metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.161D14, C14.1002- 1+4, C14.1392+ 1+4, (C4×D28)⋊15C2, C4⋊C4.118D14, C42⋊2C2⋊4D7, C28.6Q8⋊9C2, D14⋊2Q8⋊41C2, D14⋊Q8⋊43C2, D14⋊D4.4C2, (C4×C28).33C22, C22⋊C4.79D14, C28.3Q8⋊39C2, D14.14(C4○D4), Dic7⋊4D4⋊36C2, D14.D4⋊51C2, D14.5D4⋊41C2, (C2×C28).194C23, (C2×C14).251C24, C4⋊Dic7.54C22, C2.64(D4⋊8D14), C23.57(C22×D7), D14⋊C4.114C22, C22⋊Dic14⋊45C2, (C2×D28).227C22, C22.D28⋊29C2, Dic7⋊C4.56C22, (C22×C14).65C23, C22.272(C23×D7), C23.D7.67C22, C7⋊9(C22.33C24), (C4×Dic7).151C22, (C2×Dic7).265C23, (C22×D7).225C23, C2.64(D4.10D14), (C2×Dic14).184C22, (C22×Dic7).151C22, (D7×C4⋊C4)⋊41C2, C2.98(D7×C4○D4), C4⋊C4⋊D7⋊42C2, (C7×C42⋊2C2)⋊6C2, C14.209(C2×C4○D4), (C2×C4×D7).219C22, (C7×C4⋊C4).203C22, (C2×C4).209(C22×D7), (C2×C7⋊D4).71C22, (C7×C22⋊C4).76C22, SmallGroup(448,1160)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.161D14
G = < a,b,c,d | a4=b4=1, c14=d2=b2, ab=ba, cac-1=dad-1=ab2, cbc-1=a2b-1, dbd-1=a2b, dcd-1=c13 >
Subgroups: 1036 in 218 conjugacy classes, 93 normal (91 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, Dic7, C28, D14, D14, C2×C14, C2×C14, C2×C4⋊C4, C4×D4, C4⋊D4, C22⋊Q8, C22.D4, C42.C2, C42⋊2C2, C42⋊2C2, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C22×D7, C22×C14, C22.33C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C22×Dic7, C2×C7⋊D4, C28.6Q8, C4×D28, C22⋊Dic14, Dic7⋊4D4, D14.D4, D14⋊D4, C22.D28, C28.3Q8, D7×C4⋊C4, D14.5D4, D14⋊Q8, D14⋊2Q8, C4⋊C4⋊D7, C7×C42⋊2C2, C42.161D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, 2- 1+4, C22×D7, C22.33C24, C23×D7, D7×C4○D4, D4⋊8D14, D4.10D14, C42.161D14
►On 224 points
Generators in S224
(1 149 118 59)(2 164 119 74)(3 151 120 61)(4 166 121 76)(5 153 122 63)(6 168 123 78)(7 155 124 65)(8 142 125 80)(9 157 126 67)(10 144 127 82)(11 159 128 69)(12 146 129 84)(13 161 130 71)(14 148 131 58)(15 163 132 73)(16 150 133 60)(17 165 134 75)(18 152 135 62)(19 167 136 77)(20 154 137 64)(21 141 138 79)(22 156 139 66)(23 143 140 81)(24 158 113 68)(25 145 114 83)(26 160 115 70)(27 147 116 57)(28 162 117 72)(29 187 221 93)(30 174 222 108)(31 189 223 95)(32 176 224 110)(33 191 197 97)(34 178 198 112)(35 193 199 99)(36 180 200 86)(37 195 201 101)(38 182 202 88)(39 169 203 103)(40 184 204 90)(41 171 205 105)(42 186 206 92)(43 173 207 107)(44 188 208 94)(45 175 209 109)(46 190 210 96)(47 177 211 111)(48 192 212 98)(49 179 213 85)(50 194 214 100)(51 181 215 87)(52 196 216 102)(53 183 217 89)(54 170 218 104)(55 185 219 91)(56 172 220 106)
(1 99 15 85)(2 180 16 194)(3 101 17 87)(4 182 18 196)(5 103 19 89)(6 184 20 170)(7 105 21 91)(8 186 22 172)(9 107 23 93)(10 188 24 174)(11 109 25 95)(12 190 26 176)(13 111 27 97)(14 192 28 178)(29 157 43 143)(30 82 44 68)(31 159 45 145)(32 84 46 70)(33 161 47 147)(34 58 48 72)(35 163 49 149)(36 60 50 74)(37 165 51 151)(38 62 52 76)(39 167 53 153)(40 64 54 78)(41 141 55 155)(42 66 56 80)(57 197 71 211)(59 199 73 213)(61 201 75 215)(63 203 77 217)(65 205 79 219)(67 207 81 221)(69 209 83 223)(86 133 100 119)(88 135 102 121)(90 137 104 123)(92 139 106 125)(94 113 108 127)(96 115 110 129)(98 117 112 131)(114 189 128 175)(116 191 130 177)(118 193 132 179)(120 195 134 181)(122 169 136 183)(124 171 138 185)(126 173 140 187)(142 206 156 220)(144 208 158 222)(146 210 160 224)(148 212 162 198)(150 214 164 200)(152 216 166 202)(154 218 168 204)
(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 40 43 54)(30 53 44 39)(31 38 45 52)(32 51 46 37)(33 36 47 50)(34 49 48 35)(41 56 55 42)(57 74 71 60)(58 59 72 73)(61 70 75 84)(62 83 76 69)(63 68 77 82)(64 81 78 67)(65 66 79 80)(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)(113 122 127 136)(114 135 128 121)(115 120 129 134)(116 133 130 119)(117 118 131 132)(123 140 137 126)(124 125 138 139)(141 142 155 156)(143 168 157 154)(144 153 158 167)(145 166 159 152)(146 151 160 165)(147 164 161 150)(148 149 162 163)(169 188 183 174)(170 173 184 187)(171 186 185 172)(175 182 189 196)(176 195 190 181)(177 180 191 194)(178 193 192 179)(197 200 211 214)(198 213 212 199)(201 224 215 210)(202 209 216 223)(203 222 217 208)(204 207 218 221)(205 220 219 206)
G:=sub<Sym(224)| (1,149,118,59)(2,164,119,74)(3,151,120,61)(4,166,121,76)(5,153,122,63)(6,168,123,78)(7,155,124,65)(8,142,125,80)(9,157,126,67)(10,144,127,82)(11,159,128,69)(12,146,129,84)(13,161,130,71)(14,148,131,58)(15,163,132,73)(16,150,133,60)(17,165,134,75)(18,152,135,62)(19,167,136,77)(20,154,137,64)(21,141,138,79)(22,156,139,66)(23,143,140,81)(24,158,113,68)(25,145,114,83)(26,160,115,70)(27,147,116,57)(28,162,117,72)(29,187,221,93)(30,174,222,108)(31,189,223,95)(32,176,224,110)(33,191,197,97)(34,178,198,112)(35,193,199,99)(36,180,200,86)(37,195,201,101)(38,182,202,88)(39,169,203,103)(40,184,204,90)(41,171,205,105)(42,186,206,92)(43,173,207,107)(44,188,208,94)(45,175,209,109)(46,190,210,96)(47,177,211,111)(48,192,212,98)(49,179,213,85)(50,194,214,100)(51,181,215,87)(52,196,216,102)(53,183,217,89)(54,170,218,104)(55,185,219,91)(56,172,220,106), (1,99,15,85)(2,180,16,194)(3,101,17,87)(4,182,18,196)(5,103,19,89)(6,184,20,170)(7,105,21,91)(8,186,22,172)(9,107,23,93)(10,188,24,174)(11,109,25,95)(12,190,26,176)(13,111,27,97)(14,192,28,178)(29,157,43,143)(30,82,44,68)(31,159,45,145)(32,84,46,70)(33,161,47,147)(34,58,48,72)(35,163,49,149)(36,60,50,74)(37,165,51,151)(38,62,52,76)(39,167,53,153)(40,64,54,78)(41,141,55,155)(42,66,56,80)(57,197,71,211)(59,199,73,213)(61,201,75,215)(63,203,77,217)(65,205,79,219)(67,207,81,221)(69,209,83,223)(86,133,100,119)(88,135,102,121)(90,137,104,123)(92,139,106,125)(94,113,108,127)(96,115,110,129)(98,117,112,131)(114,189,128,175)(116,191,130,177)(118,193,132,179)(120,195,134,181)(122,169,136,183)(124,171,138,185)(126,173,140,187)(142,206,156,220)(144,208,158,222)(146,210,160,224)(148,212,162,198)(150,214,164,200)(152,216,166,202)(154,218,168,204), (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)(29,40,43,54)(30,53,44,39)(31,38,45,52)(32,51,46,37)(33,36,47,50)(34,49,48,35)(41,56,55,42)(57,74,71,60)(58,59,72,73)(61,70,75,84)(62,83,76,69)(63,68,77,82)(64,81,78,67)(65,66,79,80)(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)(113,122,127,136)(114,135,128,121)(115,120,129,134)(116,133,130,119)(117,118,131,132)(123,140,137,126)(124,125,138,139)(141,142,155,156)(143,168,157,154)(144,153,158,167)(145,166,159,152)(146,151,160,165)(147,164,161,150)(148,149,162,163)(169,188,183,174)(170,173,184,187)(171,186,185,172)(175,182,189,196)(176,195,190,181)(177,180,191,194)(178,193,192,179)(197,200,211,214)(198,213,212,199)(201,224,215,210)(202,209,216,223)(203,222,217,208)(204,207,218,221)(205,220,219,206)>;
G:=Group( (1,149,118,59)(2,164,119,74)(3,151,120,61)(4,166,121,76)(5,153,122,63)(6,168,123,78)(7,155,124,65)(8,142,125,80)(9,157,126,67)(10,144,127,82)(11,159,128,69)(12,146,129,84)(13,161,130,71)(14,148,131,58)(15,163,132,73)(16,150,133,60)(17,165,134,75)(18,152,135,62)(19,167,136,77)(20,154,137,64)(21,141,138,79)(22,156,139,66)(23,143,140,81)(24,158,113,68)(25,145,114,83)(26,160,115,70)(27,147,116,57)(28,162,117,72)(29,187,221,93)(30,174,222,108)(31,189,223,95)(32,176,224,110)(33,191,197,97)(34,178,198,112)(35,193,199,99)(36,180,200,86)(37,195,201,101)(38,182,202,88)(39,169,203,103)(40,184,204,90)(41,171,205,105)(42,186,206,92)(43,173,207,107)(44,188,208,94)(45,175,209,109)(46,190,210,96)(47,177,211,111)(48,192,212,98)(49,179,213,85)(50,194,214,100)(51,181,215,87)(52,196,216,102)(53,183,217,89)(54,170,218,104)(55,185,219,91)(56,172,220,106), (1,99,15,85)(2,180,16,194)(3,101,17,87)(4,182,18,196)(5,103,19,89)(6,184,20,170)(7,105,21,91)(8,186,22,172)(9,107,23,93)(10,188,24,174)(11,109,25,95)(12,190,26,176)(13,111,27,97)(14,192,28,178)(29,157,43,143)(30,82,44,68)(31,159,45,145)(32,84,46,70)(33,161,47,147)(34,58,48,72)(35,163,49,149)(36,60,50,74)(37,165,51,151)(38,62,52,76)(39,167,53,153)(40,64,54,78)(41,141,55,155)(42,66,56,80)(57,197,71,211)(59,199,73,213)(61,201,75,215)(63,203,77,217)(65,205,79,219)(67,207,81,221)(69,209,83,223)(86,133,100,119)(88,135,102,121)(90,137,104,123)(92,139,106,125)(94,113,108,127)(96,115,110,129)(98,117,112,131)(114,189,128,175)(116,191,130,177)(118,193,132,179)(120,195,134,181)(122,169,136,183)(124,171,138,185)(126,173,140,187)(142,206,156,220)(144,208,158,222)(146,210,160,224)(148,212,162,198)(150,214,164,200)(152,216,166,202)(154,218,168,204), (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)(29,40,43,54)(30,53,44,39)(31,38,45,52)(32,51,46,37)(33,36,47,50)(34,49,48,35)(41,56,55,42)(57,74,71,60)(58,59,72,73)(61,70,75,84)(62,83,76,69)(63,68,77,82)(64,81,78,67)(65,66,79,80)(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)(113,122,127,136)(114,135,128,121)(115,120,129,134)(116,133,130,119)(117,118,131,132)(123,140,137,126)(124,125,138,139)(141,142,155,156)(143,168,157,154)(144,153,158,167)(145,166,159,152)(146,151,160,165)(147,164,161,150)(148,149,162,163)(169,188,183,174)(170,173,184,187)(171,186,185,172)(175,182,189,196)(176,195,190,181)(177,180,191,194)(178,193,192,179)(197,200,211,214)(198,213,212,199)(201,224,215,210)(202,209,216,223)(203,222,217,208)(204,207,218,221)(205,220,219,206) );
G=PermutationGroup([[(1,149,118,59),(2,164,119,74),(3,151,120,61),(4,166,121,76),(5,153,122,63),(6,168,123,78),(7,155,124,65),(8,142,125,80),(9,157,126,67),(10,144,127,82),(11,159,128,69),(12,146,129,84),(13,161,130,71),(14,148,131,58),(15,163,132,73),(16,150,133,60),(17,165,134,75),(18,152,135,62),(19,167,136,77),(20,154,137,64),(21,141,138,79),(22,156,139,66),(23,143,140,81),(24,158,113,68),(25,145,114,83),(26,160,115,70),(27,147,116,57),(28,162,117,72),(29,187,221,93),(30,174,222,108),(31,189,223,95),(32,176,224,110),(33,191,197,97),(34,178,198,112),(35,193,199,99),(36,180,200,86),(37,195,201,101),(38,182,202,88),(39,169,203,103),(40,184,204,90),(41,171,205,105),(42,186,206,92),(43,173,207,107),(44,188,208,94),(45,175,209,109),(46,190,210,96),(47,177,211,111),(48,192,212,98),(49,179,213,85),(50,194,214,100),(51,181,215,87),(52,196,216,102),(53,183,217,89),(54,170,218,104),(55,185,219,91),(56,172,220,106)], [(1,99,15,85),(2,180,16,194),(3,101,17,87),(4,182,18,196),(5,103,19,89),(6,184,20,170),(7,105,21,91),(8,186,22,172),(9,107,23,93),(10,188,24,174),(11,109,25,95),(12,190,26,176),(13,111,27,97),(14,192,28,178),(29,157,43,143),(30,82,44,68),(31,159,45,145),(32,84,46,70),(33,161,47,147),(34,58,48,72),(35,163,49,149),(36,60,50,74),(37,165,51,151),(38,62,52,76),(39,167,53,153),(40,64,54,78),(41,141,55,155),(42,66,56,80),(57,197,71,211),(59,199,73,213),(61,201,75,215),(63,203,77,217),(65,205,79,219),(67,207,81,221),(69,209,83,223),(86,133,100,119),(88,135,102,121),(90,137,104,123),(92,139,106,125),(94,113,108,127),(96,115,110,129),(98,117,112,131),(114,189,128,175),(116,191,130,177),(118,193,132,179),(120,195,134,181),(122,169,136,183),(124,171,138,185),(126,173,140,187),(142,206,156,220),(144,208,158,222),(146,210,160,224),(148,212,162,198),(150,214,164,200),(152,216,166,202),(154,218,168,204)], [(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),(29,40,43,54),(30,53,44,39),(31,38,45,52),(32,51,46,37),(33,36,47,50),(34,49,48,35),(41,56,55,42),(57,74,71,60),(58,59,72,73),(61,70,75,84),(62,83,76,69),(63,68,77,82),(64,81,78,67),(65,66,79,80),(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),(113,122,127,136),(114,135,128,121),(115,120,129,134),(116,133,130,119),(117,118,131,132),(123,140,137,126),(124,125,138,139),(141,142,155,156),(143,168,157,154),(144,153,158,167),(145,166,159,152),(146,151,160,165),(147,164,161,150),(148,149,162,163),(169,188,183,174),(170,173,184,187),(171,186,185,172),(175,182,189,196),(176,195,190,181),(177,180,191,194),(178,193,192,179),(197,200,211,214),(198,213,212,199),(201,224,215,210),(202,209,216,223),(203,222,217,208),(204,207,218,221),(205,220,219,206)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | ··· | 4G | 4H | 4I | 4J | ··· | 4N | 7A | 7B | 7C | 14A | ··· | 14I | 14J | 14K | 14L | 28A | ··· | 28R | 28S | ··· | 28AA |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 14 | 14 | 28 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | 2+ 1+4 | 2- 1+4 | D7×C4○D4 | D4⋊8D14 | D4.10D14 |
| kernel | C42.161D14 | C28.6Q8 | C4×D28 | C22⋊Dic14 | Dic7⋊4D4 | D14.D4 | D14⋊D4 | C22.D28 | C28.3Q8 | D7×C4⋊C4 | D14.5D4 | D14⋊Q8 | D14⋊2Q8 | C4⋊C4⋊D7 | C7×C42⋊2C2 | C42⋊2C2 | D14 | C42 | C22⋊C4 | C4⋊C4 | C14 | C14 | C2 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 3 | 9 | 9 | 1 | 1 | 6 | 6 | 6 |
Matrix representation of C42.161D14 ►in GL6(𝔽29)
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 18 | 26 | 18 |
| 0 | 0 | 11 | 27 | 0 | 11 |
| 0 | 0 | 9 | 9 | 16 | 11 |
| 0 | 0 | 0 | 16 | 3 | 13 |
| 1 | 24 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 6 | 27 |
| 0 | 0 | 0 | 1 | 4 | 27 |
| 0 | 0 | 28 | 1 | 28 | 0 |
| 0 | 0 | 27 | 3 | 0 | 28 |
| 24 | 12 | 0 | 0 | 0 | 0 |
| 27 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 12 | 13 | 0 |
| 0 | 0 | 17 | 3 | 16 | 13 |
| 0 | 0 | 21 | 12 | 16 | 17 |
| 0 | 0 | 9 | 11 | 2 | 14 |
| 5 | 17 | 0 | 0 | 0 | 0 |
| 2 | 24 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 12 | 13 | 0 |
| 0 | 0 | 0 | 4 | 23 | 16 |
| 0 | 0 | 21 | 0 | 14 | 12 |
| 0 | 0 | 26 | 8 | 14 | 15 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,0,12,0,0,0,0,0,0,2,11,9,0,0,0,18,27,9,16,0,0,26,0,16,3,0,0,18,11,11,13],[1,0,0,0,0,0,24,28,0,0,0,0,0,0,1,0,28,27,0,0,0,1,1,3,0,0,6,4,28,0,0,0,27,27,0,28],[24,27,0,0,0,0,12,5,0,0,0,0,0,0,25,17,21,9,0,0,12,3,12,11,0,0,13,16,16,2,0,0,0,13,17,14],[5,2,0,0,0,0,17,24,0,0,0,0,0,0,25,0,21,26,0,0,12,4,0,8,0,0,13,23,14,14,0,0,0,16,12,15] >;
C42.161D14 in GAP, Magma, Sage, TeX
C_4^2._{161}D_{14} % in TeX
G:=Group("C4^2.161D14"); // GroupNames label
G:=SmallGroup(448,1160);
// by ID
G=gap.SmallGroup(448,1160);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,268,675,570,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a*b^2,c*b*c^-1=a^2*b^-1,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations