metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C7⋊C8⋊24D4, C7⋊5(C8⋊8D4), C22⋊Q8⋊3D7, C4⋊C4.67D14, (C2×C14)⋊6SD16, C4.174(D4×D7), (C2×C28).267D4, C28.154(C2×D4), C22⋊1(Q8⋊D7), (C2×Q8).29D14, C14.D8⋊39C2, C28⋊7D4.12C2, Q8⋊Dic7⋊15C2, C4.Dic14⋊39C2, C14.73(C2×SD16), (C22×C14).94D4, C14.101(C4○D8), C28.190(C4○D4), C4.63(D4⋊2D7), C14.97(C4⋊D4), (C2×C28).367C23, (C2×D28).99C22, (C22×C4).342D14, C23.41(C7⋊D4), (Q8×C14).47C22, C4⋊Dic7.146C22, C2.18(Dic7⋊D4), C2.20(D4.8D14), (C22×C28).171C22, (C22×C7⋊C8)⋊5C2, (C2×Q8⋊D7)⋊10C2, C2.10(C2×Q8⋊D7), (C7×C22⋊Q8)⋊3C2, (C2×C14).498(C2×D4), (C2×C7⋊C8).250C22, (C2×C4).107(C7⋊D4), (C7×C4⋊C4).114C22, (C2×C4).467(C22×D7), C22.173(C2×C7⋊D4), SmallGroup(448,582)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C7⋊C8⋊24D4
G = < a,b,c,d | a7=b8=c4=d2=1, bab-1=cac-1=a-1, ad=da, cbc-1=b3, bd=db, dcd=c-1 >
Subgroups: 636 in 124 conjugacy classes, 45 normal (39 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, SD16, C22×C4, C2×D4, C2×Q8, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C14, D4⋊C4, Q8⋊C4, C4.Q8, C4⋊D4, C22⋊Q8, C22×C8, C2×SD16, C7⋊C8, C7⋊C8, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×Q8, C22×D7, C22×C14, C8⋊8D4, C2×C7⋊C8, C2×C7⋊C8, C4⋊Dic7, D14⋊C4, Q8⋊D7, C7×C22⋊C4, C7×C4⋊C4, C7×C4⋊C4, C2×D28, C2×C7⋊D4, C22×C28, Q8×C14, C4.Dic14, C14.D8, Q8⋊Dic7, C22×C7⋊C8, C28⋊7D4, C2×Q8⋊D7, C7×C22⋊Q8, C7⋊C8⋊24D4
Quotients: C1, C2, C22, D4, C23, D7, SD16, C2×D4, C4○D4, D14, C4⋊D4, C2×SD16, C4○D8, C7⋊D4, C22×D7, C8⋊8D4, Q8⋊D7, D4×D7, D4⋊2D7, C2×C7⋊D4, Dic7⋊D4, C2×Q8⋊D7, D4.8D14, C7⋊C8⋊24D4
►On 224 points
Generators in S224
(1 184 187 126 115 214 217)(2 218 215 116 127 188 177)(3 178 189 128 117 216 219)(4 220 209 118 121 190 179)(5 180 191 122 119 210 221)(6 222 211 120 123 192 181)(7 182 185 124 113 212 223)(8 224 213 114 125 186 183)(9 195 156 24 174 138 135)(10 136 139 175 17 157 196)(11 197 158 18 176 140 129)(12 130 141 169 19 159 198)(13 199 160 20 170 142 131)(14 132 143 171 21 153 200)(15 193 154 22 172 144 133)(16 134 137 173 23 155 194)(25 87 76 48 151 105 36)(26 37 106 152 41 77 88)(27 81 78 42 145 107 38)(28 39 108 146 43 79 82)(29 83 80 44 147 109 40)(30 33 110 148 45 73 84)(31 85 74 46 149 111 34)(32 35 112 150 47 75 86)(49 207 104 93 161 63 66)(50 67 64 162 94 97 208)(51 201 98 95 163 57 68)(52 69 58 164 96 99 202)(53 203 100 89 165 59 70)(54 71 60 166 90 101 204)(55 205 102 91 167 61 72)(56 65 62 168 92 103 206)
(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)(2 154 48 167)(3 157 41 162)(4 160 42 165)(5 155 43 168)(6 158 44 163)(7 153 45 166)(8 156 46 161)(9 111 104 213)(10 106 97 216)(11 109 98 211)(12 112 99 214)(13 107 100 209)(14 110 101 212)(15 105 102 215)(16 108 103 210)(17 77 64 178)(18 80 57 181)(19 75 58 184)(20 78 59 179)(21 73 60 182)(22 76 61 177)(23 79 62 180)(24 74 63 183)(25 55 127 144)(26 50 128 139)(27 53 121 142)(28 56 122 137)(29 51 123 140)(30 54 124 143)(31 49 125 138)(32 52 126 141)(33 204 113 132)(34 207 114 135)(35 202 115 130)(36 205 116 133)(37 208 117 136)(38 203 118 131)(39 206 119 134)(40 201 120 129)(65 191 173 82)(66 186 174 85)(67 189 175 88)(68 192 176 83)(69 187 169 86)(70 190 170 81)(71 185 171 84)(72 188 172 87)(89 220 199 145)(90 223 200 148)(91 218 193 151)(92 221 194 146)(93 224 195 149)(94 219 196 152)(95 222 197 147)(96 217 198 150)
(9 104)(10 97)(11 98)(12 99)(13 100)(14 101)(15 102)(16 103)(17 64)(18 57)(19 58)(20 59)(21 60)(22 61)(23 62)(24 63)(49 138)(50 139)(51 140)(52 141)(53 142)(54 143)(55 144)(56 137)(65 173)(66 174)(67 175)(68 176)(69 169)(70 170)(71 171)(72 172)(89 199)(90 200)(91 193)(92 194)(93 195)(94 196)(95 197)(96 198)(129 201)(130 202)(131 203)(132 204)(133 205)(134 206)(135 207)(136 208)(153 166)(154 167)(155 168)(156 161)(157 162)(158 163)(159 164)(160 165)
G:=sub<Sym(224)| (1,184,187,126,115,214,217)(2,218,215,116,127,188,177)(3,178,189,128,117,216,219)(4,220,209,118,121,190,179)(5,180,191,122,119,210,221)(6,222,211,120,123,192,181)(7,182,185,124,113,212,223)(8,224,213,114,125,186,183)(9,195,156,24,174,138,135)(10,136,139,175,17,157,196)(11,197,158,18,176,140,129)(12,130,141,169,19,159,198)(13,199,160,20,170,142,131)(14,132,143,171,21,153,200)(15,193,154,22,172,144,133)(16,134,137,173,23,155,194)(25,87,76,48,151,105,36)(26,37,106,152,41,77,88)(27,81,78,42,145,107,38)(28,39,108,146,43,79,82)(29,83,80,44,147,109,40)(30,33,110,148,45,73,84)(31,85,74,46,149,111,34)(32,35,112,150,47,75,86)(49,207,104,93,161,63,66)(50,67,64,162,94,97,208)(51,201,98,95,163,57,68)(52,69,58,164,96,99,202)(53,203,100,89,165,59,70)(54,71,60,166,90,101,204)(55,205,102,91,167,61,72)(56,65,62,168,92,103,206), (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)(2,154,48,167)(3,157,41,162)(4,160,42,165)(5,155,43,168)(6,158,44,163)(7,153,45,166)(8,156,46,161)(9,111,104,213)(10,106,97,216)(11,109,98,211)(12,112,99,214)(13,107,100,209)(14,110,101,212)(15,105,102,215)(16,108,103,210)(17,77,64,178)(18,80,57,181)(19,75,58,184)(20,78,59,179)(21,73,60,182)(22,76,61,177)(23,79,62,180)(24,74,63,183)(25,55,127,144)(26,50,128,139)(27,53,121,142)(28,56,122,137)(29,51,123,140)(30,54,124,143)(31,49,125,138)(32,52,126,141)(33,204,113,132)(34,207,114,135)(35,202,115,130)(36,205,116,133)(37,208,117,136)(38,203,118,131)(39,206,119,134)(40,201,120,129)(65,191,173,82)(66,186,174,85)(67,189,175,88)(68,192,176,83)(69,187,169,86)(70,190,170,81)(71,185,171,84)(72,188,172,87)(89,220,199,145)(90,223,200,148)(91,218,193,151)(92,221,194,146)(93,224,195,149)(94,219,196,152)(95,222,197,147)(96,217,198,150), (9,104)(10,97)(11,98)(12,99)(13,100)(14,101)(15,102)(16,103)(17,64)(18,57)(19,58)(20,59)(21,60)(22,61)(23,62)(24,63)(49,138)(50,139)(51,140)(52,141)(53,142)(54,143)(55,144)(56,137)(65,173)(66,174)(67,175)(68,176)(69,169)(70,170)(71,171)(72,172)(89,199)(90,200)(91,193)(92,194)(93,195)(94,196)(95,197)(96,198)(129,201)(130,202)(131,203)(132,204)(133,205)(134,206)(135,207)(136,208)(153,166)(154,167)(155,168)(156,161)(157,162)(158,163)(159,164)(160,165)>;
G:=Group( (1,184,187,126,115,214,217)(2,218,215,116,127,188,177)(3,178,189,128,117,216,219)(4,220,209,118,121,190,179)(5,180,191,122,119,210,221)(6,222,211,120,123,192,181)(7,182,185,124,113,212,223)(8,224,213,114,125,186,183)(9,195,156,24,174,138,135)(10,136,139,175,17,157,196)(11,197,158,18,176,140,129)(12,130,141,169,19,159,198)(13,199,160,20,170,142,131)(14,132,143,171,21,153,200)(15,193,154,22,172,144,133)(16,134,137,173,23,155,194)(25,87,76,48,151,105,36)(26,37,106,152,41,77,88)(27,81,78,42,145,107,38)(28,39,108,146,43,79,82)(29,83,80,44,147,109,40)(30,33,110,148,45,73,84)(31,85,74,46,149,111,34)(32,35,112,150,47,75,86)(49,207,104,93,161,63,66)(50,67,64,162,94,97,208)(51,201,98,95,163,57,68)(52,69,58,164,96,99,202)(53,203,100,89,165,59,70)(54,71,60,166,90,101,204)(55,205,102,91,167,61,72)(56,65,62,168,92,103,206), (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)(2,154,48,167)(3,157,41,162)(4,160,42,165)(5,155,43,168)(6,158,44,163)(7,153,45,166)(8,156,46,161)(9,111,104,213)(10,106,97,216)(11,109,98,211)(12,112,99,214)(13,107,100,209)(14,110,101,212)(15,105,102,215)(16,108,103,210)(17,77,64,178)(18,80,57,181)(19,75,58,184)(20,78,59,179)(21,73,60,182)(22,76,61,177)(23,79,62,180)(24,74,63,183)(25,55,127,144)(26,50,128,139)(27,53,121,142)(28,56,122,137)(29,51,123,140)(30,54,124,143)(31,49,125,138)(32,52,126,141)(33,204,113,132)(34,207,114,135)(35,202,115,130)(36,205,116,133)(37,208,117,136)(38,203,118,131)(39,206,119,134)(40,201,120,129)(65,191,173,82)(66,186,174,85)(67,189,175,88)(68,192,176,83)(69,187,169,86)(70,190,170,81)(71,185,171,84)(72,188,172,87)(89,220,199,145)(90,223,200,148)(91,218,193,151)(92,221,194,146)(93,224,195,149)(94,219,196,152)(95,222,197,147)(96,217,198,150), (9,104)(10,97)(11,98)(12,99)(13,100)(14,101)(15,102)(16,103)(17,64)(18,57)(19,58)(20,59)(21,60)(22,61)(23,62)(24,63)(49,138)(50,139)(51,140)(52,141)(53,142)(54,143)(55,144)(56,137)(65,173)(66,174)(67,175)(68,176)(69,169)(70,170)(71,171)(72,172)(89,199)(90,200)(91,193)(92,194)(93,195)(94,196)(95,197)(96,198)(129,201)(130,202)(131,203)(132,204)(133,205)(134,206)(135,207)(136,208)(153,166)(154,167)(155,168)(156,161)(157,162)(158,163)(159,164)(160,165) );
G=PermutationGroup([[(1,184,187,126,115,214,217),(2,218,215,116,127,188,177),(3,178,189,128,117,216,219),(4,220,209,118,121,190,179),(5,180,191,122,119,210,221),(6,222,211,120,123,192,181),(7,182,185,124,113,212,223),(8,224,213,114,125,186,183),(9,195,156,24,174,138,135),(10,136,139,175,17,157,196),(11,197,158,18,176,140,129),(12,130,141,169,19,159,198),(13,199,160,20,170,142,131),(14,132,143,171,21,153,200),(15,193,154,22,172,144,133),(16,134,137,173,23,155,194),(25,87,76,48,151,105,36),(26,37,106,152,41,77,88),(27,81,78,42,145,107,38),(28,39,108,146,43,79,82),(29,83,80,44,147,109,40),(30,33,110,148,45,73,84),(31,85,74,46,149,111,34),(32,35,112,150,47,75,86),(49,207,104,93,161,63,66),(50,67,64,162,94,97,208),(51,201,98,95,163,57,68),(52,69,58,164,96,99,202),(53,203,100,89,165,59,70),(54,71,60,166,90,101,204),(55,205,102,91,167,61,72),(56,65,62,168,92,103,206)], [(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),(2,154,48,167),(3,157,41,162),(4,160,42,165),(5,155,43,168),(6,158,44,163),(7,153,45,166),(8,156,46,161),(9,111,104,213),(10,106,97,216),(11,109,98,211),(12,112,99,214),(13,107,100,209),(14,110,101,212),(15,105,102,215),(16,108,103,210),(17,77,64,178),(18,80,57,181),(19,75,58,184),(20,78,59,179),(21,73,60,182),(22,76,61,177),(23,79,62,180),(24,74,63,183),(25,55,127,144),(26,50,128,139),(27,53,121,142),(28,56,122,137),(29,51,123,140),(30,54,124,143),(31,49,125,138),(32,52,126,141),(33,204,113,132),(34,207,114,135),(35,202,115,130),(36,205,116,133),(37,208,117,136),(38,203,118,131),(39,206,119,134),(40,201,120,129),(65,191,173,82),(66,186,174,85),(67,189,175,88),(68,192,176,83),(69,187,169,86),(70,190,170,81),(71,185,171,84),(72,188,172,87),(89,220,199,145),(90,223,200,148),(91,218,193,151),(92,221,194,146),(93,224,195,149),(94,219,196,152),(95,222,197,147),(96,217,198,150)], [(9,104),(10,97),(11,98),(12,99),(13,100),(14,101),(15,102),(16,103),(17,64),(18,57),(19,58),(20,59),(21,60),(22,61),(23,62),(24,63),(49,138),(50,139),(51,140),(52,141),(53,142),(54,143),(55,144),(56,137),(65,173),(66,174),(67,175),(68,176),(69,169),(70,170),(71,171),(72,172),(89,199),(90,200),(91,193),(92,194),(93,195),(94,196),(95,197),(96,198),(129,201),(130,202),(131,203),(132,204),(133,205),(134,206),(135,207),(136,208),(153,166),(154,167),(155,168),(156,161),(157,162),(158,163),(159,164),(160,165)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 7A | 7B | 7C | 8A | ··· | 8H | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 56 | 2 | 2 | 2 | 2 | 8 | 8 | 56 | 2 | 2 | 2 | 14 | ··· | 14 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | ||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D7 | C4○D4 | SD16 | D14 | D14 | D14 | C4○D8 | C7⋊D4 | C7⋊D4 | D4×D7 | D4⋊2D7 | Q8⋊D7 | D4.8D14 |
| kernel | C7⋊C8⋊24D4 | C4.Dic14 | C14.D8 | Q8⋊Dic7 | C22×C7⋊C8 | C28⋊7D4 | C2×Q8⋊D7 | C7×C22⋊Q8 | C7⋊C8 | C2×C28 | C22×C14 | C22⋊Q8 | C28 | C2×C14 | C4⋊C4 | C22×C4 | C2×Q8 | C14 | C2×C4 | C23 | C4 | C4 | C22 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 3 | 2 | 4 | 3 | 3 | 3 | 4 | 6 | 6 | 3 | 3 | 6 | 6 |
Matrix representation of C7⋊C8⋊24D4 ►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 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 18 | 0 | 0 | 0 | 0 | 0 |
| 0 | 69 | 0 | 0 | 0 | 0 |
| 0 | 0 | 103 | 103 | 0 | 0 |
| 0 | 0 | 89 | 10 | 0 | 0 |
| 0 | 0 | 0 | 0 | 69 | 0 |
| 0 | 0 | 0 | 0 | 49 | 18 |
| 0 | 69 | 0 | 0 | 0 | 0 |
| 18 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 103 | 103 | 0 | 0 |
| 0 | 0 | 89 | 10 | 0 | 0 |
| 0 | 0 | 0 | 0 | 54 | 96 |
| 0 | 0 | 0 | 0 | 105 | 59 |
| 1 | 0 | 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 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(6,GF(113))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,24,1,0,0,0,0,112,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[18,0,0,0,0,0,0,69,0,0,0,0,0,0,103,89,0,0,0,0,103,10,0,0,0,0,0,0,69,49,0,0,0,0,0,18],[0,18,0,0,0,0,69,0,0,0,0,0,0,0,103,89,0,0,0,0,103,10,0,0,0,0,0,0,54,105,0,0,0,0,96,59],[1,0,0,0,0,0,0,112,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1] >;
C7⋊C8⋊24D4 in GAP, Magma, Sage, TeX
C_7\rtimes C_8\rtimes_{24}D_4 % in TeX
G:=Group("C7:C8:24D4"); // GroupNames label
G:=SmallGroup(448,582);
// by ID
G=gap.SmallGroup(448,582);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,254,219,184,1123,297,136,18822]);
// 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,b*d=d*b,d*c*d=c^-1>;
// generators/relations