metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.228D14, (C4×D7)⋊10D4, (C4×D4)⋊10D7, C28⋊Q8⋊47C2, (D4×C28)⋊12C2, (C4×D28)⋊26C2, C28⋊1(C4○D4), C4⋊2(C4○D28), D14.1(C2×D4), C4.220(D4×D7), (D7×C42)⋊4C2, C4⋊D28⋊43C2, C28⋊D4⋊32C2, C28⋊2D4⋊45C2, C4⋊C4.282D14, C28.379(C2×D4), Dic7.3(C2×D4), D14⋊D4⋊48C2, Dic7⋊1(C4○D4), (C2×D4).212D14, (C2×C14).92C24, C14.48(C22×D4), (C2×C28).492C23, (C4×C28).151C22, C22⋊C4.109D14, (C22×C4).207D14, C23.93(C22×D7), D14⋊C4.122C22, Dic7.D4⋊50C2, (D4×C14).255C22, (C2×D28).259C22, C4⋊Dic7.363C22, C7⋊2(C22.26C24), (C22×D7).30C23, C22.117(C23×D7), Dic7⋊C4.110C22, (C22×C28).106C22, (C22×C14).162C23, (C2×Dic7).203C23, (C4×Dic7).251C22, C23.D7.105C22, (C2×Dic14).238C22, C2.20(C2×D4×D7), (C4×C7⋊D4)⋊4C2, (C2×C4○D28)⋊6C2, C2.21(D7×C4○D4), C2.44(C2×C4○D28), C14.40(C2×C4○D4), (C2×C4×D7).292C22, (C7×C4⋊C4).325C22, (C2×C4).578(C22×D7), (C2×C7⋊D4).112C22, (C7×C22⋊C4).121C22, SmallGroup(448,1001)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.228D14
G = < a,b,c,d | a4=b4=c14=1, d2=b2, ab=ba, cac-1=dad-1=a-1, bc=cb, bd=db, dcd-1=b2c-1 >
Subgroups: 1492 in 310 conjugacy classes, 109 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, C4○D4, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C42, C4×D4, C4×D4, C4⋊D4, C4.4D4, C4⋊1D4, C4⋊Q8, C2×C4○D4, Dic14, C4×D7, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C22×D7, C22×D7, C22×C14, C22.26C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×C4×D7, C2×D28, C2×D28, C4○D28, C2×C7⋊D4, C22×C28, D4×C14, D7×C42, C4×D28, D14⋊D4, Dic7.D4, C28⋊Q8, C4⋊D28, C4×C7⋊D4, C28⋊2D4, C28⋊D4, D4×C28, C2×C4○D28, C42.228D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C22×D4, C2×C4○D4, C22×D7, C22.26C24, C4○D28, D4×D7, C23×D7, C2×C4○D28, C2×D4×D7, D7×C4○D4, C42.228D14
►On 224 points
Generators in S224
(1 61 199 37)(2 38 200 62)(3 63 201 39)(4 40 202 64)(5 65 203 41)(6 42 204 66)(7 67 205 29)(8 30 206 68)(9 69 207 31)(10 32 208 70)(11 57 209 33)(12 34 210 58)(13 59 197 35)(14 36 198 60)(15 107 45 218)(16 219 46 108)(17 109 47 220)(18 221 48 110)(19 111 49 222)(20 223 50 112)(21 99 51 224)(22 211 52 100)(23 101 53 212)(24 213 54 102)(25 103 55 214)(26 215 56 104)(27 105 43 216)(28 217 44 106)(71 153 90 133)(72 134 91 154)(73 141 92 135)(74 136 93 142)(75 143 94 137)(76 138 95 144)(77 145 96 139)(78 140 97 146)(79 147 98 127)(80 128 85 148)(81 149 86 129)(82 130 87 150)(83 151 88 131)(84 132 89 152)(113 194 173 163)(114 164 174 195)(115 196 175 165)(116 166 176 183)(117 184 177 167)(118 168 178 185)(119 186 179 155)(120 156 180 187)(121 188 181 157)(122 158 182 189)(123 190 169 159)(124 160 170 191)(125 192 171 161)(126 162 172 193)
(1 180 148 105)(2 181 149 106)(3 182 150 107)(4 169 151 108)(5 170 152 109)(6 171 153 110)(7 172 154 111)(8 173 141 112)(9 174 142 99)(10 175 143 100)(11 176 144 101)(12 177 145 102)(13 178 146 103)(14 179 147 104)(15 39 158 87)(16 40 159 88)(17 41 160 89)(18 42 161 90)(19 29 162 91)(20 30 163 92)(21 31 164 93)(22 32 165 94)(23 33 166 95)(24 34 167 96)(25 35 168 97)(26 36 155 98)(27 37 156 85)(28 38 157 86)(43 61 187 80)(44 62 188 81)(45 63 189 82)(46 64 190 83)(47 65 191 84)(48 66 192 71)(49 67 193 72)(50 68 194 73)(51 69 195 74)(52 70 196 75)(53 57 183 76)(54 58 184 77)(55 59 185 78)(56 60 186 79)(113 135 223 206)(114 136 224 207)(115 137 211 208)(116 138 212 209)(117 139 213 210)(118 140 214 197)(119 127 215 198)(120 128 216 199)(121 129 217 200)(122 130 218 201)(123 131 219 202)(124 132 220 203)(125 133 221 204)(126 134 222 205)
(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 14 148 147)(2 146 149 13)(3 12 150 145)(4 144 151 11)(5 10 152 143)(6 142 153 9)(7 8 154 141)(15 24 158 167)(16 166 159 23)(17 22 160 165)(18 164 161 21)(19 20 162 163)(25 28 168 157)(26 156 155 27)(29 30 91 92)(31 42 93 90)(32 89 94 41)(33 40 95 88)(34 87 96 39)(35 38 97 86)(36 85 98 37)(43 56 187 186)(44 185 188 55)(45 54 189 184)(46 183 190 53)(47 52 191 196)(48 195 192 51)(49 50 193 194)(57 64 76 83)(58 82 77 63)(59 62 78 81)(60 80 79 61)(65 70 84 75)(66 74 71 69)(67 68 72 73)(99 110 174 171)(100 170 175 109)(101 108 176 169)(102 182 177 107)(103 106 178 181)(104 180 179 105)(111 112 172 173)(113 222 223 126)(114 125 224 221)(115 220 211 124)(116 123 212 219)(117 218 213 122)(118 121 214 217)(119 216 215 120)(127 199 198 128)(129 197 200 140)(130 139 201 210)(131 209 202 138)(132 137 203 208)(133 207 204 136)(134 135 205 206)
G:=sub<Sym(224)| (1,61,199,37)(2,38,200,62)(3,63,201,39)(4,40,202,64)(5,65,203,41)(6,42,204,66)(7,67,205,29)(8,30,206,68)(9,69,207,31)(10,32,208,70)(11,57,209,33)(12,34,210,58)(13,59,197,35)(14,36,198,60)(15,107,45,218)(16,219,46,108)(17,109,47,220)(18,221,48,110)(19,111,49,222)(20,223,50,112)(21,99,51,224)(22,211,52,100)(23,101,53,212)(24,213,54,102)(25,103,55,214)(26,215,56,104)(27,105,43,216)(28,217,44,106)(71,153,90,133)(72,134,91,154)(73,141,92,135)(74,136,93,142)(75,143,94,137)(76,138,95,144)(77,145,96,139)(78,140,97,146)(79,147,98,127)(80,128,85,148)(81,149,86,129)(82,130,87,150)(83,151,88,131)(84,132,89,152)(113,194,173,163)(114,164,174,195)(115,196,175,165)(116,166,176,183)(117,184,177,167)(118,168,178,185)(119,186,179,155)(120,156,180,187)(121,188,181,157)(122,158,182,189)(123,190,169,159)(124,160,170,191)(125,192,171,161)(126,162,172,193), (1,180,148,105)(2,181,149,106)(3,182,150,107)(4,169,151,108)(5,170,152,109)(6,171,153,110)(7,172,154,111)(8,173,141,112)(9,174,142,99)(10,175,143,100)(11,176,144,101)(12,177,145,102)(13,178,146,103)(14,179,147,104)(15,39,158,87)(16,40,159,88)(17,41,160,89)(18,42,161,90)(19,29,162,91)(20,30,163,92)(21,31,164,93)(22,32,165,94)(23,33,166,95)(24,34,167,96)(25,35,168,97)(26,36,155,98)(27,37,156,85)(28,38,157,86)(43,61,187,80)(44,62,188,81)(45,63,189,82)(46,64,190,83)(47,65,191,84)(48,66,192,71)(49,67,193,72)(50,68,194,73)(51,69,195,74)(52,70,196,75)(53,57,183,76)(54,58,184,77)(55,59,185,78)(56,60,186,79)(113,135,223,206)(114,136,224,207)(115,137,211,208)(116,138,212,209)(117,139,213,210)(118,140,214,197)(119,127,215,198)(120,128,216,199)(121,129,217,200)(122,130,218,201)(123,131,219,202)(124,132,220,203)(125,133,221,204)(126,134,222,205), (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), (1,14,148,147)(2,146,149,13)(3,12,150,145)(4,144,151,11)(5,10,152,143)(6,142,153,9)(7,8,154,141)(15,24,158,167)(16,166,159,23)(17,22,160,165)(18,164,161,21)(19,20,162,163)(25,28,168,157)(26,156,155,27)(29,30,91,92)(31,42,93,90)(32,89,94,41)(33,40,95,88)(34,87,96,39)(35,38,97,86)(36,85,98,37)(43,56,187,186)(44,185,188,55)(45,54,189,184)(46,183,190,53)(47,52,191,196)(48,195,192,51)(49,50,193,194)(57,64,76,83)(58,82,77,63)(59,62,78,81)(60,80,79,61)(65,70,84,75)(66,74,71,69)(67,68,72,73)(99,110,174,171)(100,170,175,109)(101,108,176,169)(102,182,177,107)(103,106,178,181)(104,180,179,105)(111,112,172,173)(113,222,223,126)(114,125,224,221)(115,220,211,124)(116,123,212,219)(117,218,213,122)(118,121,214,217)(119,216,215,120)(127,199,198,128)(129,197,200,140)(130,139,201,210)(131,209,202,138)(132,137,203,208)(133,207,204,136)(134,135,205,206)>;
G:=Group( (1,61,199,37)(2,38,200,62)(3,63,201,39)(4,40,202,64)(5,65,203,41)(6,42,204,66)(7,67,205,29)(8,30,206,68)(9,69,207,31)(10,32,208,70)(11,57,209,33)(12,34,210,58)(13,59,197,35)(14,36,198,60)(15,107,45,218)(16,219,46,108)(17,109,47,220)(18,221,48,110)(19,111,49,222)(20,223,50,112)(21,99,51,224)(22,211,52,100)(23,101,53,212)(24,213,54,102)(25,103,55,214)(26,215,56,104)(27,105,43,216)(28,217,44,106)(71,153,90,133)(72,134,91,154)(73,141,92,135)(74,136,93,142)(75,143,94,137)(76,138,95,144)(77,145,96,139)(78,140,97,146)(79,147,98,127)(80,128,85,148)(81,149,86,129)(82,130,87,150)(83,151,88,131)(84,132,89,152)(113,194,173,163)(114,164,174,195)(115,196,175,165)(116,166,176,183)(117,184,177,167)(118,168,178,185)(119,186,179,155)(120,156,180,187)(121,188,181,157)(122,158,182,189)(123,190,169,159)(124,160,170,191)(125,192,171,161)(126,162,172,193), (1,180,148,105)(2,181,149,106)(3,182,150,107)(4,169,151,108)(5,170,152,109)(6,171,153,110)(7,172,154,111)(8,173,141,112)(9,174,142,99)(10,175,143,100)(11,176,144,101)(12,177,145,102)(13,178,146,103)(14,179,147,104)(15,39,158,87)(16,40,159,88)(17,41,160,89)(18,42,161,90)(19,29,162,91)(20,30,163,92)(21,31,164,93)(22,32,165,94)(23,33,166,95)(24,34,167,96)(25,35,168,97)(26,36,155,98)(27,37,156,85)(28,38,157,86)(43,61,187,80)(44,62,188,81)(45,63,189,82)(46,64,190,83)(47,65,191,84)(48,66,192,71)(49,67,193,72)(50,68,194,73)(51,69,195,74)(52,70,196,75)(53,57,183,76)(54,58,184,77)(55,59,185,78)(56,60,186,79)(113,135,223,206)(114,136,224,207)(115,137,211,208)(116,138,212,209)(117,139,213,210)(118,140,214,197)(119,127,215,198)(120,128,216,199)(121,129,217,200)(122,130,218,201)(123,131,219,202)(124,132,220,203)(125,133,221,204)(126,134,222,205), (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), (1,14,148,147)(2,146,149,13)(3,12,150,145)(4,144,151,11)(5,10,152,143)(6,142,153,9)(7,8,154,141)(15,24,158,167)(16,166,159,23)(17,22,160,165)(18,164,161,21)(19,20,162,163)(25,28,168,157)(26,156,155,27)(29,30,91,92)(31,42,93,90)(32,89,94,41)(33,40,95,88)(34,87,96,39)(35,38,97,86)(36,85,98,37)(43,56,187,186)(44,185,188,55)(45,54,189,184)(46,183,190,53)(47,52,191,196)(48,195,192,51)(49,50,193,194)(57,64,76,83)(58,82,77,63)(59,62,78,81)(60,80,79,61)(65,70,84,75)(66,74,71,69)(67,68,72,73)(99,110,174,171)(100,170,175,109)(101,108,176,169)(102,182,177,107)(103,106,178,181)(104,180,179,105)(111,112,172,173)(113,222,223,126)(114,125,224,221)(115,220,211,124)(116,123,212,219)(117,218,213,122)(118,121,214,217)(119,216,215,120)(127,199,198,128)(129,197,200,140)(130,139,201,210)(131,209,202,138)(132,137,203,208)(133,207,204,136)(134,135,205,206) );
G=PermutationGroup([[(1,61,199,37),(2,38,200,62),(3,63,201,39),(4,40,202,64),(5,65,203,41),(6,42,204,66),(7,67,205,29),(8,30,206,68),(9,69,207,31),(10,32,208,70),(11,57,209,33),(12,34,210,58),(13,59,197,35),(14,36,198,60),(15,107,45,218),(16,219,46,108),(17,109,47,220),(18,221,48,110),(19,111,49,222),(20,223,50,112),(21,99,51,224),(22,211,52,100),(23,101,53,212),(24,213,54,102),(25,103,55,214),(26,215,56,104),(27,105,43,216),(28,217,44,106),(71,153,90,133),(72,134,91,154),(73,141,92,135),(74,136,93,142),(75,143,94,137),(76,138,95,144),(77,145,96,139),(78,140,97,146),(79,147,98,127),(80,128,85,148),(81,149,86,129),(82,130,87,150),(83,151,88,131),(84,132,89,152),(113,194,173,163),(114,164,174,195),(115,196,175,165),(116,166,176,183),(117,184,177,167),(118,168,178,185),(119,186,179,155),(120,156,180,187),(121,188,181,157),(122,158,182,189),(123,190,169,159),(124,160,170,191),(125,192,171,161),(126,162,172,193)], [(1,180,148,105),(2,181,149,106),(3,182,150,107),(4,169,151,108),(5,170,152,109),(6,171,153,110),(7,172,154,111),(8,173,141,112),(9,174,142,99),(10,175,143,100),(11,176,144,101),(12,177,145,102),(13,178,146,103),(14,179,147,104),(15,39,158,87),(16,40,159,88),(17,41,160,89),(18,42,161,90),(19,29,162,91),(20,30,163,92),(21,31,164,93),(22,32,165,94),(23,33,166,95),(24,34,167,96),(25,35,168,97),(26,36,155,98),(27,37,156,85),(28,38,157,86),(43,61,187,80),(44,62,188,81),(45,63,189,82),(46,64,190,83),(47,65,191,84),(48,66,192,71),(49,67,193,72),(50,68,194,73),(51,69,195,74),(52,70,196,75),(53,57,183,76),(54,58,184,77),(55,59,185,78),(56,60,186,79),(113,135,223,206),(114,136,224,207),(115,137,211,208),(116,138,212,209),(117,139,213,210),(118,140,214,197),(119,127,215,198),(120,128,216,199),(121,129,217,200),(122,130,218,201),(123,131,219,202),(124,132,220,203),(125,133,221,204),(126,134,222,205)], [(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)], [(1,14,148,147),(2,146,149,13),(3,12,150,145),(4,144,151,11),(5,10,152,143),(6,142,153,9),(7,8,154,141),(15,24,158,167),(16,166,159,23),(17,22,160,165),(18,164,161,21),(19,20,162,163),(25,28,168,157),(26,156,155,27),(29,30,91,92),(31,42,93,90),(32,89,94,41),(33,40,95,88),(34,87,96,39),(35,38,97,86),(36,85,98,37),(43,56,187,186),(44,185,188,55),(45,54,189,184),(46,183,190,53),(47,52,191,196),(48,195,192,51),(49,50,193,194),(57,64,76,83),(58,82,77,63),(59,62,78,81),(60,80,79,61),(65,70,84,75),(66,74,71,69),(67,68,72,73),(99,110,174,171),(100,170,175,109),(101,108,176,169),(102,182,177,107),(103,106,178,181),(104,180,179,105),(111,112,172,173),(113,222,223,126),(114,125,224,221),(115,220,211,124),(116,123,212,219),(117,218,213,122),(118,121,214,217),(119,216,215,120),(127,199,198,128),(129,197,200,140),(130,139,201,210),(131,209,202,138),(132,137,203,208),(133,207,204,136),(134,135,205,206)]])
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | ··· | 4P | 4Q | 4R | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 28 | 28 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 14 | ··· | 14 | 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 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | D14 | D14 | C4○D28 | D4×D7 | D7×C4○D4 |
| kernel | C42.228D14 | D7×C42 | C4×D28 | D14⋊D4 | Dic7.D4 | C28⋊Q8 | C4⋊D28 | C4×C7⋊D4 | C28⋊2D4 | C28⋊D4 | D4×C28 | C2×C4○D28 | C4×D7 | C4×D4 | Dic7 | C28 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C4 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 4 | 3 | 4 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 6 | 6 |
Matrix representation of C42.228D14 ►in GL4(𝔽29) generated by
| 28 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 17 | 0 |
| 0 | 0 | 17 | 12 |
| 17 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 |
| 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 17 |
| 22 | 7 | 0 | 0 |
| 22 | 3 | 0 | 0 |
| 0 | 0 | 1 | 27 |
| 0 | 0 | 0 | 28 |
| 7 | 22 | 0 | 0 |
| 3 | 22 | 0 | 0 |
| 0 | 0 | 28 | 2 |
| 0 | 0 | 28 | 1 |
G:=sub<GL(4,GF(29))| [28,0,0,0,0,28,0,0,0,0,17,17,0,0,0,12],[17,0,0,0,0,17,0,0,0,0,17,0,0,0,0,17],[22,22,0,0,7,3,0,0,0,0,1,0,0,0,27,28],[7,3,0,0,22,22,0,0,0,0,28,28,0,0,2,1] >;
C42.228D14 in GAP, Magma, Sage, TeX
C_4^2._{228}D_{14} % in TeX
G:=Group("C4^2.228D14"); // GroupNames label
G:=SmallGroup(448,1001);
// by ID
G=gap.SmallGroup(448,1001);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,100,675,570,18822]);
// 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^-1,b*c=c*b,b*d=d*b,d*c*d^-1=b^2*c^-1>;
// generators/relations