144),(42,160,56,146),(57,170,71,184),(58,92,72,106),(59,172,73,186),(60,94,74,108),(61,174,75,188),(62,96,76,110),(63,176,77,190),(64,98,78,112),(65,178,79,192),(66,100,80,86),(67,180,81,194),(68,102,82,88),(69,182,83,196),(70,104,84,90),(85,212,99,198),(87,214,101,200),(89,216,103,202),(91,218,105,204),(93,220,107,206),(95,222,109,208),(97,224,111,210),(113,167,127,153),(115,141,129,155),(117,143,131,157),(119,145,133,159),(121,147,135,161),(123,149,137,163),(125,151,139,165),(169,217,183,203),(171,219,185,205),(173,221,187,207),(175,223,189,209),(177,197,191,211),(179,199,193,213),(181,201,195,215)], [(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)], [(1,28,144,143),(2,142,145,27),(3,26,146,141),(4,168,147,25),(5,24,148,167),(6,166,149,23),(7,22,150,165),(8,164,151,21),(9,20,152,163),(10,162,153,19),(11,18,154,161),(12,160,155,17),(13,16,156,159),(14,158,157,15),(29,114,121,50),(30,49,122,113),(31,140,123,48),(32,47,124,139),(33,138,125,46),(34,45,126,137),(35,136,127,44),(36,43,128,135),(37,134,129,42),(38,41,130,133),(39,132,131,40),(51,120,115,56),(52,55,116,119),(53,118,117,54),(57,80,204,199),(58,198,205,79),(59,78,206,197),(60,224,207,77),(61,76,208,223),(62,222,209,75),(63,74,210,221),(64,220,211,73),(65,72,212,219),(66,218,213,71),(67,70,214,217),(68,216,215,69),(81,84,200,203),(82,202,201,83),(85,92,192,171),(86,170,193,91),(87,90,194,169),(88,196,195,89),(93,112,172,191),(94,190,173,111),(95,110,174,189),(96,188,175,109),(97,108,176,187),(98,186,177,107),(99,106,178,185),(100,184,179,105),(101,104,180,183),(102,182,181,103)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 12 | 0 | 0 | 0 | 0 | 0 |
| 28 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 17 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 16 |
| 0 | 0 | 0 | 0 | 16 | 27 |
| 1 | 24 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 19 | 0 | 0 |
| 0 | 0 | 10 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 28 | 5 | 0 | 0 | 0 | 0 |
| 17 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 19 | 0 | 0 |
| 0 | 0 | 7 | 10 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 0 | 0 | 0 | 1 | 0 |
G:=sub<GL(6,GF(29))| [12,28,0,0,0,0,0,17,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[28,17,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,2,16,0,0,0,0,16,27],[1,0,0,0,0,0,24,28,0,0,0,0,0,0,19,10,0,0,0,0,19,7,0,0,0,0,0,0,0,28,0,0,0,0,1,0],[28,17,0,0,0,0,5,1,0,0,0,0,0,0,19,7,0,0,0,0,19,10,0,0,0,0,0,0,0,1,0,0,0,0,28,0] >;
70 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 4Q | 4R | 4S | 4T | 4U | 4V | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| 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 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 7 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
70 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | Q8 | D7 | C4○D4 | D14 | D14 | Q8×D7 | D7×C4○D4 |
| kernel | C42.236D14 | C28.6Q8 | D7×C42 | Dic7⋊3Q8 | C28⋊Q8 | C4⋊C4⋊7D7 | D14⋊Q8 | C7×C42.C2 | C4×D7 | C42.C2 | Dic7 | C42 | C4⋊C4 | C4 | C2 |
| # reps | 1 | 1 | 1 | 4 | 2 | 2 | 4 | 1 | 4 | 3 | 8 | 3 | 18 | 6 | 12 |
In GAP, Magma, Sage, TeX
C_4^2._{236}D_{14} % in TeX
G:=Group("C4^2.236D14"); // GroupNames label
G:=SmallGroup(448,1141);
// by ID
G=gap.SmallGroup(448,1141);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,100,1123,570,409,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=b^2,d^2=a^2*b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=d*b*d^-1=a^2*b^-1,d*c*d^-1=a^2*c^13>;
// generators/relations
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