metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.132D14, C14.122- 1+4, (C4×Q8)⋊14D7, (Q8×C28)⋊16C2, C4⋊C4.299D14, D14⋊3Q8⋊9C2, (C4×D28).22C2, Dic7.Q8⋊9C2, C4.68(C4○D28), C42⋊2D7⋊18C2, C42⋊D7⋊34C2, (C2×Q8).180D14, C28.6Q8⋊19C2, D14.18(C4○D4), C28.119(C4○D4), (C2×C14).125C24, (C4×C28).177C22, (C2×C28).623C23, D14⋊C4.89C22, D14.5D4.1C2, (C2×D28).218C22, Dic7⋊C4.76C22, C4⋊Dic7.309C22, (Q8×C14).225C22, (C2×Dic7).56C23, (C22×D7).47C23, C22.146(C23×D7), C7⋊5(C22.46C24), (C4×Dic7).209C22, C2.13(Q8.10D14), (D7×C4⋊C4)⋊19C2, C2.32(D7×C4○D4), C4⋊C4⋊7D7⋊17C2, C2.64(C2×C4○D28), (C2×C4×D7).75C22, C14.147(C2×C4○D4), (C7×C4⋊C4).353C22, (C2×C4).289(C22×D7), SmallGroup(448,1034)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.132D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2b2, ab=ba, cac-1=dad-1=a-1, bc=cb, dbd-1=a2b-1, dcd-1=c13 >
Subgroups: 900 in 214 conjugacy classes, 97 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, Dic7, C28, C28, D14, D14, C2×C14, C2×C4⋊C4, C42⋊C2, C4×D4, C4×Q8, C22⋊Q8, C22.D4, C42.C2, C42⋊2C2, C4×D7, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C22.46C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, D14⋊C4, C4×C28, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×C4×D7, C2×C4×D7, C2×D28, Q8×C14, C28.6Q8, C42⋊D7, C4×D28, C42⋊2D7, Dic7.Q8, D7×C4⋊C4, C4⋊C4⋊7D7, D14.5D4, D14⋊3Q8, Q8×C28, C42.132D14
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, Q8.10D14, D7×C4○D4, C42.132D14
►On 224 points
Generators in S224
(1 202 117 39)(2 40 118 203)(3 204 119 41)(4 42 120 205)(5 206 121 43)(6 44 122 207)(7 208 123 45)(8 46 124 209)(9 210 125 47)(10 48 126 211)(11 212 127 49)(12 50 128 213)(13 214 129 51)(14 52 130 215)(15 216 131 53)(16 54 132 217)(17 218 133 55)(18 56 134 219)(19 220 135 29)(20 30 136 221)(21 222 137 31)(22 32 138 223)(23 224 139 33)(24 34 140 197)(25 198 113 35)(26 36 114 199)(27 200 115 37)(28 38 116 201)(57 189 154 85)(58 86 155 190)(59 191 156 87)(60 88 157 192)(61 193 158 89)(62 90 159 194)(63 195 160 91)(64 92 161 196)(65 169 162 93)(66 94 163 170)(67 171 164 95)(68 96 165 172)(69 173 166 97)(70 98 167 174)(71 175 168 99)(72 100 141 176)(73 177 142 101)(74 102 143 178)(75 179 144 103)(76 104 145 180)(77 181 146 105)(78 106 147 182)(79 183 148 107)(80 108 149 184)(81 185 150 109)(82 110 151 186)(83 187 152 111)(84 112 153 188)
(1 99 131 189)(2 100 132 190)(3 101 133 191)(4 102 134 192)(5 103 135 193)(6 104 136 194)(7 105 137 195)(8 106 138 196)(9 107 139 169)(10 108 140 170)(11 109 113 171)(12 110 114 172)(13 111 115 173)(14 112 116 174)(15 85 117 175)(16 86 118 176)(17 87 119 177)(18 88 120 178)(19 89 121 179)(20 90 122 180)(21 91 123 181)(22 92 124 182)(23 93 125 183)(24 94 126 184)(25 95 127 185)(26 96 128 186)(27 97 129 187)(28 98 130 188)(29 158 206 75)(30 159 207 76)(31 160 208 77)(32 161 209 78)(33 162 210 79)(34 163 211 80)(35 164 212 81)(36 165 213 82)(37 166 214 83)(38 167 215 84)(39 168 216 57)(40 141 217 58)(41 142 218 59)(42 143 219 60)(43 144 220 61)(44 145 221 62)(45 146 222 63)(46 147 223 64)(47 148 224 65)(48 149 197 66)(49 150 198 67)(50 151 199 68)(51 152 200 69)(52 153 201 70)(53 154 202 71)(54 155 203 72)(55 156 204 73)(56 157 205 74)
(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 15 28)(2 27 16 13)(3 12 17 26)(4 25 18 11)(5 10 19 24)(6 23 20 9)(7 8 21 22)(29 34 43 48)(30 47 44 33)(31 32 45 46)(35 56 49 42)(36 41 50 55)(37 54 51 40)(38 39 52 53)(57 84 71 70)(58 69 72 83)(59 82 73 68)(60 67 74 81)(61 80 75 66)(62 65 76 79)(63 78 77 64)(85 112 99 98)(86 97 100 111)(87 110 101 96)(88 95 102 109)(89 108 103 94)(90 93 104 107)(91 106 105 92)(113 134 127 120)(114 119 128 133)(115 132 129 118)(116 117 130 131)(121 126 135 140)(122 139 136 125)(123 124 137 138)(141 152 155 166)(142 165 156 151)(143 150 157 164)(144 163 158 149)(145 148 159 162)(146 161 160 147)(153 168 167 154)(169 180 183 194)(170 193 184 179)(171 178 185 192)(172 191 186 177)(173 176 187 190)(174 189 188 175)(181 196 195 182)(197 206 211 220)(198 219 212 205)(199 204 213 218)(200 217 214 203)(201 202 215 216)(207 224 221 210)(208 209 222 223)
G:=sub<Sym(224)| (1,202,117,39)(2,40,118,203)(3,204,119,41)(4,42,120,205)(5,206,121,43)(6,44,122,207)(7,208,123,45)(8,46,124,209)(9,210,125,47)(10,48,126,211)(11,212,127,49)(12,50,128,213)(13,214,129,51)(14,52,130,215)(15,216,131,53)(16,54,132,217)(17,218,133,55)(18,56,134,219)(19,220,135,29)(20,30,136,221)(21,222,137,31)(22,32,138,223)(23,224,139,33)(24,34,140,197)(25,198,113,35)(26,36,114,199)(27,200,115,37)(28,38,116,201)(57,189,154,85)(58,86,155,190)(59,191,156,87)(60,88,157,192)(61,193,158,89)(62,90,159,194)(63,195,160,91)(64,92,161,196)(65,169,162,93)(66,94,163,170)(67,171,164,95)(68,96,165,172)(69,173,166,97)(70,98,167,174)(71,175,168,99)(72,100,141,176)(73,177,142,101)(74,102,143,178)(75,179,144,103)(76,104,145,180)(77,181,146,105)(78,106,147,182)(79,183,148,107)(80,108,149,184)(81,185,150,109)(82,110,151,186)(83,187,152,111)(84,112,153,188), (1,99,131,189)(2,100,132,190)(3,101,133,191)(4,102,134,192)(5,103,135,193)(6,104,136,194)(7,105,137,195)(8,106,138,196)(9,107,139,169)(10,108,140,170)(11,109,113,171)(12,110,114,172)(13,111,115,173)(14,112,116,174)(15,85,117,175)(16,86,118,176)(17,87,119,177)(18,88,120,178)(19,89,121,179)(20,90,122,180)(21,91,123,181)(22,92,124,182)(23,93,125,183)(24,94,126,184)(25,95,127,185)(26,96,128,186)(27,97,129,187)(28,98,130,188)(29,158,206,75)(30,159,207,76)(31,160,208,77)(32,161,209,78)(33,162,210,79)(34,163,211,80)(35,164,212,81)(36,165,213,82)(37,166,214,83)(38,167,215,84)(39,168,216,57)(40,141,217,58)(41,142,218,59)(42,143,219,60)(43,144,220,61)(44,145,221,62)(45,146,222,63)(46,147,223,64)(47,148,224,65)(48,149,197,66)(49,150,198,67)(50,151,199,68)(51,152,200,69)(52,153,201,70)(53,154,202,71)(54,155,203,72)(55,156,204,73)(56,157,205,74), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,34,43,48)(30,47,44,33)(31,32,45,46)(35,56,49,42)(36,41,50,55)(37,54,51,40)(38,39,52,53)(57,84,71,70)(58,69,72,83)(59,82,73,68)(60,67,74,81)(61,80,75,66)(62,65,76,79)(63,78,77,64)(85,112,99,98)(86,97,100,111)(87,110,101,96)(88,95,102,109)(89,108,103,94)(90,93,104,107)(91,106,105,92)(113,134,127,120)(114,119,128,133)(115,132,129,118)(116,117,130,131)(121,126,135,140)(122,139,136,125)(123,124,137,138)(141,152,155,166)(142,165,156,151)(143,150,157,164)(144,163,158,149)(145,148,159,162)(146,161,160,147)(153,168,167,154)(169,180,183,194)(170,193,184,179)(171,178,185,192)(172,191,186,177)(173,176,187,190)(174,189,188,175)(181,196,195,182)(197,206,211,220)(198,219,212,205)(199,204,213,218)(200,217,214,203)(201,202,215,216)(207,224,221,210)(208,209,222,223)>;
G:=Group( (1,202,117,39)(2,40,118,203)(3,204,119,41)(4,42,120,205)(5,206,121,43)(6,44,122,207)(7,208,123,45)(8,46,124,209)(9,210,125,47)(10,48,126,211)(11,212,127,49)(12,50,128,213)(13,214,129,51)(14,52,130,215)(15,216,131,53)(16,54,132,217)(17,218,133,55)(18,56,134,219)(19,220,135,29)(20,30,136,221)(21,222,137,31)(22,32,138,223)(23,224,139,33)(24,34,140,197)(25,198,113,35)(26,36,114,199)(27,200,115,37)(28,38,116,201)(57,189,154,85)(58,86,155,190)(59,191,156,87)(60,88,157,192)(61,193,158,89)(62,90,159,194)(63,195,160,91)(64,92,161,196)(65,169,162,93)(66,94,163,170)(67,171,164,95)(68,96,165,172)(69,173,166,97)(70,98,167,174)(71,175,168,99)(72,100,141,176)(73,177,142,101)(74,102,143,178)(75,179,144,103)(76,104,145,180)(77,181,146,105)(78,106,147,182)(79,183,148,107)(80,108,149,184)(81,185,150,109)(82,110,151,186)(83,187,152,111)(84,112,153,188), (1,99,131,189)(2,100,132,190)(3,101,133,191)(4,102,134,192)(5,103,135,193)(6,104,136,194)(7,105,137,195)(8,106,138,196)(9,107,139,169)(10,108,140,170)(11,109,113,171)(12,110,114,172)(13,111,115,173)(14,112,116,174)(15,85,117,175)(16,86,118,176)(17,87,119,177)(18,88,120,178)(19,89,121,179)(20,90,122,180)(21,91,123,181)(22,92,124,182)(23,93,125,183)(24,94,126,184)(25,95,127,185)(26,96,128,186)(27,97,129,187)(28,98,130,188)(29,158,206,75)(30,159,207,76)(31,160,208,77)(32,161,209,78)(33,162,210,79)(34,163,211,80)(35,164,212,81)(36,165,213,82)(37,166,214,83)(38,167,215,84)(39,168,216,57)(40,141,217,58)(41,142,218,59)(42,143,219,60)(43,144,220,61)(44,145,221,62)(45,146,222,63)(46,147,223,64)(47,148,224,65)(48,149,197,66)(49,150,198,67)(50,151,199,68)(51,152,200,69)(52,153,201,70)(53,154,202,71)(54,155,203,72)(55,156,204,73)(56,157,205,74), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,34,43,48)(30,47,44,33)(31,32,45,46)(35,56,49,42)(36,41,50,55)(37,54,51,40)(38,39,52,53)(57,84,71,70)(58,69,72,83)(59,82,73,68)(60,67,74,81)(61,80,75,66)(62,65,76,79)(63,78,77,64)(85,112,99,98)(86,97,100,111)(87,110,101,96)(88,95,102,109)(89,108,103,94)(90,93,104,107)(91,106,105,92)(113,134,127,120)(114,119,128,133)(115,132,129,118)(116,117,130,131)(121,126,135,140)(122,139,136,125)(123,124,137,138)(141,152,155,166)(142,165,156,151)(143,150,157,164)(144,163,158,149)(145,148,159,162)(146,161,160,147)(153,168,167,154)(169,180,183,194)(170,193,184,179)(171,178,185,192)(172,191,186,177)(173,176,187,190)(174,189,188,175)(181,196,195,182)(197,206,211,220)(198,219,212,205)(199,204,213,218)(200,217,214,203)(201,202,215,216)(207,224,221,210)(208,209,222,223) );
G=PermutationGroup([[(1,202,117,39),(2,40,118,203),(3,204,119,41),(4,42,120,205),(5,206,121,43),(6,44,122,207),(7,208,123,45),(8,46,124,209),(9,210,125,47),(10,48,126,211),(11,212,127,49),(12,50,128,213),(13,214,129,51),(14,52,130,215),(15,216,131,53),(16,54,132,217),(17,218,133,55),(18,56,134,219),(19,220,135,29),(20,30,136,221),(21,222,137,31),(22,32,138,223),(23,224,139,33),(24,34,140,197),(25,198,113,35),(26,36,114,199),(27,200,115,37),(28,38,116,201),(57,189,154,85),(58,86,155,190),(59,191,156,87),(60,88,157,192),(61,193,158,89),(62,90,159,194),(63,195,160,91),(64,92,161,196),(65,169,162,93),(66,94,163,170),(67,171,164,95),(68,96,165,172),(69,173,166,97),(70,98,167,174),(71,175,168,99),(72,100,141,176),(73,177,142,101),(74,102,143,178),(75,179,144,103),(76,104,145,180),(77,181,146,105),(78,106,147,182),(79,183,148,107),(80,108,149,184),(81,185,150,109),(82,110,151,186),(83,187,152,111),(84,112,153,188)], [(1,99,131,189),(2,100,132,190),(3,101,133,191),(4,102,134,192),(5,103,135,193),(6,104,136,194),(7,105,137,195),(8,106,138,196),(9,107,139,169),(10,108,140,170),(11,109,113,171),(12,110,114,172),(13,111,115,173),(14,112,116,174),(15,85,117,175),(16,86,118,176),(17,87,119,177),(18,88,120,178),(19,89,121,179),(20,90,122,180),(21,91,123,181),(22,92,124,182),(23,93,125,183),(24,94,126,184),(25,95,127,185),(26,96,128,186),(27,97,129,187),(28,98,130,188),(29,158,206,75),(30,159,207,76),(31,160,208,77),(32,161,209,78),(33,162,210,79),(34,163,211,80),(35,164,212,81),(36,165,213,82),(37,166,214,83),(38,167,215,84),(39,168,216,57),(40,141,217,58),(41,142,218,59),(42,143,219,60),(43,144,220,61),(44,145,221,62),(45,146,222,63),(46,147,223,64),(47,148,224,65),(48,149,197,66),(49,150,198,67),(50,151,199,68),(51,152,200,69),(52,153,201,70),(53,154,202,71),(54,155,203,72),(55,156,204,73),(56,157,205,74)], [(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)], [(1,14,15,28),(2,27,16,13),(3,12,17,26),(4,25,18,11),(5,10,19,24),(6,23,20,9),(7,8,21,22),(29,34,43,48),(30,47,44,33),(31,32,45,46),(35,56,49,42),(36,41,50,55),(37,54,51,40),(38,39,52,53),(57,84,71,70),(58,69,72,83),(59,82,73,68),(60,67,74,81),(61,80,75,66),(62,65,76,79),(63,78,77,64),(85,112,99,98),(86,97,100,111),(87,110,101,96),(88,95,102,109),(89,108,103,94),(90,93,104,107),(91,106,105,92),(113,134,127,120),(114,119,128,133),(115,132,129,118),(116,117,130,131),(121,126,135,140),(122,139,136,125),(123,124,137,138),(141,152,155,166),(142,165,156,151),(143,150,157,164),(144,163,158,149),(145,148,159,162),(146,161,160,147),(153,168,167,154),(169,180,183,194),(170,193,184,179),(171,178,185,192),(172,191,186,177),(173,176,187,190),(174,189,188,175),(181,196,195,182),(197,206,211,220),(198,219,212,205),(199,204,213,218),(200,217,214,203),(201,202,215,216),(207,224,221,210),(208,209,222,223)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | ··· | 4R | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 28 | 2 | ··· | 2 | 4 | 4 | 4 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | C4○D28 | 2- 1+4 | Q8.10D14 | D7×C4○D4 |
| kernel | C42.132D14 | C28.6Q8 | C42⋊D7 | C4×D28 | C42⋊2D7 | Dic7.Q8 | D7×C4⋊C4 | C4⋊C4⋊7D7 | D14.5D4 | D14⋊3Q8 | Q8×C28 | C4×Q8 | C28 | D14 | C42 | C4⋊C4 | C2×Q8 | C4 | C14 | C2 | C2 |
| # reps | 1 | 1 | 2 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 3 | 4 | 4 | 9 | 9 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of C42.132D14 ►in GL4(𝔽29) generated by
| 28 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 12 | 27 |
| 0 | 0 | 0 | 17 |
| 21 | 18 | 0 | 0 |
| 27 | 8 | 0 | 0 |
| 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 12 |
| 4 | 9 | 0 | 0 |
| 28 | 12 | 0 | 0 |
| 0 | 0 | 12 | 27 |
| 0 | 0 | 28 | 17 |
| 3 | 22 | 0 | 0 |
| 18 | 26 | 0 | 0 |
| 0 | 0 | 12 | 27 |
| 0 | 0 | 28 | 17 |
G:=sub<GL(4,GF(29))| [28,0,0,0,0,28,0,0,0,0,12,0,0,0,27,17],[21,27,0,0,18,8,0,0,0,0,12,0,0,0,0,12],[4,28,0,0,9,12,0,0,0,0,12,28,0,0,27,17],[3,18,0,0,22,26,0,0,0,0,12,28,0,0,27,17] >;
C42.132D14 in GAP, Magma, Sage, TeX
C_4^2._{132}D_{14} % in TeX
G:=Group("C4^2.132D14"); // GroupNames label
G:=SmallGroup(448,1034);
// by ID
G=gap.SmallGroup(448,1034);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,268,1571,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^2*b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,b*c=c*b,d*b*d^-1=a^2*b^-1,d*c*d^-1=c^13>;
// generators/relations