metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C7⋊C8.6D4, C4⋊C4.71D14, C4.177(D4×D7), (C2×C28).80D4, C7⋊3(C8.D4), C22⋊Q8.7D7, C28.158(C2×D4), (C2×Q8).33D14, Q8⋊Dic7⋊18C2, C14.Q16⋊40C2, C4.Dic14⋊40C2, (C22×C14).98D4, C28.193(C4○D4), C4.66(D4⋊2D7), (C2×C28).371C23, (C22×C4).131D14, C23.29(C7⋊D4), (Q8×C14).51C22, C14.100(C4⋊D4), C28.48D4.13C2, C14.92(C8.C22), C4⋊Dic7.149C22, C2.21(Dic7⋊D4), C2.16(D4.9D14), C2.13(C28.C23), (C22×C28).175C22, (C2×Dic14).106C22, (C2×C7⋊Q16)⋊11C2, (C7×C22⋊Q8).6C2, (C2×C14).502(C2×D4), (C2×C4).58(C7⋊D4), (C2×C7⋊C8).118C22, (C7×C4⋊C4).118C22, (C2×C4).471(C22×D7), C22.177(C2×C7⋊D4), (C2×C4.Dic7).20C2, SmallGroup(448,586)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C7⋊C8.6D4
G = < a,b,c,d | a7=b8=c4=d2=1, bab-1=cac-1=a-1, ad=da, cbc-1=b3, dbd=b5, dcd=b4c-1 >
Subgroups: 444 in 110 conjugacy classes, 41 normal (39 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, Q8, C23, C14, C14, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, M4(2), Q16, C22×C4, C2×Q8, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, Q8⋊C4, C4.Q8, C22⋊Q8, C22⋊Q8, C2×M4(2), C2×Q16, C7⋊C8, C7⋊C8, Dic14, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×C14, C8.D4, C2×C7⋊C8, C4.Dic7, Dic7⋊C4, C4⋊Dic7, C7⋊Q16, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C22×C28, Q8×C14, C4.Dic14, C14.Q16, Q8⋊Dic7, C2×C4.Dic7, C28.48D4, C2×C7⋊Q16, C7×C22⋊Q8, C7⋊C8.6D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4⋊D4, C8.C22, C7⋊D4, C22×D7, C8.D4, D4×D7, D4⋊2D7, C2×C7⋊D4, Dic7⋊D4, C28.C23, D4.9D14, C7⋊C8.6D4
►On 224 points
Generators in S224
(1 219 187 88 126 35 214)(2 215 36 127 81 188 220)(3 221 189 82 128 37 216)(4 209 38 121 83 190 222)(5 223 191 84 122 39 210)(6 211 40 123 85 192 224)(7 217 185 86 124 33 212)(8 213 34 125 87 186 218)(9 195 160 20 170 68 142)(10 143 69 171 21 153 196)(11 197 154 22 172 70 144)(12 137 71 173 23 155 198)(13 199 156 24 174 72 138)(14 139 65 175 17 157 200)(15 193 158 18 176 66 140)(16 141 67 169 19 159 194)(25 183 80 111 48 147 116)(26 117 148 41 112 73 184)(27 177 74 105 42 149 118)(28 119 150 43 106 75 178)(29 179 76 107 44 151 120)(30 113 152 45 108 77 180)(31 181 78 109 46 145 114)(32 115 146 47 110 79 182)(49 207 131 93 165 102 63)(50 64 103 166 94 132 208)(51 201 133 95 167 104 57)(52 58 97 168 96 134 202)(53 203 135 89 161 98 59)(54 60 99 162 90 136 204)(55 205 129 91 163 100 61)(56 62 101 164 92 130 206)
(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)
(1 155 43 164)(2 158 44 167)(3 153 45 162)(4 156 46 165)(5 159 47 168)(6 154 48 163)(7 157 41 166)(8 160 42 161)(9 118 135 34)(10 113 136 37)(11 116 129 40)(12 119 130 35)(13 114 131 38)(14 117 132 33)(15 120 133 36)(16 115 134 39)(17 112 103 217)(18 107 104 220)(19 110 97 223)(20 105 98 218)(21 108 99 221)(22 111 100 224)(23 106 101 219)(24 109 102 222)(25 205 123 144)(26 208 124 139)(27 203 125 142)(28 206 126 137)(29 201 127 140)(30 204 128 143)(31 207 121 138)(32 202 122 141)(49 83 72 181)(50 86 65 184)(51 81 66 179)(52 84 67 182)(53 87 68 177)(54 82 69 180)(55 85 70 183)(56 88 71 178)(57 188 176 76)(58 191 169 79)(59 186 170 74)(60 189 171 77)(61 192 172 80)(62 187 173 75)(63 190 174 78)(64 185 175 73)(89 213 195 149)(90 216 196 152)(91 211 197 147)(92 214 198 150)(93 209 199 145)(94 212 200 148)(95 215 193 151)(96 210 194 146)
(2 6)(4 8)(9 135)(10 132)(11 129)(12 134)(13 131)(14 136)(15 133)(16 130)(17 99)(18 104)(19 101)(20 98)(21 103)(22 100)(23 97)(24 102)(25 29)(27 31)(34 38)(36 40)(42 46)(44 48)(49 72)(50 69)(51 66)(52 71)(53 68)(54 65)(55 70)(56 67)(57 176)(58 173)(59 170)(60 175)(61 172)(62 169)(63 174)(64 171)(74 78)(76 80)(81 85)(83 87)(89 195)(90 200)(91 197)(92 194)(93 199)(94 196)(95 193)(96 198)(105 109)(107 111)(114 118)(116 120)(121 125)(123 127)(137 202)(138 207)(139 204)(140 201)(141 206)(142 203)(143 208)(144 205)(145 149)(147 151)(153 166)(154 163)(155 168)(156 165)(157 162)(158 167)(159 164)(160 161)(177 181)(179 183)(186 190)(188 192)(209 213)(211 215)(218 222)(220 224)
G:=sub<Sym(224)| (1,219,187,88,126,35,214)(2,215,36,127,81,188,220)(3,221,189,82,128,37,216)(4,209,38,121,83,190,222)(5,223,191,84,122,39,210)(6,211,40,123,85,192,224)(7,217,185,86,124,33,212)(8,213,34,125,87,186,218)(9,195,160,20,170,68,142)(10,143,69,171,21,153,196)(11,197,154,22,172,70,144)(12,137,71,173,23,155,198)(13,199,156,24,174,72,138)(14,139,65,175,17,157,200)(15,193,158,18,176,66,140)(16,141,67,169,19,159,194)(25,183,80,111,48,147,116)(26,117,148,41,112,73,184)(27,177,74,105,42,149,118)(28,119,150,43,106,75,178)(29,179,76,107,44,151,120)(30,113,152,45,108,77,180)(31,181,78,109,46,145,114)(32,115,146,47,110,79,182)(49,207,131,93,165,102,63)(50,64,103,166,94,132,208)(51,201,133,95,167,104,57)(52,58,97,168,96,134,202)(53,203,135,89,161,98,59)(54,60,99,162,90,136,204)(55,205,129,91,163,100,61)(56,62,101,164,92,130,206), (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), (1,155,43,164)(2,158,44,167)(3,153,45,162)(4,156,46,165)(5,159,47,168)(6,154,48,163)(7,157,41,166)(8,160,42,161)(9,118,135,34)(10,113,136,37)(11,116,129,40)(12,119,130,35)(13,114,131,38)(14,117,132,33)(15,120,133,36)(16,115,134,39)(17,112,103,217)(18,107,104,220)(19,110,97,223)(20,105,98,218)(21,108,99,221)(22,111,100,224)(23,106,101,219)(24,109,102,222)(25,205,123,144)(26,208,124,139)(27,203,125,142)(28,206,126,137)(29,201,127,140)(30,204,128,143)(31,207,121,138)(32,202,122,141)(49,83,72,181)(50,86,65,184)(51,81,66,179)(52,84,67,182)(53,87,68,177)(54,82,69,180)(55,85,70,183)(56,88,71,178)(57,188,176,76)(58,191,169,79)(59,186,170,74)(60,189,171,77)(61,192,172,80)(62,187,173,75)(63,190,174,78)(64,185,175,73)(89,213,195,149)(90,216,196,152)(91,211,197,147)(92,214,198,150)(93,209,199,145)(94,212,200,148)(95,215,193,151)(96,210,194,146), (2,6)(4,8)(9,135)(10,132)(11,129)(12,134)(13,131)(14,136)(15,133)(16,130)(17,99)(18,104)(19,101)(20,98)(21,103)(22,100)(23,97)(24,102)(25,29)(27,31)(34,38)(36,40)(42,46)(44,48)(49,72)(50,69)(51,66)(52,71)(53,68)(54,65)(55,70)(56,67)(57,176)(58,173)(59,170)(60,175)(61,172)(62,169)(63,174)(64,171)(74,78)(76,80)(81,85)(83,87)(89,195)(90,200)(91,197)(92,194)(93,199)(94,196)(95,193)(96,198)(105,109)(107,111)(114,118)(116,120)(121,125)(123,127)(137,202)(138,207)(139,204)(140,201)(141,206)(142,203)(143,208)(144,205)(145,149)(147,151)(153,166)(154,163)(155,168)(156,165)(157,162)(158,167)(159,164)(160,161)(177,181)(179,183)(186,190)(188,192)(209,213)(211,215)(218,222)(220,224)>;
G:=Group( (1,219,187,88,126,35,214)(2,215,36,127,81,188,220)(3,221,189,82,128,37,216)(4,209,38,121,83,190,222)(5,223,191,84,122,39,210)(6,211,40,123,85,192,224)(7,217,185,86,124,33,212)(8,213,34,125,87,186,218)(9,195,160,20,170,68,142)(10,143,69,171,21,153,196)(11,197,154,22,172,70,144)(12,137,71,173,23,155,198)(13,199,156,24,174,72,138)(14,139,65,175,17,157,200)(15,193,158,18,176,66,140)(16,141,67,169,19,159,194)(25,183,80,111,48,147,116)(26,117,148,41,112,73,184)(27,177,74,105,42,149,118)(28,119,150,43,106,75,178)(29,179,76,107,44,151,120)(30,113,152,45,108,77,180)(31,181,78,109,46,145,114)(32,115,146,47,110,79,182)(49,207,131,93,165,102,63)(50,64,103,166,94,132,208)(51,201,133,95,167,104,57)(52,58,97,168,96,134,202)(53,203,135,89,161,98,59)(54,60,99,162,90,136,204)(55,205,129,91,163,100,61)(56,62,101,164,92,130,206), (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), (1,155,43,164)(2,158,44,167)(3,153,45,162)(4,156,46,165)(5,159,47,168)(6,154,48,163)(7,157,41,166)(8,160,42,161)(9,118,135,34)(10,113,136,37)(11,116,129,40)(12,119,130,35)(13,114,131,38)(14,117,132,33)(15,120,133,36)(16,115,134,39)(17,112,103,217)(18,107,104,220)(19,110,97,223)(20,105,98,218)(21,108,99,221)(22,111,100,224)(23,106,101,219)(24,109,102,222)(25,205,123,144)(26,208,124,139)(27,203,125,142)(28,206,126,137)(29,201,127,140)(30,204,128,143)(31,207,121,138)(32,202,122,141)(49,83,72,181)(50,86,65,184)(51,81,66,179)(52,84,67,182)(53,87,68,177)(54,82,69,180)(55,85,70,183)(56,88,71,178)(57,188,176,76)(58,191,169,79)(59,186,170,74)(60,189,171,77)(61,192,172,80)(62,187,173,75)(63,190,174,78)(64,185,175,73)(89,213,195,149)(90,216,196,152)(91,211,197,147)(92,214,198,150)(93,209,199,145)(94,212,200,148)(95,215,193,151)(96,210,194,146), (2,6)(4,8)(9,135)(10,132)(11,129)(12,134)(13,131)(14,136)(15,133)(16,130)(17,99)(18,104)(19,101)(20,98)(21,103)(22,100)(23,97)(24,102)(25,29)(27,31)(34,38)(36,40)(42,46)(44,48)(49,72)(50,69)(51,66)(52,71)(53,68)(54,65)(55,70)(56,67)(57,176)(58,173)(59,170)(60,175)(61,172)(62,169)(63,174)(64,171)(74,78)(76,80)(81,85)(83,87)(89,195)(90,200)(91,197)(92,194)(93,199)(94,196)(95,193)(96,198)(105,109)(107,111)(114,118)(116,120)(121,125)(123,127)(137,202)(138,207)(139,204)(140,201)(141,206)(142,203)(143,208)(144,205)(145,149)(147,151)(153,166)(154,163)(155,168)(156,165)(157,162)(158,167)(159,164)(160,161)(177,181)(179,183)(186,190)(188,192)(209,213)(211,215)(218,222)(220,224) );
G=PermutationGroup([[(1,219,187,88,126,35,214),(2,215,36,127,81,188,220),(3,221,189,82,128,37,216),(4,209,38,121,83,190,222),(5,223,191,84,122,39,210),(6,211,40,123,85,192,224),(7,217,185,86,124,33,212),(8,213,34,125,87,186,218),(9,195,160,20,170,68,142),(10,143,69,171,21,153,196),(11,197,154,22,172,70,144),(12,137,71,173,23,155,198),(13,199,156,24,174,72,138),(14,139,65,175,17,157,200),(15,193,158,18,176,66,140),(16,141,67,169,19,159,194),(25,183,80,111,48,147,116),(26,117,148,41,112,73,184),(27,177,74,105,42,149,118),(28,119,150,43,106,75,178),(29,179,76,107,44,151,120),(30,113,152,45,108,77,180),(31,181,78,109,46,145,114),(32,115,146,47,110,79,182),(49,207,131,93,165,102,63),(50,64,103,166,94,132,208),(51,201,133,95,167,104,57),(52,58,97,168,96,134,202),(53,203,135,89,161,98,59),(54,60,99,162,90,136,204),(55,205,129,91,163,100,61),(56,62,101,164,92,130,206)], [(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)], [(1,155,43,164),(2,158,44,167),(3,153,45,162),(4,156,46,165),(5,159,47,168),(6,154,48,163),(7,157,41,166),(8,160,42,161),(9,118,135,34),(10,113,136,37),(11,116,129,40),(12,119,130,35),(13,114,131,38),(14,117,132,33),(15,120,133,36),(16,115,134,39),(17,112,103,217),(18,107,104,220),(19,110,97,223),(20,105,98,218),(21,108,99,221),(22,111,100,224),(23,106,101,219),(24,109,102,222),(25,205,123,144),(26,208,124,139),(27,203,125,142),(28,206,126,137),(29,201,127,140),(30,204,128,143),(31,207,121,138),(32,202,122,141),(49,83,72,181),(50,86,65,184),(51,81,66,179),(52,84,67,182),(53,87,68,177),(54,82,69,180),(55,85,70,183),(56,88,71,178),(57,188,176,76),(58,191,169,79),(59,186,170,74),(60,189,171,77),(61,192,172,80),(62,187,173,75),(63,190,174,78),(64,185,175,73),(89,213,195,149),(90,216,196,152),(91,211,197,147),(92,214,198,150),(93,209,199,145),(94,212,200,148),(95,215,193,151),(96,210,194,146)], [(2,6),(4,8),(9,135),(10,132),(11,129),(12,134),(13,131),(14,136),(15,133),(16,130),(17,99),(18,104),(19,101),(20,98),(21,103),(22,100),(23,97),(24,102),(25,29),(27,31),(34,38),(36,40),(42,46),(44,48),(49,72),(50,69),(51,66),(52,71),(53,68),(54,65),(55,70),(56,67),(57,176),(58,173),(59,170),(60,175),(61,172),(62,169),(63,174),(64,171),(74,78),(76,80),(81,85),(83,87),(89,195),(90,200),(91,197),(92,194),(93,199),(94,196),(95,193),(96,198),(105,109),(107,111),(114,118),(116,120),(121,125),(123,127),(137,202),(138,207),(139,204),(140,201),(141,206),(142,203),(143,208),(144,205),(145,149),(147,151),(153,166),(154,163),(155,168),(156,165),(157,162),(158,167),(159,164),(160,161),(177,181),(179,183),(186,190),(188,192),(209,213),(211,215),(218,222),(220,224)]])
58 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 2 | 2 | 4 | 8 | 8 | 56 | 56 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 8 | ··· | 8 |
58 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D7 | C4○D4 | D14 | D14 | D14 | C7⋊D4 | C7⋊D4 | C8.C22 | D4×D7 | D4⋊2D7 | C28.C23 | D4.9D14 |
| kernel | C7⋊C8.6D4 | C4.Dic14 | C14.Q16 | Q8⋊Dic7 | C2×C4.Dic7 | C28.48D4 | C2×C7⋊Q16 | C7×C22⋊Q8 | C7⋊C8 | C2×C28 | C22×C14 | C22⋊Q8 | C28 | C4⋊C4 | C22×C4 | C2×Q8 | C2×C4 | C23 | C14 | C4 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 3 | 2 | 3 | 3 | 3 | 6 | 6 | 2 | 3 | 3 | 6 | 6 |
Matrix representation of C7⋊C8.6D4 ►in GL6(𝔽113)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 24 | 112 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 24 | 112 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 30 | 40 |
| 0 | 0 | 0 | 0 | 82 | 83 |
| 0 | 0 | 77 | 12 | 0 | 0 |
| 0 | 0 | 52 | 36 | 0 | 0 |
| 109 | 3 | 0 | 0 | 0 | 0 |
| 32 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 36 | 101 | 0 | 0 |
| 0 | 0 | 61 | 77 | 0 | 0 |
| 0 | 0 | 0 | 0 | 83 | 73 |
| 0 | 0 | 0 | 0 | 31 | 30 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 78 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
G:=sub<GL(6,GF(113))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,24,1,0,0,0,0,112,0,0,0,0,0,0,0,24,1,0,0,0,0,112,0],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,77,52,0,0,0,0,12,36,0,0,30,82,0,0,0,0,40,83,0,0],[109,32,0,0,0,0,3,4,0,0,0,0,0,0,36,61,0,0,0,0,101,77,0,0,0,0,0,0,83,31,0,0,0,0,73,30],[1,78,0,0,0,0,0,112,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,112,0,0,0,0,0,0,112] >;
C7⋊C8.6D4 in GAP, Magma, Sage, TeX
C_7\rtimes C_8._6D_4
% in TeX
G:=Group("C7:C8.6D4"); // GroupNames label
G:=SmallGroup(448,586);
// by ID
G=gap.SmallGroup(448,586);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,253,254,555,184,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^7=b^8=c^4=d^2=1,b*a*b^-1=c*a*c^-1=a^-1,a*d=d*a,c*b*c^-1=b^3,d*b*d=b^5,d*c*d=b^4*c^-1>;
// generators/relations