metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.232D14, (C4×D7)⋊6Q8, C28⋊Q8⋊48C2, (C4×Q8)⋊11D7, C4.59(Q8×D7), (Q8×C28)⋊13C2, D14.1(C2×Q8), C4⋊C4.297D14, C28.117(C2×Q8), Dic7.2(C2×Q8), (D7×C42).6C2, (C4×Dic14)⋊39C2, C4.47(C4○D28), Dic7.Q8⋊46C2, (C2×Q8).177D14, D14⋊Q8.5C2, C42⋊D7.4C2, Dic7⋊Q8⋊33C2, C28.117(C4○D4), C14.30(C22×Q8), (C4×C28).174C22, (C2×C28).499C23, (C2×C14).122C24, D14⋊3Q8.14C2, D14⋊2Q8.14C2, Dic7.4(C4○D4), D14⋊C4.102C22, C4⋊Dic7.307C22, (Q8×C14).222C22, C22.143(C23×D7), Dic7⋊C4.155C22, C7⋊3(C23.37C23), (C4×Dic7).253C22, (C2×Dic7).216C23, (C22×D7).179C23, (C2×Dic14).291C22, C2.13(C2×Q8×D7), C2.30(D7×C4○D4), C2.61(C2×C4○D28), C14.54(C2×C4○D4), (C2×C4×D7).295C22, (C7×C4⋊C4).350C22, (C2×C4).584(C22×D7), SmallGroup(448,1031)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.232D14
G = < a,b,c,d | a4=b4=1, c14=a2, d2=a2b2, ab=ba, cac-1=dad-1=a-1, bc=cb, bd=db, dcd-1=b2c13 >
Subgroups: 868 in 222 conjugacy classes, 109 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, Q8, C23, D7, C14, C42, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×Q8, C2×Q8, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C42, C42⋊C2, C4×Q8, C4×Q8, C22⋊Q8, C42.C2, C4⋊Q8, Dic14, C4×D7, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C23.37C23, C4×Dic7, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C4×C28, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C2×C4×D7, Q8×C14, C4×Dic14, C4×Dic14, D7×C42, C42⋊D7, C28⋊Q8, Dic7.Q8, D14⋊Q8, D14⋊2Q8, Dic7⋊Q8, D14⋊3Q8, Q8×C28, C42.232D14
Quotients: C1, C2, C22, Q8, C23, D7, C2×Q8, C4○D4, C24, D14, C22×Q8, C2×C4○D4, C22×D7, C23.37C23, C4○D28, Q8×D7, C23×D7, C2×C4○D28, C2×Q8×D7, D7×C4○D4, C42.232D14
►On 224 points
Generators in S224
(1 154 15 168)(2 141 16 155)(3 156 17 142)(4 143 18 157)(5 158 19 144)(6 145 20 159)(7 160 21 146)(8 147 22 161)(9 162 23 148)(10 149 24 163)(11 164 25 150)(12 151 26 165)(13 166 27 152)(14 153 28 167)(29 196 43 182)(30 183 44 169)(31 170 45 184)(32 185 46 171)(33 172 47 186)(34 187 48 173)(35 174 49 188)(36 189 50 175)(37 176 51 190)(38 191 52 177)(39 178 53 192)(40 193 54 179)(41 180 55 194)(42 195 56 181)(57 100 71 86)(58 87 72 101)(59 102 73 88)(60 89 74 103)(61 104 75 90)(62 91 76 105)(63 106 77 92)(64 93 78 107)(65 108 79 94)(66 95 80 109)(67 110 81 96)(68 97 82 111)(69 112 83 98)(70 99 84 85)(113 202 127 216)(114 217 128 203)(115 204 129 218)(116 219 130 205)(117 206 131 220)(118 221 132 207)(119 208 133 222)(120 223 134 209)(121 210 135 224)(122 197 136 211)(123 212 137 198)(124 199 138 213)(125 214 139 200)(126 201 140 215)
(1 181 123 91)(2 182 124 92)(3 183 125 93)(4 184 126 94)(5 185 127 95)(6 186 128 96)(7 187 129 97)(8 188 130 98)(9 189 131 99)(10 190 132 100)(11 191 133 101)(12 192 134 102)(13 193 135 103)(14 194 136 104)(15 195 137 105)(16 196 138 106)(17 169 139 107)(18 170 140 108)(19 171 113 109)(20 172 114 110)(21 173 115 111)(22 174 116 112)(23 175 117 85)(24 176 118 86)(25 177 119 87)(26 178 120 88)(27 179 121 89)(28 180 122 90)(29 199 63 141)(30 200 64 142)(31 201 65 143)(32 202 66 144)(33 203 67 145)(34 204 68 146)(35 205 69 147)(36 206 70 148)(37 207 71 149)(38 208 72 150)(39 209 73 151)(40 210 74 152)(41 211 75 153)(42 212 76 154)(43 213 77 155)(44 214 78 156)(45 215 79 157)(46 216 80 158)(47 217 81 159)(48 218 82 160)(49 219 83 161)(50 220 84 162)(51 221 57 163)(52 222 58 164)(53 223 59 165)(54 224 60 166)(55 197 61 167)(56 198 62 168)
(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 14 137 122)(2 121 138 13)(3 12 139 120)(4 119 140 11)(5 10 113 118)(6 117 114 9)(7 8 115 116)(15 28 123 136)(16 135 124 27)(17 26 125 134)(18 133 126 25)(19 24 127 132)(20 131 128 23)(21 22 129 130)(29 60 77 40)(30 39 78 59)(31 58 79 38)(32 37 80 57)(33 84 81 36)(34 35 82 83)(41 76 61 56)(42 55 62 75)(43 74 63 54)(44 53 64 73)(45 72 65 52)(46 51 66 71)(47 70 67 50)(48 49 68 69)(85 110 189 186)(86 185 190 109)(87 108 191 184)(88 183 192 107)(89 106 193 182)(90 181 194 105)(91 104 195 180)(92 179 196 103)(93 102 169 178)(94 177 170 101)(95 100 171 176)(96 175 172 99)(97 98 173 174)(111 112 187 188)(141 224 213 152)(142 151 214 223)(143 222 215 150)(144 149 216 221)(145 220 217 148)(146 147 218 219)(153 212 197 168)(154 167 198 211)(155 210 199 166)(156 165 200 209)(157 208 201 164)(158 163 202 207)(159 206 203 162)(160 161 204 205)
G:=sub<Sym(224)| (1,154,15,168)(2,141,16,155)(3,156,17,142)(4,143,18,157)(5,158,19,144)(6,145,20,159)(7,160,21,146)(8,147,22,161)(9,162,23,148)(10,149,24,163)(11,164,25,150)(12,151,26,165)(13,166,27,152)(14,153,28,167)(29,196,43,182)(30,183,44,169)(31,170,45,184)(32,185,46,171)(33,172,47,186)(34,187,48,173)(35,174,49,188)(36,189,50,175)(37,176,51,190)(38,191,52,177)(39,178,53,192)(40,193,54,179)(41,180,55,194)(42,195,56,181)(57,100,71,86)(58,87,72,101)(59,102,73,88)(60,89,74,103)(61,104,75,90)(62,91,76,105)(63,106,77,92)(64,93,78,107)(65,108,79,94)(66,95,80,109)(67,110,81,96)(68,97,82,111)(69,112,83,98)(70,99,84,85)(113,202,127,216)(114,217,128,203)(115,204,129,218)(116,219,130,205)(117,206,131,220)(118,221,132,207)(119,208,133,222)(120,223,134,209)(121,210,135,224)(122,197,136,211)(123,212,137,198)(124,199,138,213)(125,214,139,200)(126,201,140,215), (1,181,123,91)(2,182,124,92)(3,183,125,93)(4,184,126,94)(5,185,127,95)(6,186,128,96)(7,187,129,97)(8,188,130,98)(9,189,131,99)(10,190,132,100)(11,191,133,101)(12,192,134,102)(13,193,135,103)(14,194,136,104)(15,195,137,105)(16,196,138,106)(17,169,139,107)(18,170,140,108)(19,171,113,109)(20,172,114,110)(21,173,115,111)(22,174,116,112)(23,175,117,85)(24,176,118,86)(25,177,119,87)(26,178,120,88)(27,179,121,89)(28,180,122,90)(29,199,63,141)(30,200,64,142)(31,201,65,143)(32,202,66,144)(33,203,67,145)(34,204,68,146)(35,205,69,147)(36,206,70,148)(37,207,71,149)(38,208,72,150)(39,209,73,151)(40,210,74,152)(41,211,75,153)(42,212,76,154)(43,213,77,155)(44,214,78,156)(45,215,79,157)(46,216,80,158)(47,217,81,159)(48,218,82,160)(49,219,83,161)(50,220,84,162)(51,221,57,163)(52,222,58,164)(53,223,59,165)(54,224,60,166)(55,197,61,167)(56,198,62,168), (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), (1,14,137,122)(2,121,138,13)(3,12,139,120)(4,119,140,11)(5,10,113,118)(6,117,114,9)(7,8,115,116)(15,28,123,136)(16,135,124,27)(17,26,125,134)(18,133,126,25)(19,24,127,132)(20,131,128,23)(21,22,129,130)(29,60,77,40)(30,39,78,59)(31,58,79,38)(32,37,80,57)(33,84,81,36)(34,35,82,83)(41,76,61,56)(42,55,62,75)(43,74,63,54)(44,53,64,73)(45,72,65,52)(46,51,66,71)(47,70,67,50)(48,49,68,69)(85,110,189,186)(86,185,190,109)(87,108,191,184)(88,183,192,107)(89,106,193,182)(90,181,194,105)(91,104,195,180)(92,179,196,103)(93,102,169,178)(94,177,170,101)(95,100,171,176)(96,175,172,99)(97,98,173,174)(111,112,187,188)(141,224,213,152)(142,151,214,223)(143,222,215,150)(144,149,216,221)(145,220,217,148)(146,147,218,219)(153,212,197,168)(154,167,198,211)(155,210,199,166)(156,165,200,209)(157,208,201,164)(158,163,202,207)(159,206,203,162)(160,161,204,205)>;
G:=Group( (1,154,15,168)(2,141,16,155)(3,156,17,142)(4,143,18,157)(5,158,19,144)(6,145,20,159)(7,160,21,146)(8,147,22,161)(9,162,23,148)(10,149,24,163)(11,164,25,150)(12,151,26,165)(13,166,27,152)(14,153,28,167)(29,196,43,182)(30,183,44,169)(31,170,45,184)(32,185,46,171)(33,172,47,186)(34,187,48,173)(35,174,49,188)(36,189,50,175)(37,176,51,190)(38,191,52,177)(39,178,53,192)(40,193,54,179)(41,180,55,194)(42,195,56,181)(57,100,71,86)(58,87,72,101)(59,102,73,88)(60,89,74,103)(61,104,75,90)(62,91,76,105)(63,106,77,92)(64,93,78,107)(65,108,79,94)(66,95,80,109)(67,110,81,96)(68,97,82,111)(69,112,83,98)(70,99,84,85)(113,202,127,216)(114,217,128,203)(115,204,129,218)(116,219,130,205)(117,206,131,220)(118,221,132,207)(119,208,133,222)(120,223,134,209)(121,210,135,224)(122,197,136,211)(123,212,137,198)(124,199,138,213)(125,214,139,200)(126,201,140,215), (1,181,123,91)(2,182,124,92)(3,183,125,93)(4,184,126,94)(5,185,127,95)(6,186,128,96)(7,187,129,97)(8,188,130,98)(9,189,131,99)(10,190,132,100)(11,191,133,101)(12,192,134,102)(13,193,135,103)(14,194,136,104)(15,195,137,105)(16,196,138,106)(17,169,139,107)(18,170,140,108)(19,171,113,109)(20,172,114,110)(21,173,115,111)(22,174,116,112)(23,175,117,85)(24,176,118,86)(25,177,119,87)(26,178,120,88)(27,179,121,89)(28,180,122,90)(29,199,63,141)(30,200,64,142)(31,201,65,143)(32,202,66,144)(33,203,67,145)(34,204,68,146)(35,205,69,147)(36,206,70,148)(37,207,71,149)(38,208,72,150)(39,209,73,151)(40,210,74,152)(41,211,75,153)(42,212,76,154)(43,213,77,155)(44,214,78,156)(45,215,79,157)(46,216,80,158)(47,217,81,159)(48,218,82,160)(49,219,83,161)(50,220,84,162)(51,221,57,163)(52,222,58,164)(53,223,59,165)(54,224,60,166)(55,197,61,167)(56,198,62,168), (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), (1,14,137,122)(2,121,138,13)(3,12,139,120)(4,119,140,11)(5,10,113,118)(6,117,114,9)(7,8,115,116)(15,28,123,136)(16,135,124,27)(17,26,125,134)(18,133,126,25)(19,24,127,132)(20,131,128,23)(21,22,129,130)(29,60,77,40)(30,39,78,59)(31,58,79,38)(32,37,80,57)(33,84,81,36)(34,35,82,83)(41,76,61,56)(42,55,62,75)(43,74,63,54)(44,53,64,73)(45,72,65,52)(46,51,66,71)(47,70,67,50)(48,49,68,69)(85,110,189,186)(86,185,190,109)(87,108,191,184)(88,183,192,107)(89,106,193,182)(90,181,194,105)(91,104,195,180)(92,179,196,103)(93,102,169,178)(94,177,170,101)(95,100,171,176)(96,175,172,99)(97,98,173,174)(111,112,187,188)(141,224,213,152)(142,151,214,223)(143,222,215,150)(144,149,216,221)(145,220,217,148)(146,147,218,219)(153,212,197,168)(154,167,198,211)(155,210,199,166)(156,165,200,209)(157,208,201,164)(158,163,202,207)(159,206,203,162)(160,161,204,205) );
G=PermutationGroup([[(1,154,15,168),(2,141,16,155),(3,156,17,142),(4,143,18,157),(5,158,19,144),(6,145,20,159),(7,160,21,146),(8,147,22,161),(9,162,23,148),(10,149,24,163),(11,164,25,150),(12,151,26,165),(13,166,27,152),(14,153,28,167),(29,196,43,182),(30,183,44,169),(31,170,45,184),(32,185,46,171),(33,172,47,186),(34,187,48,173),(35,174,49,188),(36,189,50,175),(37,176,51,190),(38,191,52,177),(39,178,53,192),(40,193,54,179),(41,180,55,194),(42,195,56,181),(57,100,71,86),(58,87,72,101),(59,102,73,88),(60,89,74,103),(61,104,75,90),(62,91,76,105),(63,106,77,92),(64,93,78,107),(65,108,79,94),(66,95,80,109),(67,110,81,96),(68,97,82,111),(69,112,83,98),(70,99,84,85),(113,202,127,216),(114,217,128,203),(115,204,129,218),(116,219,130,205),(117,206,131,220),(118,221,132,207),(119,208,133,222),(120,223,134,209),(121,210,135,224),(122,197,136,211),(123,212,137,198),(124,199,138,213),(125,214,139,200),(126,201,140,215)], [(1,181,123,91),(2,182,124,92),(3,183,125,93),(4,184,126,94),(5,185,127,95),(6,186,128,96),(7,187,129,97),(8,188,130,98),(9,189,131,99),(10,190,132,100),(11,191,133,101),(12,192,134,102),(13,193,135,103),(14,194,136,104),(15,195,137,105),(16,196,138,106),(17,169,139,107),(18,170,140,108),(19,171,113,109),(20,172,114,110),(21,173,115,111),(22,174,116,112),(23,175,117,85),(24,176,118,86),(25,177,119,87),(26,178,120,88),(27,179,121,89),(28,180,122,90),(29,199,63,141),(30,200,64,142),(31,201,65,143),(32,202,66,144),(33,203,67,145),(34,204,68,146),(35,205,69,147),(36,206,70,148),(37,207,71,149),(38,208,72,150),(39,209,73,151),(40,210,74,152),(41,211,75,153),(42,212,76,154),(43,213,77,155),(44,214,78,156),(45,215,79,157),(46,216,80,158),(47,217,81,159),(48,218,82,160),(49,219,83,161),(50,220,84,162),(51,221,57,163),(52,222,58,164),(53,223,59,165),(54,224,60,166),(55,197,61,167),(56,198,62,168)], [(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)], [(1,14,137,122),(2,121,138,13),(3,12,139,120),(4,119,140,11),(5,10,113,118),(6,117,114,9),(7,8,115,116),(15,28,123,136),(16,135,124,27),(17,26,125,134),(18,133,126,25),(19,24,127,132),(20,131,128,23),(21,22,129,130),(29,60,77,40),(30,39,78,59),(31,58,79,38),(32,37,80,57),(33,84,81,36),(34,35,82,83),(41,76,61,56),(42,55,62,75),(43,74,63,54),(44,53,64,73),(45,72,65,52),(46,51,66,71),(47,70,67,50),(48,49,68,69),(85,110,189,186),(86,185,190,109),(87,108,191,184),(88,183,192,107),(89,106,193,182),(90,181,194,105),(91,104,195,180),(92,179,196,103),(93,102,169,178),(94,177,170,101),(95,100,171,176),(96,175,172,99),(97,98,173,174),(111,112,187,188),(141,224,213,152),(142,151,214,223),(143,222,215,150),(144,149,216,221),(145,220,217,148),(146,147,218,219),(153,212,197,168),(154,167,198,211),(155,210,199,166),(156,165,200,209),(157,208,201,164),(158,163,202,207),(159,206,203,162),(160,161,204,205)]])
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | ··· | 4R | 4S | 4T | 4U | 4V | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | - | + | + | + | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | Q8 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | C4○D28 | Q8×D7 | D7×C4○D4 |
| kernel | C42.232D14 | C4×Dic14 | D7×C42 | C42⋊D7 | C28⋊Q8 | Dic7.Q8 | D14⋊Q8 | D14⋊2Q8 | Dic7⋊Q8 | D14⋊3Q8 | Q8×C28 | C4×D7 | C4×Q8 | Dic7 | C28 | C42 | C4⋊C4 | C2×Q8 | C4 | C4 | C2 |
| # reps | 1 | 3 | 1 | 2 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 4 | 3 | 4 | 4 | 9 | 9 | 3 | 24 | 6 | 6 |
Matrix representation of C42.232D14 ►in GL4(𝔽29) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 12 |
| 12 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 |
| 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 12 |
| 7 | 22 | 0 | 0 |
| 7 | 26 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 28 | 0 |
| 7 | 22 | 0 | 0 |
| 3 | 22 | 0 | 0 |
| 0 | 0 | 0 | 28 |
| 0 | 0 | 28 | 0 |
G:=sub<GL(4,GF(29))| [1,0,0,0,0,1,0,0,0,0,17,0,0,0,0,12],[12,0,0,0,0,12,0,0,0,0,12,0,0,0,0,12],[7,7,0,0,22,26,0,0,0,0,0,28,0,0,1,0],[7,3,0,0,22,22,0,0,0,0,0,28,0,0,28,0] >;
C42.232D14 in GAP, Magma, Sage, TeX
C_4^2._{232}D_{14} % in TeX
G:=Group("C4^2.232D14"); // GroupNames label
G:=SmallGroup(448,1031);
// by ID
G=gap.SmallGroup(448,1031);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,100,675,570,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=a^2,d^2=a^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^13>;
// generators/relations