metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.116D14, C14.1052+ (1+4), (C4×D4)⋊24D7, (D4×C28)⋊26C2, (C4×D28)⋊33C2, C28⋊2D4⋊10C2, C28⋊D4⋊10C2, C28⋊1D4⋊16C2, C28⋊7D4⋊12C2, C4⋊C4.287D14, D14⋊D4⋊11C2, D14.D4⋊9C2, (C2×D4).223D14, C4.46(C4○D28), C42⋊D7⋊15C2, C4.Dic14⋊16C2, C28.113(C4○D4), (C4×C28).160C22, (C2×C14).106C24, (C2×C28).164C23, D14⋊C4.88C22, C22⋊C4.118D14, (C22×C4).214D14, Dic7⋊C4.7C22, C2.24(D4⋊6D14), C2.18(D4⋊8D14), (D4×C14).265C22, (C2×D28).260C22, C23.23D14⋊4C2, C4⋊Dic7.364C22, (C22×C28).83C22, (C4×Dic7).78C22, (C2×Dic7).47C23, (C22×D7).40C23, C22.131(C23×D7), C23.103(C22×D7), C23.D7.16C22, (C22×C14).176C23, C7⋊2(C22.34C24), C14.48(C2×C4○D4), C2.55(C2×C4○D28), (C2×C4×D7).203C22, (C7×C4⋊C4).334C22, (C2×C4).581(C22×D7), (C2×C7⋊D4).19C22, (C7×C22⋊C4).129C22, SmallGroup(448,1015)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1236 in 240 conjugacy classes, 95 normal (43 characteristic)
C1, C2 [×3], C2 [×5], C4 [×2], C4 [×9], C22, C22 [×15], C7, C2×C4 [×3], C2×C4 [×2], C2×C4 [×11], D4 [×12], C23 [×2], C23 [×3], D7 [×3], C14 [×3], C14 [×2], C42, C42, C22⋊C4 [×2], C22⋊C4 [×8], C4⋊C4, C4⋊C4 [×7], C22×C4 [×2], C22×C4 [×3], C2×D4, C2×D4 [×9], Dic7 [×5], C28 [×2], C28 [×4], D14 [×9], C2×C14, C2×C14 [×6], C42⋊C2, C4×D4, C4×D4, C4⋊D4 [×6], C22.D4 [×4], C42.C2, C4⋊1D4, C4×D7 [×4], D28 [×4], C2×Dic7 [×3], C2×Dic7 [×2], C7⋊D4 [×6], C2×C28 [×3], C2×C28 [×2], C2×C28 [×2], C7×D4 [×2], C22×D7, C22×D7 [×2], C22×C14 [×2], C22.34C24, C4×Dic7, Dic7⋊C4 [×2], Dic7⋊C4 [×2], C4⋊Dic7, C4⋊Dic7 [×2], D14⋊C4 [×2], D14⋊C4 [×4], C23.D7 [×2], C4×C28, C7×C22⋊C4 [×2], C7×C4⋊C4, C2×C4×D7, C2×C4×D7 [×2], C2×D28, C2×D28 [×2], C2×C7⋊D4 [×6], C22×C28 [×2], D4×C14, C42⋊D7, C4×D28, D14.D4 [×2], D14⋊D4 [×2], C4.Dic14, C28⋊1D4, C23.23D14 [×2], C28⋊7D4 [×2], C28⋊2D4, C28⋊D4, D4×C28, C42.116D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×2], C24, D14 [×7], C2×C4○D4, 2+ (1+4) [×2], C22×D7 [×7], C22.34C24, C4○D28 [×2], C23×D7, C2×C4○D28, D4⋊6D14, D4⋊8D14, C42.116D14
Generators and relations
G = < a,b,c,d | a4=b4=c14=1, d2=a2, ab=ba, cac-1=dad-1=a-1b2, bc=cb, dbd-1=a2b-1, dcd-1=a2c-1 >
►On 224 points
Generators in S224
(1 193 163 55)(2 57 164 75)(3 195 165 43)(4 59 166 77)(5 183 167 45)(6 61 168 79)(7 185 155 47)(8 63 156 81)(9 187 157 49)(10 65 158 83)(11 189 159 51)(12 67 160 71)(13 191 161 53)(14 69 162 73)(15 60 147 78)(16 184 148 46)(17 62 149 80)(18 186 150 48)(19 64 151 82)(20 188 152 50)(21 66 153 84)(22 190 154 52)(23 68 141 72)(24 192 142 54)(25 70 143 74)(26 194 144 56)(27 58 145 76)(28 196 146 44)(29 103 202 90)(30 131 203 113)(31 105 204 92)(32 133 205 115)(33 107 206 94)(34 135 207 117)(35 109 208 96)(36 137 209 119)(37 111 210 98)(38 139 197 121)(39 99 198 86)(40 127 199 123)(41 101 200 88)(42 129 201 125)(85 171 112 219)(87 173 100 221)(89 175 102 223)(91 177 104 211)(93 179 106 213)(95 181 108 215)(97 169 110 217)(114 178 132 212)(116 180 134 214)(118 182 136 216)(120 170 138 218)(122 172 140 220)(124 174 128 222)(126 176 130 224)
(1 216 143 35)(2 217 144 36)(3 218 145 37)(4 219 146 38)(5 220 147 39)(6 221 148 40)(7 222 149 41)(8 223 150 42)(9 224 151 29)(10 211 152 30)(11 212 153 31)(12 213 154 32)(13 214 141 33)(14 215 142 34)(15 198 167 172)(16 199 168 173)(17 200 155 174)(18 201 156 175)(19 202 157 176)(20 203 158 177)(21 204 159 178)(22 205 160 179)(23 206 161 180)(24 207 162 181)(25 208 163 182)(26 209 164 169)(27 210 165 170)(28 197 166 171)(43 138 58 98)(44 139 59 85)(45 140 60 86)(46 127 61 87)(47 128 62 88)(48 129 63 89)(49 130 64 90)(50 131 65 91)(51 132 66 92)(52 133 67 93)(53 134 68 94)(54 135 69 95)(55 136 70 96)(56 137 57 97)(71 106 190 115)(72 107 191 116)(73 108 192 117)(74 109 193 118)(75 110 194 119)(76 111 195 120)(77 112 196 121)(78 99 183 122)(79 100 184 123)(80 101 185 124)(81 102 186 125)(82 103 187 126)(83 104 188 113)(84 105 189 114)
(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 41 163 200)(2 199 164 40)(3 39 165 198)(4 197 166 38)(5 37 167 210)(6 209 168 36)(7 35 155 208)(8 207 156 34)(9 33 157 206)(10 205 158 32)(11 31 159 204)(12 203 160 30)(13 29 161 202)(14 201 162 42)(15 170 147 218)(16 217 148 169)(17 182 149 216)(18 215 150 181)(19 180 151 214)(20 213 152 179)(21 178 153 212)(22 211 154 177)(23 176 141 224)(24 223 142 175)(25 174 143 222)(26 221 144 173)(27 172 145 220)(28 219 146 171)(43 122 195 140)(44 139 196 121)(45 120 183 138)(46 137 184 119)(47 118 185 136)(48 135 186 117)(49 116 187 134)(50 133 188 115)(51 114 189 132)(52 131 190 113)(53 126 191 130)(54 129 192 125)(55 124 193 128)(56 127 194 123)(57 87 75 100)(58 99 76 86)(59 85 77 112)(60 111 78 98)(61 97 79 110)(62 109 80 96)(63 95 81 108)(64 107 82 94)(65 93 83 106)(66 105 84 92)(67 91 71 104)(68 103 72 90)(69 89 73 102)(70 101 74 88)
G:=sub<Sym(224)| (1,193,163,55)(2,57,164,75)(3,195,165,43)(4,59,166,77)(5,183,167,45)(6,61,168,79)(7,185,155,47)(8,63,156,81)(9,187,157,49)(10,65,158,83)(11,189,159,51)(12,67,160,71)(13,191,161,53)(14,69,162,73)(15,60,147,78)(16,184,148,46)(17,62,149,80)(18,186,150,48)(19,64,151,82)(20,188,152,50)(21,66,153,84)(22,190,154,52)(23,68,141,72)(24,192,142,54)(25,70,143,74)(26,194,144,56)(27,58,145,76)(28,196,146,44)(29,103,202,90)(30,131,203,113)(31,105,204,92)(32,133,205,115)(33,107,206,94)(34,135,207,117)(35,109,208,96)(36,137,209,119)(37,111,210,98)(38,139,197,121)(39,99,198,86)(40,127,199,123)(41,101,200,88)(42,129,201,125)(85,171,112,219)(87,173,100,221)(89,175,102,223)(91,177,104,211)(93,179,106,213)(95,181,108,215)(97,169,110,217)(114,178,132,212)(116,180,134,214)(118,182,136,216)(120,170,138,218)(122,172,140,220)(124,174,128,222)(126,176,130,224), (1,216,143,35)(2,217,144,36)(3,218,145,37)(4,219,146,38)(5,220,147,39)(6,221,148,40)(7,222,149,41)(8,223,150,42)(9,224,151,29)(10,211,152,30)(11,212,153,31)(12,213,154,32)(13,214,141,33)(14,215,142,34)(15,198,167,172)(16,199,168,173)(17,200,155,174)(18,201,156,175)(19,202,157,176)(20,203,158,177)(21,204,159,178)(22,205,160,179)(23,206,161,180)(24,207,162,181)(25,208,163,182)(26,209,164,169)(27,210,165,170)(28,197,166,171)(43,138,58,98)(44,139,59,85)(45,140,60,86)(46,127,61,87)(47,128,62,88)(48,129,63,89)(49,130,64,90)(50,131,65,91)(51,132,66,92)(52,133,67,93)(53,134,68,94)(54,135,69,95)(55,136,70,96)(56,137,57,97)(71,106,190,115)(72,107,191,116)(73,108,192,117)(74,109,193,118)(75,110,194,119)(76,111,195,120)(77,112,196,121)(78,99,183,122)(79,100,184,123)(80,101,185,124)(81,102,186,125)(82,103,187,126)(83,104,188,113)(84,105,189,114), (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), (1,41,163,200)(2,199,164,40)(3,39,165,198)(4,197,166,38)(5,37,167,210)(6,209,168,36)(7,35,155,208)(8,207,156,34)(9,33,157,206)(10,205,158,32)(11,31,159,204)(12,203,160,30)(13,29,161,202)(14,201,162,42)(15,170,147,218)(16,217,148,169)(17,182,149,216)(18,215,150,181)(19,180,151,214)(20,213,152,179)(21,178,153,212)(22,211,154,177)(23,176,141,224)(24,223,142,175)(25,174,143,222)(26,221,144,173)(27,172,145,220)(28,219,146,171)(43,122,195,140)(44,139,196,121)(45,120,183,138)(46,137,184,119)(47,118,185,136)(48,135,186,117)(49,116,187,134)(50,133,188,115)(51,114,189,132)(52,131,190,113)(53,126,191,130)(54,129,192,125)(55,124,193,128)(56,127,194,123)(57,87,75,100)(58,99,76,86)(59,85,77,112)(60,111,78,98)(61,97,79,110)(62,109,80,96)(63,95,81,108)(64,107,82,94)(65,93,83,106)(66,105,84,92)(67,91,71,104)(68,103,72,90)(69,89,73,102)(70,101,74,88)>;
G:=Group( (1,193,163,55)(2,57,164,75)(3,195,165,43)(4,59,166,77)(5,183,167,45)(6,61,168,79)(7,185,155,47)(8,63,156,81)(9,187,157,49)(10,65,158,83)(11,189,159,51)(12,67,160,71)(13,191,161,53)(14,69,162,73)(15,60,147,78)(16,184,148,46)(17,62,149,80)(18,186,150,48)(19,64,151,82)(20,188,152,50)(21,66,153,84)(22,190,154,52)(23,68,141,72)(24,192,142,54)(25,70,143,74)(26,194,144,56)(27,58,145,76)(28,196,146,44)(29,103,202,90)(30,131,203,113)(31,105,204,92)(32,133,205,115)(33,107,206,94)(34,135,207,117)(35,109,208,96)(36,137,209,119)(37,111,210,98)(38,139,197,121)(39,99,198,86)(40,127,199,123)(41,101,200,88)(42,129,201,125)(85,171,112,219)(87,173,100,221)(89,175,102,223)(91,177,104,211)(93,179,106,213)(95,181,108,215)(97,169,110,217)(114,178,132,212)(116,180,134,214)(118,182,136,216)(120,170,138,218)(122,172,140,220)(124,174,128,222)(126,176,130,224), (1,216,143,35)(2,217,144,36)(3,218,145,37)(4,219,146,38)(5,220,147,39)(6,221,148,40)(7,222,149,41)(8,223,150,42)(9,224,151,29)(10,211,152,30)(11,212,153,31)(12,213,154,32)(13,214,141,33)(14,215,142,34)(15,198,167,172)(16,199,168,173)(17,200,155,174)(18,201,156,175)(19,202,157,176)(20,203,158,177)(21,204,159,178)(22,205,160,179)(23,206,161,180)(24,207,162,181)(25,208,163,182)(26,209,164,169)(27,210,165,170)(28,197,166,171)(43,138,58,98)(44,139,59,85)(45,140,60,86)(46,127,61,87)(47,128,62,88)(48,129,63,89)(49,130,64,90)(50,131,65,91)(51,132,66,92)(52,133,67,93)(53,134,68,94)(54,135,69,95)(55,136,70,96)(56,137,57,97)(71,106,190,115)(72,107,191,116)(73,108,192,117)(74,109,193,118)(75,110,194,119)(76,111,195,120)(77,112,196,121)(78,99,183,122)(79,100,184,123)(80,101,185,124)(81,102,186,125)(82,103,187,126)(83,104,188,113)(84,105,189,114), (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), (1,41,163,200)(2,199,164,40)(3,39,165,198)(4,197,166,38)(5,37,167,210)(6,209,168,36)(7,35,155,208)(8,207,156,34)(9,33,157,206)(10,205,158,32)(11,31,159,204)(12,203,160,30)(13,29,161,202)(14,201,162,42)(15,170,147,218)(16,217,148,169)(17,182,149,216)(18,215,150,181)(19,180,151,214)(20,213,152,179)(21,178,153,212)(22,211,154,177)(23,176,141,224)(24,223,142,175)(25,174,143,222)(26,221,144,173)(27,172,145,220)(28,219,146,171)(43,122,195,140)(44,139,196,121)(45,120,183,138)(46,137,184,119)(47,118,185,136)(48,135,186,117)(49,116,187,134)(50,133,188,115)(51,114,189,132)(52,131,190,113)(53,126,191,130)(54,129,192,125)(55,124,193,128)(56,127,194,123)(57,87,75,100)(58,99,76,86)(59,85,77,112)(60,111,78,98)(61,97,79,110)(62,109,80,96)(63,95,81,108)(64,107,82,94)(65,93,83,106)(66,105,84,92)(67,91,71,104)(68,103,72,90)(69,89,73,102)(70,101,74,88) );
G=PermutationGroup([(1,193,163,55),(2,57,164,75),(3,195,165,43),(4,59,166,77),(5,183,167,45),(6,61,168,79),(7,185,155,47),(8,63,156,81),(9,187,157,49),(10,65,158,83),(11,189,159,51),(12,67,160,71),(13,191,161,53),(14,69,162,73),(15,60,147,78),(16,184,148,46),(17,62,149,80),(18,186,150,48),(19,64,151,82),(20,188,152,50),(21,66,153,84),(22,190,154,52),(23,68,141,72),(24,192,142,54),(25,70,143,74),(26,194,144,56),(27,58,145,76),(28,196,146,44),(29,103,202,90),(30,131,203,113),(31,105,204,92),(32,133,205,115),(33,107,206,94),(34,135,207,117),(35,109,208,96),(36,137,209,119),(37,111,210,98),(38,139,197,121),(39,99,198,86),(40,127,199,123),(41,101,200,88),(42,129,201,125),(85,171,112,219),(87,173,100,221),(89,175,102,223),(91,177,104,211),(93,179,106,213),(95,181,108,215),(97,169,110,217),(114,178,132,212),(116,180,134,214),(118,182,136,216),(120,170,138,218),(122,172,140,220),(124,174,128,222),(126,176,130,224)], [(1,216,143,35),(2,217,144,36),(3,218,145,37),(4,219,146,38),(5,220,147,39),(6,221,148,40),(7,222,149,41),(8,223,150,42),(9,224,151,29),(10,211,152,30),(11,212,153,31),(12,213,154,32),(13,214,141,33),(14,215,142,34),(15,198,167,172),(16,199,168,173),(17,200,155,174),(18,201,156,175),(19,202,157,176),(20,203,158,177),(21,204,159,178),(22,205,160,179),(23,206,161,180),(24,207,162,181),(25,208,163,182),(26,209,164,169),(27,210,165,170),(28,197,166,171),(43,138,58,98),(44,139,59,85),(45,140,60,86),(46,127,61,87),(47,128,62,88),(48,129,63,89),(49,130,64,90),(50,131,65,91),(51,132,66,92),(52,133,67,93),(53,134,68,94),(54,135,69,95),(55,136,70,96),(56,137,57,97),(71,106,190,115),(72,107,191,116),(73,108,192,117),(74,109,193,118),(75,110,194,119),(76,111,195,120),(77,112,196,121),(78,99,183,122),(79,100,184,123),(80,101,185,124),(81,102,186,125),(82,103,187,126),(83,104,188,113),(84,105,189,114)], [(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)], [(1,41,163,200),(2,199,164,40),(3,39,165,198),(4,197,166,38),(5,37,167,210),(6,209,168,36),(7,35,155,208),(8,207,156,34),(9,33,157,206),(10,205,158,32),(11,31,159,204),(12,203,160,30),(13,29,161,202),(14,201,162,42),(15,170,147,218),(16,217,148,169),(17,182,149,216),(18,215,150,181),(19,180,151,214),(20,213,152,179),(21,178,153,212),(22,211,154,177),(23,176,141,224),(24,223,142,175),(25,174,143,222),(26,221,144,173),(27,172,145,220),(28,219,146,171),(43,122,195,140),(44,139,196,121),(45,120,183,138),(46,137,184,119),(47,118,185,136),(48,135,186,117),(49,116,187,134),(50,133,188,115),(51,114,189,132),(52,131,190,113),(53,126,191,130),(54,129,192,125),(55,124,193,128),(56,127,194,123),(57,87,75,100),(58,99,76,86),(59,85,77,112),(60,111,78,98),(61,97,79,110),(62,109,80,96),(63,95,81,108),(64,107,82,94),(65,93,83,106),(66,105,84,92),(67,91,71,104),(68,103,72,90),(69,89,73,102),(70,101,74,88)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 23 | 20 | 5 | 7 |
| 0 | 0 | 9 | 6 | 0 | 22 |
| 0 | 0 | 15 | 15 | 26 | 9 |
| 0 | 0 | 0 | 10 | 23 | 3 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 13 | 5 | 0 | 0 |
| 0 | 0 | 24 | 16 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 5 |
| 0 | 0 | 0 | 0 | 16 | 21 |
| 18 | 18 | 0 | 0 | 0 | 0 |
| 3 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 25 | 19 | 1 |
| 0 | 0 | 4 | 11 | 19 | 9 |
| 0 | 0 | 0 | 0 | 0 | 4 |
| 0 | 0 | 0 | 0 | 7 | 22 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 24 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 26 | 3 | 0 | 0 |
| 0 | 0 | 7 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 25 | 26 |
| 0 | 0 | 0 | 0 | 5 | 4 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,0,12,0,0,0,0,0,0,23,9,15,0,0,0,20,6,15,10,0,0,5,0,26,23,0,0,7,22,9,3],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,13,24,0,0,0,0,5,16,0,0,0,0,0,0,8,16,0,0,0,0,5,21],[18,3,0,0,0,0,18,11,0,0,0,0,0,0,25,4,0,0,0,0,25,11,0,0,0,0,19,19,0,7,0,0,1,9,4,22],[17,24,0,0,0,0,0,12,0,0,0,0,0,0,26,7,0,0,0,0,3,3,0,0,0,0,0,0,25,5,0,0,0,0,26,4] >;
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | ··· | 4F | 4G | 4H | 4I | ··· | 4M | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 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 | D7 | C4○D4 | D14 | D14 | D14 | D14 | D14 | C4○D28 | 2+ (1+4) | D4⋊6D14 | D4⋊8D14 |
| kernel | C42.116D14 | C42⋊D7 | C4×D28 | D14.D4 | D14⋊D4 | C4.Dic14 | C28⋊1D4 | C23.23D14 | C28⋊7D4 | C28⋊2D4 | C28⋊D4 | D4×C28 | C4×D4 | C28 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C4 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 3 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 2 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{116}D_{14} % in TeX
G:=Group("C4^2.116D14"); // GroupNames label
G:=SmallGroup(448,1015);
// by ID
G=gap.SmallGroup(448,1015);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,219,675,192,18822]);
// 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,d*b*d^-1=a^2*b^-1,d*c*d^-1=a^2*c^-1>;
// generators/relations
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