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, C28.3Q8⋊46C2, D14.D4⋊54C2, C28.310(C4○D4), C28.17D4⋊32C2, (C4×C28).156C22, (C2×C14).101C24, (C2×C28).161C23, D14⋊C4.99C22, C22⋊C4.114D14, (C22×C4).212D14, C4.137(D4⋊2D7), C23.98(C22×D7), (D4×C14).261C22, C23.D14⋊50C2, C23.21D14⋊8C2, C4⋊Dic7.300C22, C22.126(C23×D7), Dic7⋊C4.112C22, (C22×C14).171C23, (C22×C28).110C22, C7⋊4(C23.36C23), (C4×Dic7).293C22, (C2×Dic7).208C23, (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
Generators and relations for C42.229D14
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 >
Subgroups: 916 in 234 conjugacy classes, 101 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C42, C42⋊C2, C4×D4, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22.D4, C4.4D4, C42.C2, C42⋊2C2, Dic14, C4×D7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C23.36C23, C4×Dic7, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×C7⋊D4, C22×C28, D4×C14, C4×Dic14, D7×C42, C23.D14, D14.D4, C28.3Q8, D14⋊2Q8, C23.21D14, C4×C7⋊D4, C28.17D4, C28⋊2D4, D4×C28, C42.229D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, C22×D7, C23.36C23, C4○D28, D4⋊2D7, C23×D7, C2×C4○D28, C2×D4⋊2D7, D7×C4○D4, C42.229D14
►On 224 points
Generators in S224
(1 156 205 125)(2 19 206 108)(3 158 207 113)(4 21 208 110)(5 160 209 115)(6 23 210 112)(7 162 197 117)(8 25 198 100)(9 164 199 119)(10 27 200 102)(11 166 201 121)(12 15 202 104)(13 168 203 123)(14 17 204 106)(16 145 105 97)(18 147 107 85)(20 149 109 87)(22 151 111 89)(24 153 99 91)(26 141 101 93)(28 143 103 95)(29 43 211 66)(30 130 212 176)(31 45 213 68)(32 132 214 178)(33 47 215 70)(34 134 216 180)(35 49 217 58)(36 136 218 182)(37 51 219 60)(38 138 220 170)(39 53 221 62)(40 140 222 172)(41 55 223 64)(42 128 224 174)(44 193 67 76)(46 195 69 78)(48 183 57 80)(50 185 59 82)(52 187 61 84)(54 189 63 72)(56 191 65 74)(71 139 188 171)(73 127 190 173)(75 129 192 175)(77 131 194 177)(79 133 196 179)(81 135 184 181)(83 137 186 169)(86 157 148 126)(88 159 150 114)(90 161 152 116)(92 163 154 118)(94 165 142 120)(96 167 144 122)(98 155 146 124)
(1 35 147 184)(2 36 148 185)(3 37 149 186)(4 38 150 187)(5 39 151 188)(6 40 152 189)(7 41 153 190)(8 42 154 191)(9 29 141 192)(10 30 142 193)(11 31 143 194)(12 32 144 195)(13 33 145 196)(14 34 146 183)(15 132 122 69)(16 133 123 70)(17 134 124 57)(18 135 125 58)(19 136 126 59)(20 137 113 60)(21 138 114 61)(22 139 115 62)(23 140 116 63)(24 127 117 64)(25 128 118 65)(26 129 119 66)(27 130 120 67)(28 131 121 68)(43 101 175 164)(44 102 176 165)(45 103 177 166)(46 104 178 167)(47 105 179 168)(48 106 180 155)(49 107 181 156)(50 108 182 157)(51 109 169 158)(52 110 170 159)(53 111 171 160)(54 112 172 161)(55 99 173 162)(56 100 174 163)(71 209 221 89)(72 210 222 90)(73 197 223 91)(74 198 224 92)(75 199 211 93)(76 200 212 94)(77 201 213 95)(78 202 214 96)(79 203 215 97)(80 204 216 98)(81 205 217 85)(82 206 218 86)(83 207 219 87)(84 208 220 88)
(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 14 205 204)(2 203 206 13)(3 12 207 202)(4 201 208 11)(5 10 209 200)(6 199 210 9)(7 8 197 198)(15 109 104 20)(16 19 105 108)(17 107 106 18)(21 103 110 28)(22 27 111 102)(23 101 112 26)(24 25 99 100)(29 40 211 222)(30 221 212 39)(31 38 213 220)(32 219 214 37)(33 36 215 218)(34 217 216 35)(41 42 223 224)(43 54 66 63)(44 62 67 53)(45 52 68 61)(46 60 69 51)(47 50 70 59)(48 58 57 49)(55 56 64 65)(71 76 188 193)(72 192 189 75)(73 74 190 191)(77 84 194 187)(78 186 195 83)(79 82 196 185)(80 184 183 81)(85 98 147 146)(86 145 148 97)(87 96 149 144)(88 143 150 95)(89 94 151 142)(90 141 152 93)(91 92 153 154)(113 122 158 167)(114 166 159 121)(115 120 160 165)(116 164 161 119)(117 118 162 163)(123 126 168 157)(124 156 155 125)(127 128 173 174)(129 140 175 172)(130 171 176 139)(131 138 177 170)(132 169 178 137)(133 136 179 182)(134 181 180 135)
G:=sub<Sym(224)| (1,156,205,125)(2,19,206,108)(3,158,207,113)(4,21,208,110)(5,160,209,115)(6,23,210,112)(7,162,197,117)(8,25,198,100)(9,164,199,119)(10,27,200,102)(11,166,201,121)(12,15,202,104)(13,168,203,123)(14,17,204,106)(16,145,105,97)(18,147,107,85)(20,149,109,87)(22,151,111,89)(24,153,99,91)(26,141,101,93)(28,143,103,95)(29,43,211,66)(30,130,212,176)(31,45,213,68)(32,132,214,178)(33,47,215,70)(34,134,216,180)(35,49,217,58)(36,136,218,182)(37,51,219,60)(38,138,220,170)(39,53,221,62)(40,140,222,172)(41,55,223,64)(42,128,224,174)(44,193,67,76)(46,195,69,78)(48,183,57,80)(50,185,59,82)(52,187,61,84)(54,189,63,72)(56,191,65,74)(71,139,188,171)(73,127,190,173)(75,129,192,175)(77,131,194,177)(79,133,196,179)(81,135,184,181)(83,137,186,169)(86,157,148,126)(88,159,150,114)(90,161,152,116)(92,163,154,118)(94,165,142,120)(96,167,144,122)(98,155,146,124), (1,35,147,184)(2,36,148,185)(3,37,149,186)(4,38,150,187)(5,39,151,188)(6,40,152,189)(7,41,153,190)(8,42,154,191)(9,29,141,192)(10,30,142,193)(11,31,143,194)(12,32,144,195)(13,33,145,196)(14,34,146,183)(15,132,122,69)(16,133,123,70)(17,134,124,57)(18,135,125,58)(19,136,126,59)(20,137,113,60)(21,138,114,61)(22,139,115,62)(23,140,116,63)(24,127,117,64)(25,128,118,65)(26,129,119,66)(27,130,120,67)(28,131,121,68)(43,101,175,164)(44,102,176,165)(45,103,177,166)(46,104,178,167)(47,105,179,168)(48,106,180,155)(49,107,181,156)(50,108,182,157)(51,109,169,158)(52,110,170,159)(53,111,171,160)(54,112,172,161)(55,99,173,162)(56,100,174,163)(71,209,221,89)(72,210,222,90)(73,197,223,91)(74,198,224,92)(75,199,211,93)(76,200,212,94)(77,201,213,95)(78,202,214,96)(79,203,215,97)(80,204,216,98)(81,205,217,85)(82,206,218,86)(83,207,219,87)(84,208,220,88), (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), (1,14,205,204)(2,203,206,13)(3,12,207,202)(4,201,208,11)(5,10,209,200)(6,199,210,9)(7,8,197,198)(15,109,104,20)(16,19,105,108)(17,107,106,18)(21,103,110,28)(22,27,111,102)(23,101,112,26)(24,25,99,100)(29,40,211,222)(30,221,212,39)(31,38,213,220)(32,219,214,37)(33,36,215,218)(34,217,216,35)(41,42,223,224)(43,54,66,63)(44,62,67,53)(45,52,68,61)(46,60,69,51)(47,50,70,59)(48,58,57,49)(55,56,64,65)(71,76,188,193)(72,192,189,75)(73,74,190,191)(77,84,194,187)(78,186,195,83)(79,82,196,185)(80,184,183,81)(85,98,147,146)(86,145,148,97)(87,96,149,144)(88,143,150,95)(89,94,151,142)(90,141,152,93)(91,92,153,154)(113,122,158,167)(114,166,159,121)(115,120,160,165)(116,164,161,119)(117,118,162,163)(123,126,168,157)(124,156,155,125)(127,128,173,174)(129,140,175,172)(130,171,176,139)(131,138,177,170)(132,169,178,137)(133,136,179,182)(134,181,180,135)>;
G:=Group( (1,156,205,125)(2,19,206,108)(3,158,207,113)(4,21,208,110)(5,160,209,115)(6,23,210,112)(7,162,197,117)(8,25,198,100)(9,164,199,119)(10,27,200,102)(11,166,201,121)(12,15,202,104)(13,168,203,123)(14,17,204,106)(16,145,105,97)(18,147,107,85)(20,149,109,87)(22,151,111,89)(24,153,99,91)(26,141,101,93)(28,143,103,95)(29,43,211,66)(30,130,212,176)(31,45,213,68)(32,132,214,178)(33,47,215,70)(34,134,216,180)(35,49,217,58)(36,136,218,182)(37,51,219,60)(38,138,220,170)(39,53,221,62)(40,140,222,172)(41,55,223,64)(42,128,224,174)(44,193,67,76)(46,195,69,78)(48,183,57,80)(50,185,59,82)(52,187,61,84)(54,189,63,72)(56,191,65,74)(71,139,188,171)(73,127,190,173)(75,129,192,175)(77,131,194,177)(79,133,196,179)(81,135,184,181)(83,137,186,169)(86,157,148,126)(88,159,150,114)(90,161,152,116)(92,163,154,118)(94,165,142,120)(96,167,144,122)(98,155,146,124), (1,35,147,184)(2,36,148,185)(3,37,149,186)(4,38,150,187)(5,39,151,188)(6,40,152,189)(7,41,153,190)(8,42,154,191)(9,29,141,192)(10,30,142,193)(11,31,143,194)(12,32,144,195)(13,33,145,196)(14,34,146,183)(15,132,122,69)(16,133,123,70)(17,134,124,57)(18,135,125,58)(19,136,126,59)(20,137,113,60)(21,138,114,61)(22,139,115,62)(23,140,116,63)(24,127,117,64)(25,128,118,65)(26,129,119,66)(27,130,120,67)(28,131,121,68)(43,101,175,164)(44,102,176,165)(45,103,177,166)(46,104,178,167)(47,105,179,168)(48,106,180,155)(49,107,181,156)(50,108,182,157)(51,109,169,158)(52,110,170,159)(53,111,171,160)(54,112,172,161)(55,99,173,162)(56,100,174,163)(71,209,221,89)(72,210,222,90)(73,197,223,91)(74,198,224,92)(75,199,211,93)(76,200,212,94)(77,201,213,95)(78,202,214,96)(79,203,215,97)(80,204,216,98)(81,205,217,85)(82,206,218,86)(83,207,219,87)(84,208,220,88), (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), (1,14,205,204)(2,203,206,13)(3,12,207,202)(4,201,208,11)(5,10,209,200)(6,199,210,9)(7,8,197,198)(15,109,104,20)(16,19,105,108)(17,107,106,18)(21,103,110,28)(22,27,111,102)(23,101,112,26)(24,25,99,100)(29,40,211,222)(30,221,212,39)(31,38,213,220)(32,219,214,37)(33,36,215,218)(34,217,216,35)(41,42,223,224)(43,54,66,63)(44,62,67,53)(45,52,68,61)(46,60,69,51)(47,50,70,59)(48,58,57,49)(55,56,64,65)(71,76,188,193)(72,192,189,75)(73,74,190,191)(77,84,194,187)(78,186,195,83)(79,82,196,185)(80,184,183,81)(85,98,147,146)(86,145,148,97)(87,96,149,144)(88,143,150,95)(89,94,151,142)(90,141,152,93)(91,92,153,154)(113,122,158,167)(114,166,159,121)(115,120,160,165)(116,164,161,119)(117,118,162,163)(123,126,168,157)(124,156,155,125)(127,128,173,174)(129,140,175,172)(130,171,176,139)(131,138,177,170)(132,169,178,137)(133,136,179,182)(134,181,180,135) );
G=PermutationGroup([[(1,156,205,125),(2,19,206,108),(3,158,207,113),(4,21,208,110),(5,160,209,115),(6,23,210,112),(7,162,197,117),(8,25,198,100),(9,164,199,119),(10,27,200,102),(11,166,201,121),(12,15,202,104),(13,168,203,123),(14,17,204,106),(16,145,105,97),(18,147,107,85),(20,149,109,87),(22,151,111,89),(24,153,99,91),(26,141,101,93),(28,143,103,95),(29,43,211,66),(30,130,212,176),(31,45,213,68),(32,132,214,178),(33,47,215,70),(34,134,216,180),(35,49,217,58),(36,136,218,182),(37,51,219,60),(38,138,220,170),(39,53,221,62),(40,140,222,172),(41,55,223,64),(42,128,224,174),(44,193,67,76),(46,195,69,78),(48,183,57,80),(50,185,59,82),(52,187,61,84),(54,189,63,72),(56,191,65,74),(71,139,188,171),(73,127,190,173),(75,129,192,175),(77,131,194,177),(79,133,196,179),(81,135,184,181),(83,137,186,169),(86,157,148,126),(88,159,150,114),(90,161,152,116),(92,163,154,118),(94,165,142,120),(96,167,144,122),(98,155,146,124)], [(1,35,147,184),(2,36,148,185),(3,37,149,186),(4,38,150,187),(5,39,151,188),(6,40,152,189),(7,41,153,190),(8,42,154,191),(9,29,141,192),(10,30,142,193),(11,31,143,194),(12,32,144,195),(13,33,145,196),(14,34,146,183),(15,132,122,69),(16,133,123,70),(17,134,124,57),(18,135,125,58),(19,136,126,59),(20,137,113,60),(21,138,114,61),(22,139,115,62),(23,140,116,63),(24,127,117,64),(25,128,118,65),(26,129,119,66),(27,130,120,67),(28,131,121,68),(43,101,175,164),(44,102,176,165),(45,103,177,166),(46,104,178,167),(47,105,179,168),(48,106,180,155),(49,107,181,156),(50,108,182,157),(51,109,169,158),(52,110,170,159),(53,111,171,160),(54,112,172,161),(55,99,173,162),(56,100,174,163),(71,209,221,89),(72,210,222,90),(73,197,223,91),(74,198,224,92),(75,199,211,93),(76,200,212,94),(77,201,213,95),(78,202,214,96),(79,203,215,97),(80,204,216,98),(81,205,217,85),(82,206,218,86),(83,207,219,87),(84,208,220,88)], [(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)], [(1,14,205,204),(2,203,206,13),(3,12,207,202),(4,201,208,11),(5,10,209,200),(6,199,210,9),(7,8,197,198),(15,109,104,20),(16,19,105,108),(17,107,106,18),(21,103,110,28),(22,27,111,102),(23,101,112,26),(24,25,99,100),(29,40,211,222),(30,221,212,39),(31,38,213,220),(32,219,214,37),(33,36,215,218),(34,217,216,35),(41,42,223,224),(43,54,66,63),(44,62,67,53),(45,52,68,61),(46,60,69,51),(47,50,70,59),(48,58,57,49),(55,56,64,65),(71,76,188,193),(72,192,189,75),(73,74,190,191),(77,84,194,187),(78,186,195,83),(79,82,196,185),(80,184,183,81),(85,98,147,146),(86,145,148,97),(87,96,149,144),(88,143,150,95),(89,94,151,142),(90,141,152,93),(91,92,153,154),(113,122,158,167),(114,166,159,121),(115,120,160,165),(116,164,161,119),(117,118,162,163),(123,126,168,157),(124,156,155,125),(127,128,173,174),(129,140,175,172),(130,171,176,139),(131,138,177,170),(132,169,178,137),(133,136,179,182),(134,181,180,135)]])
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 | C28.3Q8 | 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 |
Matrix representation of C42.229D14 ►in 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] >;
C42.229D14 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