metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C7⋊C8.29D4, (C2×C14)⋊3Q16, C4⋊C4.70D14, C4.176(D4×D7), C22⋊Q8.6D7, (C2×C28).268D4, C28.157(C2×D4), C7⋊3(C8.18D4), (C2×Q8).32D14, C14.39(C2×Q16), Q8⋊Dic7⋊17C2, C28.Q8⋊41C2, C14.Q16⋊39C2, C22⋊1(C7⋊Q16), (C22×C14).97D4, C28.192(C4○D4), C14.102(C4○D8), C4.65(D4⋊2D7), C14.99(C4⋊D4), (C2×C28).370C23, (C22×C4).343D14, C23.42(C7⋊D4), (Q8×C14).50C22, C28.48D4.12C2, C4⋊Dic7.148C22, C2.20(Dic7⋊D4), C2.21(D4.8D14), (C22×C28).174C22, (C2×Dic14).105C22, (C22×C7⋊C8).9C2, (C2×C7⋊Q16)⋊10C2, C2.10(C2×C7⋊Q16), (C7×C22⋊Q8).5C2, (C2×C14).501(C2×D4), (C2×C7⋊C8).251C22, (C2×C4).108(C7⋊D4), (C7×C4⋊C4).117C22, (C2×C4).470(C22×D7), C22.176(C2×C7⋊D4), SmallGroup(448,585)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C7⋊C8.29D4
G = < a,b,c,d | a7=b8=c4=d2=1, bab-1=cac-1=a-1, ad=da, cbc-1=b-1, bd=db, dcd=b4c-1 >
Subgroups: 444 in 114 conjugacy classes, 45 normal (39 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, Q8, C23, C14, C14, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, Q16, C22×C4, C2×Q8, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C2×C14, Q8⋊C4, C2.D8, C22⋊Q8, C22⋊Q8, C22×C8, C2×Q16, C7⋊C8, C7⋊C8, Dic14, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×C14, C8.18D4, C2×C7⋊C8, C2×C7⋊C8, Dic7⋊C4, C4⋊Dic7, C7⋊Q16, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C22×C28, Q8×C14, C28.Q8, C14.Q16, Q8⋊Dic7, C22×C7⋊C8, C28.48D4, C2×C7⋊Q16, C7×C22⋊Q8, C7⋊C8.29D4
Quotients: C1, C2, C22, D4, C23, D7, Q16, C2×D4, C4○D4, D14, C4⋊D4, C2×Q16, C4○D8, C7⋊D4, C22×D7, C8.18D4, C7⋊Q16, D4×D7, D4⋊2D7, C2×C7⋊D4, Dic7⋊D4, C2×C7⋊Q16, D4.8D14, C7⋊C8.29D4
►On 224 points
Generators in S224
(1 184 33 108 77 28 214)(2 215 29 78 109 34 177)(3 178 35 110 79 30 216)(4 209 31 80 111 36 179)(5 180 37 112 73 32 210)(6 211 25 74 105 38 181)(7 182 39 106 75 26 212)(8 213 27 76 107 40 183)(9 195 160 20 170 104 57)(10 58 97 171 21 153 196)(11 197 154 22 172 98 59)(12 60 99 173 23 155 198)(13 199 156 24 174 100 61)(14 62 101 175 17 157 200)(15 193 158 18 176 102 63)(16 64 103 169 19 159 194)(41 84 115 219 187 124 148)(42 149 125 188 220 116 85)(43 86 117 221 189 126 150)(44 151 127 190 222 118 87)(45 88 119 223 191 128 152)(46 145 121 192 224 120 81)(47 82 113 217 185 122 146)(48 147 123 186 218 114 83)(49 207 138 93 165 66 133)(50 134 67 166 94 139 208)(51 201 140 95 167 68 135)(52 136 69 168 96 141 202)(53 203 142 89 161 70 129)(54 130 71 162 90 143 204)(55 205 144 91 163 72 131)(56 132 65 164 92 137 206)
(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)(2 154 44 163)(3 153 45 162)(4 160 46 161)(5 159 47 168)(6 158 48 167)(7 157 41 166)(8 156 42 165)(9 121 142 31)(10 128 143 30)(11 127 144 29)(12 126 137 28)(13 125 138 27)(14 124 139 26)(15 123 140 25)(16 122 141 32)(17 84 67 182)(18 83 68 181)(19 82 69 180)(20 81 70 179)(21 88 71 178)(22 87 72 177)(23 86 65 184)(24 85 66 183)(33 173 117 132)(34 172 118 131)(35 171 119 130)(36 170 120 129)(37 169 113 136)(38 176 114 135)(39 175 115 134)(40 174 116 133)(49 107 100 220)(50 106 101 219)(51 105 102 218)(52 112 103 217)(53 111 104 224)(54 110 97 223)(55 109 98 222)(56 108 99 221)(57 192 203 80)(58 191 204 79)(59 190 205 78)(60 189 206 77)(61 188 207 76)(62 187 208 75)(63 186 201 74)(64 185 202 73)(89 209 195 145)(90 216 196 152)(91 215 197 151)(92 214 198 150)(93 213 199 149)(94 212 200 148)(95 211 193 147)(96 210 194 146)
(9 138)(10 139)(11 140)(12 141)(13 142)(14 143)(15 144)(16 137)(17 71)(18 72)(19 65)(20 66)(21 67)(22 68)(23 69)(24 70)(49 104)(50 97)(51 98)(52 99)(53 100)(54 101)(55 102)(56 103)(57 207)(58 208)(59 201)(60 202)(61 203)(62 204)(63 205)(64 206)(89 199)(90 200)(91 193)(92 194)(93 195)(94 196)(95 197)(96 198)(129 174)(130 175)(131 176)(132 169)(133 170)(134 171)(135 172)(136 173)(153 166)(154 167)(155 168)(156 161)(157 162)(158 163)(159 164)(160 165)
G:=sub<Sym(224)| (1,184,33,108,77,28,214)(2,215,29,78,109,34,177)(3,178,35,110,79,30,216)(4,209,31,80,111,36,179)(5,180,37,112,73,32,210)(6,211,25,74,105,38,181)(7,182,39,106,75,26,212)(8,213,27,76,107,40,183)(9,195,160,20,170,104,57)(10,58,97,171,21,153,196)(11,197,154,22,172,98,59)(12,60,99,173,23,155,198)(13,199,156,24,174,100,61)(14,62,101,175,17,157,200)(15,193,158,18,176,102,63)(16,64,103,169,19,159,194)(41,84,115,219,187,124,148)(42,149,125,188,220,116,85)(43,86,117,221,189,126,150)(44,151,127,190,222,118,87)(45,88,119,223,191,128,152)(46,145,121,192,224,120,81)(47,82,113,217,185,122,146)(48,147,123,186,218,114,83)(49,207,138,93,165,66,133)(50,134,67,166,94,139,208)(51,201,140,95,167,68,135)(52,136,69,168,96,141,202)(53,203,142,89,161,70,129)(54,130,71,162,90,143,204)(55,205,144,91,163,72,131)(56,132,65,164,92,137,206), (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)(2,154,44,163)(3,153,45,162)(4,160,46,161)(5,159,47,168)(6,158,48,167)(7,157,41,166)(8,156,42,165)(9,121,142,31)(10,128,143,30)(11,127,144,29)(12,126,137,28)(13,125,138,27)(14,124,139,26)(15,123,140,25)(16,122,141,32)(17,84,67,182)(18,83,68,181)(19,82,69,180)(20,81,70,179)(21,88,71,178)(22,87,72,177)(23,86,65,184)(24,85,66,183)(33,173,117,132)(34,172,118,131)(35,171,119,130)(36,170,120,129)(37,169,113,136)(38,176,114,135)(39,175,115,134)(40,174,116,133)(49,107,100,220)(50,106,101,219)(51,105,102,218)(52,112,103,217)(53,111,104,224)(54,110,97,223)(55,109,98,222)(56,108,99,221)(57,192,203,80)(58,191,204,79)(59,190,205,78)(60,189,206,77)(61,188,207,76)(62,187,208,75)(63,186,201,74)(64,185,202,73)(89,209,195,145)(90,216,196,152)(91,215,197,151)(92,214,198,150)(93,213,199,149)(94,212,200,148)(95,211,193,147)(96,210,194,146), (9,138)(10,139)(11,140)(12,141)(13,142)(14,143)(15,144)(16,137)(17,71)(18,72)(19,65)(20,66)(21,67)(22,68)(23,69)(24,70)(49,104)(50,97)(51,98)(52,99)(53,100)(54,101)(55,102)(56,103)(57,207)(58,208)(59,201)(60,202)(61,203)(62,204)(63,205)(64,206)(89,199)(90,200)(91,193)(92,194)(93,195)(94,196)(95,197)(96,198)(129,174)(130,175)(131,176)(132,169)(133,170)(134,171)(135,172)(136,173)(153,166)(154,167)(155,168)(156,161)(157,162)(158,163)(159,164)(160,165)>;
G:=Group( (1,184,33,108,77,28,214)(2,215,29,78,109,34,177)(3,178,35,110,79,30,216)(4,209,31,80,111,36,179)(5,180,37,112,73,32,210)(6,211,25,74,105,38,181)(7,182,39,106,75,26,212)(8,213,27,76,107,40,183)(9,195,160,20,170,104,57)(10,58,97,171,21,153,196)(11,197,154,22,172,98,59)(12,60,99,173,23,155,198)(13,199,156,24,174,100,61)(14,62,101,175,17,157,200)(15,193,158,18,176,102,63)(16,64,103,169,19,159,194)(41,84,115,219,187,124,148)(42,149,125,188,220,116,85)(43,86,117,221,189,126,150)(44,151,127,190,222,118,87)(45,88,119,223,191,128,152)(46,145,121,192,224,120,81)(47,82,113,217,185,122,146)(48,147,123,186,218,114,83)(49,207,138,93,165,66,133)(50,134,67,166,94,139,208)(51,201,140,95,167,68,135)(52,136,69,168,96,141,202)(53,203,142,89,161,70,129)(54,130,71,162,90,143,204)(55,205,144,91,163,72,131)(56,132,65,164,92,137,206), (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)(2,154,44,163)(3,153,45,162)(4,160,46,161)(5,159,47,168)(6,158,48,167)(7,157,41,166)(8,156,42,165)(9,121,142,31)(10,128,143,30)(11,127,144,29)(12,126,137,28)(13,125,138,27)(14,124,139,26)(15,123,140,25)(16,122,141,32)(17,84,67,182)(18,83,68,181)(19,82,69,180)(20,81,70,179)(21,88,71,178)(22,87,72,177)(23,86,65,184)(24,85,66,183)(33,173,117,132)(34,172,118,131)(35,171,119,130)(36,170,120,129)(37,169,113,136)(38,176,114,135)(39,175,115,134)(40,174,116,133)(49,107,100,220)(50,106,101,219)(51,105,102,218)(52,112,103,217)(53,111,104,224)(54,110,97,223)(55,109,98,222)(56,108,99,221)(57,192,203,80)(58,191,204,79)(59,190,205,78)(60,189,206,77)(61,188,207,76)(62,187,208,75)(63,186,201,74)(64,185,202,73)(89,209,195,145)(90,216,196,152)(91,215,197,151)(92,214,198,150)(93,213,199,149)(94,212,200,148)(95,211,193,147)(96,210,194,146), (9,138)(10,139)(11,140)(12,141)(13,142)(14,143)(15,144)(16,137)(17,71)(18,72)(19,65)(20,66)(21,67)(22,68)(23,69)(24,70)(49,104)(50,97)(51,98)(52,99)(53,100)(54,101)(55,102)(56,103)(57,207)(58,208)(59,201)(60,202)(61,203)(62,204)(63,205)(64,206)(89,199)(90,200)(91,193)(92,194)(93,195)(94,196)(95,197)(96,198)(129,174)(130,175)(131,176)(132,169)(133,170)(134,171)(135,172)(136,173)(153,166)(154,167)(155,168)(156,161)(157,162)(158,163)(159,164)(160,165) );
G=PermutationGroup([[(1,184,33,108,77,28,214),(2,215,29,78,109,34,177),(3,178,35,110,79,30,216),(4,209,31,80,111,36,179),(5,180,37,112,73,32,210),(6,211,25,74,105,38,181),(7,182,39,106,75,26,212),(8,213,27,76,107,40,183),(9,195,160,20,170,104,57),(10,58,97,171,21,153,196),(11,197,154,22,172,98,59),(12,60,99,173,23,155,198),(13,199,156,24,174,100,61),(14,62,101,175,17,157,200),(15,193,158,18,176,102,63),(16,64,103,169,19,159,194),(41,84,115,219,187,124,148),(42,149,125,188,220,116,85),(43,86,117,221,189,126,150),(44,151,127,190,222,118,87),(45,88,119,223,191,128,152),(46,145,121,192,224,120,81),(47,82,113,217,185,122,146),(48,147,123,186,218,114,83),(49,207,138,93,165,66,133),(50,134,67,166,94,139,208),(51,201,140,95,167,68,135),(52,136,69,168,96,141,202),(53,203,142,89,161,70,129),(54,130,71,162,90,143,204),(55,205,144,91,163,72,131),(56,132,65,164,92,137,206)], [(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),(2,154,44,163),(3,153,45,162),(4,160,46,161),(5,159,47,168),(6,158,48,167),(7,157,41,166),(8,156,42,165),(9,121,142,31),(10,128,143,30),(11,127,144,29),(12,126,137,28),(13,125,138,27),(14,124,139,26),(15,123,140,25),(16,122,141,32),(17,84,67,182),(18,83,68,181),(19,82,69,180),(20,81,70,179),(21,88,71,178),(22,87,72,177),(23,86,65,184),(24,85,66,183),(33,173,117,132),(34,172,118,131),(35,171,119,130),(36,170,120,129),(37,169,113,136),(38,176,114,135),(39,175,115,134),(40,174,116,133),(49,107,100,220),(50,106,101,219),(51,105,102,218),(52,112,103,217),(53,111,104,224),(54,110,97,223),(55,109,98,222),(56,108,99,221),(57,192,203,80),(58,191,204,79),(59,190,205,78),(60,189,206,77),(61,188,207,76),(62,187,208,75),(63,186,201,74),(64,185,202,73),(89,209,195,145),(90,216,196,152),(91,215,197,151),(92,214,198,150),(93,213,199,149),(94,212,200,148),(95,211,193,147),(96,210,194,146)], [(9,138),(10,139),(11,140),(12,141),(13,142),(14,143),(15,144),(16,137),(17,71),(18,72),(19,65),(20,66),(21,67),(22,68),(23,69),(24,70),(49,104),(50,97),(51,98),(52,99),(53,100),(54,101),(55,102),(56,103),(57,207),(58,208),(59,201),(60,202),(61,203),(62,204),(63,205),(64,206),(89,199),(90,200),(91,193),(92,194),(93,195),(94,196),(95,197),(96,198),(129,174),(130,175),(131,176),(132,169),(133,170),(134,171),(135,172),(136,173),(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 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 7A | 7B | 7C | 8A | ··· | 8H | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 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 | 2 | 2 | 2 | 2 | 8 | 8 | 56 | 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 | Q16 | D14 | D14 | D14 | C4○D8 | C7⋊D4 | C7⋊D4 | D4×D7 | D4⋊2D7 | C7⋊Q16 | D4.8D14 |
| kernel | C7⋊C8.29D4 | C28.Q8 | C14.Q16 | Q8⋊Dic7 | C22×C7⋊C8 | C28.48D4 | C2×C7⋊Q16 | 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⋊C8.29D4 ►in GL6(𝔽113)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 112 | 0 | 0 |
| 0 | 0 | 26 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 69 | 0 | 0 | 0 | 0 | 0 |
| 0 | 95 | 0 | 0 | 0 | 0 |
| 0 | 0 | 44 | 28 | 0 | 0 |
| 0 | 0 | 64 | 69 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 0 | 95 | 0 | 0 | 0 | 0 |
| 69 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 53 | 31 | 0 | 0 |
| 0 | 0 | 37 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 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 | 112 |
G:=sub<GL(6,GF(113))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,25,26,0,0,0,0,112,112,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[69,0,0,0,0,0,0,95,0,0,0,0,0,0,44,64,0,0,0,0,28,69,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[0,69,0,0,0,0,95,0,0,0,0,0,0,0,53,37,0,0,0,0,31,60,0,0,0,0,0,0,0,112,0,0,0,0,1,0],[1,0,0,0,0,0,0,112,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,112] >;
C7⋊C8.29D4 in GAP, Magma, Sage, TeX
C_7\rtimes C_8._{29}D_4 % in TeX
G:=Group("C7:C8.29D4"); // GroupNames label
G:=SmallGroup(448,585);
// by ID
G=gap.SmallGroup(448,585);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,253,254,219,184,1123,297,136,18822]);
// 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^-1,b*d=d*b,d*c*d=b^4*c^-1>;
// generators/relations