metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C7⋊C8⋊6D4, C7⋊5(C8⋊D4), C22⋊Q8⋊4D7, C4⋊C4.68D14, C4.175(D4×D7), (C2×C28).78D4, C28.155(C2×D4), (C2×Q8).30D14, C14.D8⋊40C2, C28⋊7D4.13C2, Q8⋊Dic7⋊16C2, C28.Q8⋊40C2, (C22×C14).95D4, C28.191(C4○D4), C4.64(D4⋊2D7), C14.98(C4⋊D4), (C2×C28).368C23, (C22×C4).129D14, C23.28(C7⋊D4), (Q8×C14).48C22, C2.16(D4⋊D14), C14.117(C8⋊C22), (C2×D28).100C22, C14.91(C8.C22), C4⋊Dic7.147C22, C2.19(Dic7⋊D4), C2.12(C28.C23), (C22×C28).172C22, (C2×Q8⋊D7)⋊11C2, (C7×C22⋊Q8)⋊4C2, (C2×C14).499(C2×D4), (C2×C4).56(C7⋊D4), (C2×C7⋊C8).116C22, (C2×C4.Dic7)⋊13C2, (C7×C4⋊C4).115C22, (C2×C4).468(C22×D7), C22.174(C2×C7⋊D4), SmallGroup(448,583)
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=b-1, dbd=b5, dcd=c-1 >
Subgroups: 636 in 120 conjugacy classes, 41 normal (39 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, M4(2), SD16, C22×C4, C2×D4, C2×Q8, Dic7, C28, C28, D14, C2×C14, C2×C14, D4⋊C4, Q8⋊C4, C2.D8, C4⋊D4, C22⋊Q8, C2×M4(2), C2×SD16, C7⋊C8, C7⋊C8, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×Q8, C22×D7, C22×C14, C8⋊D4, C2×C7⋊C8, C4.Dic7, C4⋊Dic7, D14⋊C4, Q8⋊D7, C7×C22⋊C4, C7×C4⋊C4, C7×C4⋊C4, C2×D28, C2×C7⋊D4, C22×C28, Q8×C14, C28.Q8, C14.D8, Q8⋊Dic7, C2×C4.Dic7, C28⋊7D4, C2×Q8⋊D7, C7×C22⋊Q8, C7⋊C8⋊6D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4⋊D4, C8⋊C22, C8.C22, C7⋊D4, C22×D7, C8⋊D4, D4×D7, D4⋊2D7, C2×C7⋊D4, Dic7⋊D4, C28.C23, D4⋊D14, C7⋊C8⋊6D4
►On 224 points
Generators in S224
(1 184 26 112 88 39 217)(2 218 40 81 105 27 177)(3 178 28 106 82 33 219)(4 220 34 83 107 29 179)(5 180 30 108 84 35 221)(6 222 36 85 109 31 181)(7 182 32 110 86 37 223)(8 224 38 87 111 25 183)(9 195 156 24 174 104 72)(10 65 97 175 17 157 196)(11 197 158 18 176 98 66)(12 67 99 169 19 159 198)(13 199 160 20 170 100 68)(14 69 101 171 21 153 200)(15 193 154 22 172 102 70)(16 71 103 173 23 155 194)(41 77 122 216 191 113 152)(42 145 114 192 209 123 78)(43 79 124 210 185 115 146)(44 147 116 186 211 125 80)(45 73 126 212 187 117 148)(46 149 118 188 213 127 74)(47 75 128 214 189 119 150)(48 151 120 190 215 121 76)(49 207 131 93 161 63 144)(50 137 64 162 94 132 208)(51 201 133 95 163 57 138)(52 139 58 164 96 134 202)(53 203 135 89 165 59 140)(54 141 60 166 90 136 204)(55 205 129 91 167 61 142)(56 143 62 168 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)
(1 159 47 164)(2 158 48 163)(3 157 41 162)(4 156 42 161)(5 155 43 168)(6 154 44 167)(7 153 45 166)(8 160 46 165)(9 114 131 34)(10 113 132 33)(11 120 133 40)(12 119 134 39)(13 118 135 38)(14 117 136 37)(15 116 129 36)(16 115 130 35)(17 77 64 178)(18 76 57 177)(19 75 58 184)(20 74 59 183)(21 73 60 182)(22 80 61 181)(23 79 62 180)(24 78 63 179)(25 170 127 140)(26 169 128 139)(27 176 121 138)(28 175 122 137)(29 174 123 144)(30 173 124 143)(31 172 125 142)(32 171 126 141)(49 107 104 209)(50 106 97 216)(51 105 98 215)(52 112 99 214)(53 111 100 213)(54 110 101 212)(55 109 102 211)(56 108 103 210)(65 191 208 82)(66 190 201 81)(67 189 202 88)(68 188 203 87)(69 187 204 86)(70 186 205 85)(71 185 206 84)(72 192 207 83)(89 224 199 149)(90 223 200 148)(91 222 193 147)(92 221 194 146)(93 220 195 145)(94 219 196 152)(95 218 197 151)(96 217 198 150)
(2 6)(4 8)(9 135)(10 132)(11 129)(12 134)(13 131)(14 136)(15 133)(16 130)(17 64)(18 61)(19 58)(20 63)(21 60)(22 57)(23 62)(24 59)(25 29)(27 31)(34 38)(36 40)(42 46)(44 48)(49 100)(50 97)(51 102)(52 99)(53 104)(54 101)(55 98)(56 103)(65 208)(66 205)(67 202)(68 207)(69 204)(70 201)(71 206)(72 203)(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)(137 175)(138 172)(139 169)(140 174)(141 171)(142 176)(143 173)(144 170)(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)| (1,184,26,112,88,39,217)(2,218,40,81,105,27,177)(3,178,28,106,82,33,219)(4,220,34,83,107,29,179)(5,180,30,108,84,35,221)(6,222,36,85,109,31,181)(7,182,32,110,86,37,223)(8,224,38,87,111,25,183)(9,195,156,24,174,104,72)(10,65,97,175,17,157,196)(11,197,158,18,176,98,66)(12,67,99,169,19,159,198)(13,199,160,20,170,100,68)(14,69,101,171,21,153,200)(15,193,154,22,172,102,70)(16,71,103,173,23,155,194)(41,77,122,216,191,113,152)(42,145,114,192,209,123,78)(43,79,124,210,185,115,146)(44,147,116,186,211,125,80)(45,73,126,212,187,117,148)(46,149,118,188,213,127,74)(47,75,128,214,189,119,150)(48,151,120,190,215,121,76)(49,207,131,93,161,63,144)(50,137,64,162,94,132,208)(51,201,133,95,163,57,138)(52,139,58,164,96,134,202)(53,203,135,89,165,59,140)(54,141,60,166,90,136,204)(55,205,129,91,167,61,142)(56,143,62,168,92,130,206), (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), (1,159,47,164)(2,158,48,163)(3,157,41,162)(4,156,42,161)(5,155,43,168)(6,154,44,167)(7,153,45,166)(8,160,46,165)(9,114,131,34)(10,113,132,33)(11,120,133,40)(12,119,134,39)(13,118,135,38)(14,117,136,37)(15,116,129,36)(16,115,130,35)(17,77,64,178)(18,76,57,177)(19,75,58,184)(20,74,59,183)(21,73,60,182)(22,80,61,181)(23,79,62,180)(24,78,63,179)(25,170,127,140)(26,169,128,139)(27,176,121,138)(28,175,122,137)(29,174,123,144)(30,173,124,143)(31,172,125,142)(32,171,126,141)(49,107,104,209)(50,106,97,216)(51,105,98,215)(52,112,99,214)(53,111,100,213)(54,110,101,212)(55,109,102,211)(56,108,103,210)(65,191,208,82)(66,190,201,81)(67,189,202,88)(68,188,203,87)(69,187,204,86)(70,186,205,85)(71,185,206,84)(72,192,207,83)(89,224,199,149)(90,223,200,148)(91,222,193,147)(92,221,194,146)(93,220,195,145)(94,219,196,152)(95,218,197,151)(96,217,198,150), (2,6)(4,8)(9,135)(10,132)(11,129)(12,134)(13,131)(14,136)(15,133)(16,130)(17,64)(18,61)(19,58)(20,63)(21,60)(22,57)(23,62)(24,59)(25,29)(27,31)(34,38)(36,40)(42,46)(44,48)(49,100)(50,97)(51,102)(52,99)(53,104)(54,101)(55,98)(56,103)(65,208)(66,205)(67,202)(68,207)(69,204)(70,201)(71,206)(72,203)(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)(137,175)(138,172)(139,169)(140,174)(141,171)(142,176)(143,173)(144,170)(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( (1,184,26,112,88,39,217)(2,218,40,81,105,27,177)(3,178,28,106,82,33,219)(4,220,34,83,107,29,179)(5,180,30,108,84,35,221)(6,222,36,85,109,31,181)(7,182,32,110,86,37,223)(8,224,38,87,111,25,183)(9,195,156,24,174,104,72)(10,65,97,175,17,157,196)(11,197,158,18,176,98,66)(12,67,99,169,19,159,198)(13,199,160,20,170,100,68)(14,69,101,171,21,153,200)(15,193,154,22,172,102,70)(16,71,103,173,23,155,194)(41,77,122,216,191,113,152)(42,145,114,192,209,123,78)(43,79,124,210,185,115,146)(44,147,116,186,211,125,80)(45,73,126,212,187,117,148)(46,149,118,188,213,127,74)(47,75,128,214,189,119,150)(48,151,120,190,215,121,76)(49,207,131,93,161,63,144)(50,137,64,162,94,132,208)(51,201,133,95,163,57,138)(52,139,58,164,96,134,202)(53,203,135,89,165,59,140)(54,141,60,166,90,136,204)(55,205,129,91,167,61,142)(56,143,62,168,92,130,206), (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), (1,159,47,164)(2,158,48,163)(3,157,41,162)(4,156,42,161)(5,155,43,168)(6,154,44,167)(7,153,45,166)(8,160,46,165)(9,114,131,34)(10,113,132,33)(11,120,133,40)(12,119,134,39)(13,118,135,38)(14,117,136,37)(15,116,129,36)(16,115,130,35)(17,77,64,178)(18,76,57,177)(19,75,58,184)(20,74,59,183)(21,73,60,182)(22,80,61,181)(23,79,62,180)(24,78,63,179)(25,170,127,140)(26,169,128,139)(27,176,121,138)(28,175,122,137)(29,174,123,144)(30,173,124,143)(31,172,125,142)(32,171,126,141)(49,107,104,209)(50,106,97,216)(51,105,98,215)(52,112,99,214)(53,111,100,213)(54,110,101,212)(55,109,102,211)(56,108,103,210)(65,191,208,82)(66,190,201,81)(67,189,202,88)(68,188,203,87)(69,187,204,86)(70,186,205,85)(71,185,206,84)(72,192,207,83)(89,224,199,149)(90,223,200,148)(91,222,193,147)(92,221,194,146)(93,220,195,145)(94,219,196,152)(95,218,197,151)(96,217,198,150), (2,6)(4,8)(9,135)(10,132)(11,129)(12,134)(13,131)(14,136)(15,133)(16,130)(17,64)(18,61)(19,58)(20,63)(21,60)(22,57)(23,62)(24,59)(25,29)(27,31)(34,38)(36,40)(42,46)(44,48)(49,100)(50,97)(51,102)(52,99)(53,104)(54,101)(55,98)(56,103)(65,208)(66,205)(67,202)(68,207)(69,204)(70,201)(71,206)(72,203)(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)(137,175)(138,172)(139,169)(140,174)(141,171)(142,176)(143,173)(144,170)(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([[(1,184,26,112,88,39,217),(2,218,40,81,105,27,177),(3,178,28,106,82,33,219),(4,220,34,83,107,29,179),(5,180,30,108,84,35,221),(6,222,36,85,109,31,181),(7,182,32,110,86,37,223),(8,224,38,87,111,25,183),(9,195,156,24,174,104,72),(10,65,97,175,17,157,196),(11,197,158,18,176,98,66),(12,67,99,169,19,159,198),(13,199,160,20,170,100,68),(14,69,101,171,21,153,200),(15,193,154,22,172,102,70),(16,71,103,173,23,155,194),(41,77,122,216,191,113,152),(42,145,114,192,209,123,78),(43,79,124,210,185,115,146),(44,147,116,186,211,125,80),(45,73,126,212,187,117,148),(46,149,118,188,213,127,74),(47,75,128,214,189,119,150),(48,151,120,190,215,121,76),(49,207,131,93,161,63,144),(50,137,64,162,94,132,208),(51,201,133,95,163,57,138),(52,139,58,164,96,134,202),(53,203,135,89,165,59,140),(54,141,60,166,90,136,204),(55,205,129,91,167,61,142),(56,143,62,168,92,130,206)], [(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)], [(1,159,47,164),(2,158,48,163),(3,157,41,162),(4,156,42,161),(5,155,43,168),(6,154,44,167),(7,153,45,166),(8,160,46,165),(9,114,131,34),(10,113,132,33),(11,120,133,40),(12,119,134,39),(13,118,135,38),(14,117,136,37),(15,116,129,36),(16,115,130,35),(17,77,64,178),(18,76,57,177),(19,75,58,184),(20,74,59,183),(21,73,60,182),(22,80,61,181),(23,79,62,180),(24,78,63,179),(25,170,127,140),(26,169,128,139),(27,176,121,138),(28,175,122,137),(29,174,123,144),(30,173,124,143),(31,172,125,142),(32,171,126,141),(49,107,104,209),(50,106,97,216),(51,105,98,215),(52,112,99,214),(53,111,100,213),(54,110,101,212),(55,109,102,211),(56,108,103,210),(65,191,208,82),(66,190,201,81),(67,189,202,88),(68,188,203,87),(69,187,204,86),(70,186,205,85),(71,185,206,84),(72,192,207,83),(89,224,199,149),(90,223,200,148),(91,222,193,147),(92,221,194,146),(93,220,195,145),(94,219,196,152),(95,218,197,151),(96,217,198,150)], [(2,6),(4,8),(9,135),(10,132),(11,129),(12,134),(13,131),(14,136),(15,133),(16,130),(17,64),(18,61),(19,58),(20,63),(21,60),(22,57),(23,62),(24,59),(25,29),(27,31),(34,38),(36,40),(42,46),(44,48),(49,100),(50,97),(51,102),(52,99),(53,104),(54,101),(55,98),(56,103),(65,208),(66,205),(67,202),(68,207),(69,204),(70,201),(71,206),(72,203),(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),(137,175),(138,172),(139,169),(140,174),(141,171),(142,176),(143,173),(144,170),(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 | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 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 | 56 | 2 | 2 | 4 | 8 | 8 | 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 | 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 | C8.C22 | D4×D7 | D4⋊2D7 | C28.C23 | D4⋊D14 |
| kernel | C7⋊C8⋊6D4 | C28.Q8 | C14.D8 | Q8⋊Dic7 | C2×C4.Dic7 | C28⋊7D4 | C2×Q8⋊D7 | C7×C22⋊Q8 | C7⋊C8 | C2×C28 | C22×C14 | C22⋊Q8 | C28 | C4⋊C4 | C22×C4 | C2×Q8 | C2×C4 | C23 | C14 | C14 | C4 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 3 | 2 | 3 | 3 | 3 | 6 | 6 | 1 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of C7⋊C8⋊6D4 ►in GL8(𝔽113)
| 73 | 112 | 0 | 0 | 0 | 0 | 0 | 0 |
| 15 | 6 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 49 | 14 | 0 | 0 | 0 | 0 | 0 | 0 |
| 103 | 64 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 0 | 89 | 18 |
| 0 | 0 | 0 | 0 | 12 | 0 | 92 | 110 |
| 0 | 0 | 0 | 0 | 12 | 101 | 101 | 9 |
| 0 | 0 | 0 | 0 | 3 | 9 | 101 | 9 |
| 49 | 14 | 0 | 0 | 0 | 0 | 0 | 0 |
| 103 | 64 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 111 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 112 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 1 | 112 | 112 | 0 |
| 112 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 112 |
G:=sub<GL(8,GF(113))| [73,15,0,0,0,0,0,0,112,6,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[49,103,0,0,0,0,0,0,14,64,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,3,12,12,3,0,0,0,0,0,0,101,9,0,0,0,0,89,92,101,101,0,0,0,0,18,110,9,9],[49,103,0,0,0,0,0,0,14,64,0,0,0,0,0,0,0,0,0,112,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,0,0,0,0,0,112,0,0,0,0,111,112,112,112,0,0,0,0,0,1,0,0],[112,0,0,0,0,0,0,0,0,112,0,0,0,0,0,0,0,0,112,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,112,0,0,0,0,0,0,0,0,112] >;
C7⋊C8⋊6D4 in GAP, Magma, Sage, TeX
C_7\rtimes C_8\rtimes_6D_4
% in TeX
G:=Group("C7:C8:6D4"); // GroupNames label
G:=SmallGroup(448,583);
// by ID
G=gap.SmallGroup(448,583);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,254,555,184,1123,297,136,18822]);
// 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^-1,d*b*d=b^5,d*c*d=c^-1>;
// generators/relations