metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.96D14, C14.522- 1+4, C4⋊C4.273D14, D14⋊Q8⋊5C2, C42⋊D7⋊3C2, C42⋊2D7⋊5C2, Dic7.Q8⋊5C2, C28.6Q8⋊7C2, (C4×Dic14)⋊10C2, C42⋊C2⋊15D7, (C2×C14).75C24, (C4×C28).26C22, C22⋊C4.99D14, (C2×C28).150C23, D14⋊C4.63C22, Dic7⋊4D4.6C2, C22⋊Dic14⋊5C2, (C22×C4).196D14, C4⋊Dic7.35C22, Dic7.17(C4○D4), C23.D7.5C22, C22.19(C4○D28), Dic7⋊C4.99C22, (C2×Dic7).28C23, C22.D28.1C2, (C22×D7).23C23, C22.104(C23×D7), C23.160(C22×D7), C23.11D14⋊26C2, (C22×C14).145C23, (C22×C28).436C22, C7⋊3(C22.46C24), (C4×Dic7).197C22, C23.23D14.3C2, C2.10(D4.10D14), (C2×Dic14).231C22, (C22×Dic7).89C22, C4⋊C4⋊D7⋊5C2, C2.14(D7×C4○D4), C2.34(C2×C4○D28), C14.31(C2×C4○D4), (C2×Dic7⋊C4)⋊46C2, (C2×C4×D7).193C22, (C7×C42⋊C2)⋊17C2, (C2×C14).42(C4○D4), (C7×C4⋊C4).311C22, (C2×C4).277(C22×D7), (C2×C7⋊D4).10C22, (C7×C22⋊C4).139C22, SmallGroup(448,984)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.96D14
G = < a,b,c,d | a4=b4=c14=1, d2=b2, ab=ba, cac-1=dad-1=ab2, bc=cb, dbd-1=a2b, dcd-1=b2c-1 >
Subgroups: 852 in 214 conjugacy classes, 97 normal (91 characteristic)
C1, C2, C2, C4, C22, 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, C22×C4, C2×D4, C2×Q8, Dic7, Dic7, C28, D14, C2×C14, C2×C14, C2×C14, C2×C4⋊C4, C42⋊C2, C42⋊C2, C4×D4, C4×Q8, C22⋊Q8, C22.D4, C42.C2, C42⋊2C2, Dic14, C4×D7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C22×D7, C22×C14, C22.46C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C22×Dic7, C2×C7⋊D4, C22×C28, C4×Dic14, C28.6Q8, C42⋊D7, C42⋊2D7, C23.11D14, C22⋊Dic14, Dic7⋊4D4, C22.D28, Dic7.Q8, D14⋊Q8, C4⋊C4⋊D7, C2×Dic7⋊C4, C23.23D14, C7×C42⋊C2, C42.96D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2- 1+4, C22×D7, C22.46C24, C4○D28, C23×D7, C2×C4○D28, D7×C4○D4, D4.10D14, C42.96D14
►On 224 points
Generators in S224
(1 168 108 172)(2 162 109 180)(3 156 110 174)(4 164 111 182)(5 158 112 176)(6 166 106 170)(7 160 107 178)(8 157 22 175)(9 165 23 169)(10 159 24 177)(11 167 25 171)(12 161 26 179)(13 155 27 173)(14 163 28 181)(15 223 64 122)(16 217 65 116)(17 211 66 124)(18 219 67 118)(19 213 68 126)(20 221 69 120)(21 215 70 114)(29 133 46 191)(30 127 47 185)(31 135 48 193)(32 129 49 187)(33 137 43 195)(34 131 44 189)(35 139 45 183)(36 128 55 186)(37 136 56 194)(38 130 50 188)(39 138 51 196)(40 132 52 190)(41 140 53 184)(42 134 54 192)(57 220 93 119)(58 214 94 113)(59 222 95 121)(60 216 96 115)(61 224 97 123)(62 218 98 117)(63 212 92 125)(71 210 91 154)(72 204 85 148)(73 198 86 142)(74 206 87 150)(75 200 88 144)(76 208 89 152)(77 202 90 146)(78 151 102 207)(79 145 103 201)(80 153 104 209)(81 147 105 203)(82 141 99 197)(83 149 100 205)(84 143 101 199)
(1 38 12 33)(2 39 13 34)(3 40 14 35)(4 41 8 29)(5 42 9 30)(6 36 10 31)(7 37 11 32)(15 100 60 73)(16 101 61 74)(17 102 62 75)(18 103 63 76)(19 104 57 77)(20 105 58 71)(21 99 59 72)(22 46 111 53)(23 47 112 54)(24 48 106 55)(25 49 107 56)(26 43 108 50)(27 44 109 51)(28 45 110 52)(64 83 96 86)(65 84 97 87)(66 78 98 88)(67 79 92 89)(68 80 93 90)(69 81 94 91)(70 82 95 85)(113 154 120 147)(114 141 121 148)(115 142 122 149)(116 143 123 150)(117 144 124 151)(118 145 125 152)(119 146 126 153)(127 158 134 165)(128 159 135 166)(129 160 136 167)(130 161 137 168)(131 162 138 155)(132 163 139 156)(133 164 140 157)(169 185 176 192)(170 186 177 193)(171 187 178 194)(172 188 179 195)(173 189 180 196)(174 190 181 183)(175 191 182 184)(197 222 204 215)(198 223 205 216)(199 224 206 217)(200 211 207 218)(201 212 208 219)(202 213 209 220)(203 214 210 221)
(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)
(1 218 12 211)(2 224 13 217)(3 216 14 223)(4 222 8 215)(5 214 9 221)(6 220 10 213)(7 212 11 219)(15 181 60 174)(16 173 61 180)(17 179 62 172)(18 171 63 178)(19 177 57 170)(20 169 58 176)(21 175 59 182)(22 114 111 121)(23 120 112 113)(24 126 106 119)(25 118 107 125)(26 124 108 117)(27 116 109 123)(28 122 110 115)(29 141 41 148)(30 147 42 154)(31 153 36 146)(32 145 37 152)(33 151 38 144)(34 143 39 150)(35 149 40 142)(43 207 50 200)(44 199 51 206)(45 205 52 198)(46 197 53 204)(47 203 54 210)(48 209 55 202)(49 201 56 208)(64 163 96 156)(65 155 97 162)(66 161 98 168)(67 167 92 160)(68 159 93 166)(69 165 94 158)(70 157 95 164)(71 134 105 127)(72 140 99 133)(73 132 100 139)(74 138 101 131)(75 130 102 137)(76 136 103 129)(77 128 104 135)(78 195 88 188)(79 187 89 194)(80 193 90 186)(81 185 91 192)(82 191 85 184)(83 183 86 190)(84 189 87 196)
G:=sub<Sym(224)| (1,168,108,172)(2,162,109,180)(3,156,110,174)(4,164,111,182)(5,158,112,176)(6,166,106,170)(7,160,107,178)(8,157,22,175)(9,165,23,169)(10,159,24,177)(11,167,25,171)(12,161,26,179)(13,155,27,173)(14,163,28,181)(15,223,64,122)(16,217,65,116)(17,211,66,124)(18,219,67,118)(19,213,68,126)(20,221,69,120)(21,215,70,114)(29,133,46,191)(30,127,47,185)(31,135,48,193)(32,129,49,187)(33,137,43,195)(34,131,44,189)(35,139,45,183)(36,128,55,186)(37,136,56,194)(38,130,50,188)(39,138,51,196)(40,132,52,190)(41,140,53,184)(42,134,54,192)(57,220,93,119)(58,214,94,113)(59,222,95,121)(60,216,96,115)(61,224,97,123)(62,218,98,117)(63,212,92,125)(71,210,91,154)(72,204,85,148)(73,198,86,142)(74,206,87,150)(75,200,88,144)(76,208,89,152)(77,202,90,146)(78,151,102,207)(79,145,103,201)(80,153,104,209)(81,147,105,203)(82,141,99,197)(83,149,100,205)(84,143,101,199), (1,38,12,33)(2,39,13,34)(3,40,14,35)(4,41,8,29)(5,42,9,30)(6,36,10,31)(7,37,11,32)(15,100,60,73)(16,101,61,74)(17,102,62,75)(18,103,63,76)(19,104,57,77)(20,105,58,71)(21,99,59,72)(22,46,111,53)(23,47,112,54)(24,48,106,55)(25,49,107,56)(26,43,108,50)(27,44,109,51)(28,45,110,52)(64,83,96,86)(65,84,97,87)(66,78,98,88)(67,79,92,89)(68,80,93,90)(69,81,94,91)(70,82,95,85)(113,154,120,147)(114,141,121,148)(115,142,122,149)(116,143,123,150)(117,144,124,151)(118,145,125,152)(119,146,126,153)(127,158,134,165)(128,159,135,166)(129,160,136,167)(130,161,137,168)(131,162,138,155)(132,163,139,156)(133,164,140,157)(169,185,176,192)(170,186,177,193)(171,187,178,194)(172,188,179,195)(173,189,180,196)(174,190,181,183)(175,191,182,184)(197,222,204,215)(198,223,205,216)(199,224,206,217)(200,211,207,218)(201,212,208,219)(202,213,209,220)(203,214,210,221), (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), (1,218,12,211)(2,224,13,217)(3,216,14,223)(4,222,8,215)(5,214,9,221)(6,220,10,213)(7,212,11,219)(15,181,60,174)(16,173,61,180)(17,179,62,172)(18,171,63,178)(19,177,57,170)(20,169,58,176)(21,175,59,182)(22,114,111,121)(23,120,112,113)(24,126,106,119)(25,118,107,125)(26,124,108,117)(27,116,109,123)(28,122,110,115)(29,141,41,148)(30,147,42,154)(31,153,36,146)(32,145,37,152)(33,151,38,144)(34,143,39,150)(35,149,40,142)(43,207,50,200)(44,199,51,206)(45,205,52,198)(46,197,53,204)(47,203,54,210)(48,209,55,202)(49,201,56,208)(64,163,96,156)(65,155,97,162)(66,161,98,168)(67,167,92,160)(68,159,93,166)(69,165,94,158)(70,157,95,164)(71,134,105,127)(72,140,99,133)(73,132,100,139)(74,138,101,131)(75,130,102,137)(76,136,103,129)(77,128,104,135)(78,195,88,188)(79,187,89,194)(80,193,90,186)(81,185,91,192)(82,191,85,184)(83,183,86,190)(84,189,87,196)>;
G:=Group( (1,168,108,172)(2,162,109,180)(3,156,110,174)(4,164,111,182)(5,158,112,176)(6,166,106,170)(7,160,107,178)(8,157,22,175)(9,165,23,169)(10,159,24,177)(11,167,25,171)(12,161,26,179)(13,155,27,173)(14,163,28,181)(15,223,64,122)(16,217,65,116)(17,211,66,124)(18,219,67,118)(19,213,68,126)(20,221,69,120)(21,215,70,114)(29,133,46,191)(30,127,47,185)(31,135,48,193)(32,129,49,187)(33,137,43,195)(34,131,44,189)(35,139,45,183)(36,128,55,186)(37,136,56,194)(38,130,50,188)(39,138,51,196)(40,132,52,190)(41,140,53,184)(42,134,54,192)(57,220,93,119)(58,214,94,113)(59,222,95,121)(60,216,96,115)(61,224,97,123)(62,218,98,117)(63,212,92,125)(71,210,91,154)(72,204,85,148)(73,198,86,142)(74,206,87,150)(75,200,88,144)(76,208,89,152)(77,202,90,146)(78,151,102,207)(79,145,103,201)(80,153,104,209)(81,147,105,203)(82,141,99,197)(83,149,100,205)(84,143,101,199), (1,38,12,33)(2,39,13,34)(3,40,14,35)(4,41,8,29)(5,42,9,30)(6,36,10,31)(7,37,11,32)(15,100,60,73)(16,101,61,74)(17,102,62,75)(18,103,63,76)(19,104,57,77)(20,105,58,71)(21,99,59,72)(22,46,111,53)(23,47,112,54)(24,48,106,55)(25,49,107,56)(26,43,108,50)(27,44,109,51)(28,45,110,52)(64,83,96,86)(65,84,97,87)(66,78,98,88)(67,79,92,89)(68,80,93,90)(69,81,94,91)(70,82,95,85)(113,154,120,147)(114,141,121,148)(115,142,122,149)(116,143,123,150)(117,144,124,151)(118,145,125,152)(119,146,126,153)(127,158,134,165)(128,159,135,166)(129,160,136,167)(130,161,137,168)(131,162,138,155)(132,163,139,156)(133,164,140,157)(169,185,176,192)(170,186,177,193)(171,187,178,194)(172,188,179,195)(173,189,180,196)(174,190,181,183)(175,191,182,184)(197,222,204,215)(198,223,205,216)(199,224,206,217)(200,211,207,218)(201,212,208,219)(202,213,209,220)(203,214,210,221), (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), (1,218,12,211)(2,224,13,217)(3,216,14,223)(4,222,8,215)(5,214,9,221)(6,220,10,213)(7,212,11,219)(15,181,60,174)(16,173,61,180)(17,179,62,172)(18,171,63,178)(19,177,57,170)(20,169,58,176)(21,175,59,182)(22,114,111,121)(23,120,112,113)(24,126,106,119)(25,118,107,125)(26,124,108,117)(27,116,109,123)(28,122,110,115)(29,141,41,148)(30,147,42,154)(31,153,36,146)(32,145,37,152)(33,151,38,144)(34,143,39,150)(35,149,40,142)(43,207,50,200)(44,199,51,206)(45,205,52,198)(46,197,53,204)(47,203,54,210)(48,209,55,202)(49,201,56,208)(64,163,96,156)(65,155,97,162)(66,161,98,168)(67,167,92,160)(68,159,93,166)(69,165,94,158)(70,157,95,164)(71,134,105,127)(72,140,99,133)(73,132,100,139)(74,138,101,131)(75,130,102,137)(76,136,103,129)(77,128,104,135)(78,195,88,188)(79,187,89,194)(80,193,90,186)(81,185,91,192)(82,191,85,184)(83,183,86,190)(84,189,87,196) );
G=PermutationGroup([[(1,168,108,172),(2,162,109,180),(3,156,110,174),(4,164,111,182),(5,158,112,176),(6,166,106,170),(7,160,107,178),(8,157,22,175),(9,165,23,169),(10,159,24,177),(11,167,25,171),(12,161,26,179),(13,155,27,173),(14,163,28,181),(15,223,64,122),(16,217,65,116),(17,211,66,124),(18,219,67,118),(19,213,68,126),(20,221,69,120),(21,215,70,114),(29,133,46,191),(30,127,47,185),(31,135,48,193),(32,129,49,187),(33,137,43,195),(34,131,44,189),(35,139,45,183),(36,128,55,186),(37,136,56,194),(38,130,50,188),(39,138,51,196),(40,132,52,190),(41,140,53,184),(42,134,54,192),(57,220,93,119),(58,214,94,113),(59,222,95,121),(60,216,96,115),(61,224,97,123),(62,218,98,117),(63,212,92,125),(71,210,91,154),(72,204,85,148),(73,198,86,142),(74,206,87,150),(75,200,88,144),(76,208,89,152),(77,202,90,146),(78,151,102,207),(79,145,103,201),(80,153,104,209),(81,147,105,203),(82,141,99,197),(83,149,100,205),(84,143,101,199)], [(1,38,12,33),(2,39,13,34),(3,40,14,35),(4,41,8,29),(5,42,9,30),(6,36,10,31),(7,37,11,32),(15,100,60,73),(16,101,61,74),(17,102,62,75),(18,103,63,76),(19,104,57,77),(20,105,58,71),(21,99,59,72),(22,46,111,53),(23,47,112,54),(24,48,106,55),(25,49,107,56),(26,43,108,50),(27,44,109,51),(28,45,110,52),(64,83,96,86),(65,84,97,87),(66,78,98,88),(67,79,92,89),(68,80,93,90),(69,81,94,91),(70,82,95,85),(113,154,120,147),(114,141,121,148),(115,142,122,149),(116,143,123,150),(117,144,124,151),(118,145,125,152),(119,146,126,153),(127,158,134,165),(128,159,135,166),(129,160,136,167),(130,161,137,168),(131,162,138,155),(132,163,139,156),(133,164,140,157),(169,185,176,192),(170,186,177,193),(171,187,178,194),(172,188,179,195),(173,189,180,196),(174,190,181,183),(175,191,182,184),(197,222,204,215),(198,223,205,216),(199,224,206,217),(200,211,207,218),(201,212,208,219),(202,213,209,220),(203,214,210,221)], [(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)], [(1,218,12,211),(2,224,13,217),(3,216,14,223),(4,222,8,215),(5,214,9,221),(6,220,10,213),(7,212,11,219),(15,181,60,174),(16,173,61,180),(17,179,62,172),(18,171,63,178),(19,177,57,170),(20,169,58,176),(21,175,59,182),(22,114,111,121),(23,120,112,113),(24,126,106,119),(25,118,107,125),(26,124,108,117),(27,116,109,123),(28,122,110,115),(29,141,41,148),(30,147,42,154),(31,153,36,146),(32,145,37,152),(33,151,38,144),(34,143,39,150),(35,149,40,142),(43,207,50,200),(44,199,51,206),(45,205,52,198),(46,197,53,204),(47,203,54,210),(48,209,55,202),(49,201,56,208),(64,163,96,156),(65,155,97,162),(66,161,98,168),(67,167,92,160),(68,159,93,166),(69,165,94,158),(70,157,95,164),(71,134,105,127),(72,140,99,133),(73,132,100,139),(74,138,101,131),(75,130,102,137),(76,136,103,129),(77,128,104,135),(78,195,88,188),(79,187,89,194),(80,193,90,186),(81,185,91,192),(82,191,85,184),(83,183,86,190),(84,189,87,196)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | ··· | 4R | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 2 | 2 | 28 | 2 | ··· | 2 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | D14 | C4○D28 | 2- 1+4 | D7×C4○D4 | D4.10D14 |
| kernel | C42.96D14 | C4×Dic14 | C28.6Q8 | C42⋊D7 | C42⋊2D7 | C23.11D14 | C22⋊Dic14 | Dic7⋊4D4 | C22.D28 | Dic7.Q8 | D14⋊Q8 | C4⋊C4⋊D7 | C2×Dic7⋊C4 | C23.23D14 | C7×C42⋊C2 | C42⋊C2 | Dic7 | C2×C14 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C22 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 4 | 6 | 6 | 6 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of C42.96D14 ►in GL4(𝔽29) generated by
| 12 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 |
| 0 | 0 | 12 | 28 |
| 0 | 0 | 27 | 17 |
| 11 | 2 | 0 | 0 |
| 27 | 18 | 0 | 0 |
| 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 17 |
| 25 | 25 | 0 | 0 |
| 4 | 11 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 24 | 28 |
| 3 | 7 | 0 | 0 |
| 3 | 26 | 0 | 0 |
| 0 | 0 | 17 | 1 |
| 0 | 0 | 0 | 12 |
G:=sub<GL(4,GF(29))| [12,0,0,0,0,12,0,0,0,0,12,27,0,0,28,17],[11,27,0,0,2,18,0,0,0,0,17,0,0,0,0,17],[25,4,0,0,25,11,0,0,0,0,1,24,0,0,0,28],[3,3,0,0,7,26,0,0,0,0,17,0,0,0,1,12] >;
C42.96D14 in GAP, Magma, Sage, TeX
C_4^2._{96}D_{14} % in TeX
G:=Group("C4^2.96D14"); // GroupNames label
G:=SmallGroup(448,984);
// by ID
G=gap.SmallGroup(448,984);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,387,100,675,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a*b^2,b*c=c*b,d*b*d^-1=a^2*b,d*c*d^-1=b^2*c^-1>;
// generators/relations