metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C7⋊C8⋊23D4, C7⋊4(C8⋊8D4), C4⋊C4.61D14, (C2×C14)⋊4SD16, C4⋊D4.6D7, C4.172(D4×D7), (C2×D4).41D14, (C2×C28).264D4, C28.150(C2×D4), C14.98(C4○D8), C14.Q16⋊35C2, D4⋊Dic7⋊17C2, C22⋊1(D4.D7), C4.Dic14⋊36C2, C14.56(C2×SD16), (C22×C14).87D4, C28.185(C4○D4), C28.48D4⋊24C2, C4.61(D4⋊2D7), C14.95(C4⋊D4), (C2×C28).360C23, (D4×C14).57C22, (C22×C4).341D14, C23.40(C7⋊D4), C4⋊Dic7.144C22, C2.16(Dic7⋊D4), C2.17(D4.8D14), (C22×C28).164C22, (C2×Dic14).103C22, (C22×C7⋊C8)⋊4C2, (C2×D4.D7)⋊10C2, (C7×C4⋊D4).5C2, C2.10(C2×D4.D7), (C2×C14).491(C2×D4), (C2×C7⋊C8).249C22, (C2×C4).106(C7⋊D4), (C7×C4⋊C4).108C22, (C2×C4).460(C22×D7), C22.166(C2×C7⋊D4), SmallGroup(448,575)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C7⋊C8⋊23D4
G = < a,b,c,d | a7=b8=c4=d2=1, bab-1=a-1, ac=ca, ad=da, cbc-1=b3, bd=db, dcd=c-1 >
Subgroups: 492 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, C14, C14, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, SD16, C22×C4, C2×D4, C2×D4, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C2×C14, D4⋊C4, Q8⋊C4, C4.Q8, C4⋊D4, C22⋊Q8, C22×C8, C2×SD16, C7⋊C8, C7⋊C8, Dic14, C2×Dic7, C2×C28, C2×C28, C7×D4, C22×C14, C22×C14, C8⋊8D4, C2×C7⋊C8, C2×C7⋊C8, Dic7⋊C4, C4⋊Dic7, D4.D7, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C22×C28, D4×C14, D4×C14, C4.Dic14, C14.Q16, D4⋊Dic7, C22×C7⋊C8, C28.48D4, C2×D4.D7, C7×C4⋊D4, C7⋊C8⋊23D4
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, D4.D7, D4×D7, D4⋊2D7, C2×C7⋊D4, C2×D4.D7, Dic7⋊D4, D4.8D14, C7⋊C8⋊23D4
►On 224 points
Generators in S224
(1 184 26 77 115 39 217)(2 218 40 116 78 27 177)(3 178 28 79 117 33 219)(4 220 34 118 80 29 179)(5 180 30 73 119 35 221)(6 222 36 120 74 31 181)(7 182 32 75 113 37 223)(8 224 38 114 76 25 183)(9 195 160 24 174 93 61)(10 62 94 175 17 153 196)(11 197 154 18 176 95 63)(12 64 96 169 19 155 198)(13 199 156 20 170 89 57)(14 58 90 171 21 157 200)(15 193 158 22 172 91 59)(16 60 92 173 23 159 194)(41 84 122 216 191 106 152)(42 145 107 192 209 123 85)(43 86 124 210 185 108 146)(44 147 109 186 211 125 87)(45 88 126 212 187 110 148)(46 149 111 188 213 127 81)(47 82 128 214 189 112 150)(48 151 105 190 215 121 83)(49 207 135 104 161 66 140)(50 141 67 162 97 136 208)(51 201 129 98 163 68 142)(52 143 69 164 99 130 202)(53 203 131 100 165 70 144)(54 137 71 166 101 132 204)(55 205 133 102 167 72 138)(56 139 65 168 103 134 206)
(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)
(1 156 47 165)(2 159 48 168)(3 154 41 163)(4 157 42 166)(5 160 43 161)(6 155 44 164)(7 158 45 167)(8 153 46 162)(9 108 135 35)(10 111 136 38)(11 106 129 33)(12 109 130 36)(13 112 131 39)(14 107 132 34)(15 110 133 37)(16 105 134 40)(17 81 67 183)(18 84 68 178)(19 87 69 181)(20 82 70 184)(21 85 71 179)(22 88 72 182)(23 83 65 177)(24 86 66 180)(25 175 127 141)(26 170 128 144)(27 173 121 139)(28 176 122 142)(29 171 123 137)(30 174 124 140)(31 169 125 143)(32 172 126 138)(49 73 93 210)(50 76 94 213)(51 79 95 216)(52 74 96 211)(53 77 89 214)(54 80 90 209)(55 75 91 212)(56 78 92 215)(57 189 203 115)(58 192 204 118)(59 187 205 113)(60 190 206 116)(61 185 207 119)(62 188 208 114)(63 191 201 117)(64 186 202 120)(97 224 196 149)(98 219 197 152)(99 222 198 147)(100 217 199 150)(101 220 200 145)(102 223 193 148)(103 218 194 151)(104 221 195 146)
(9 135)(10 136)(11 129)(12 130)(13 131)(14 132)(15 133)(16 134)(17 67)(18 68)(19 69)(20 70)(21 71)(22 72)(23 65)(24 66)(49 93)(50 94)(51 95)(52 96)(53 89)(54 90)(55 91)(56 92)(57 203)(58 204)(59 205)(60 206)(61 207)(62 208)(63 201)(64 202)(97 196)(98 197)(99 198)(100 199)(101 200)(102 193)(103 194)(104 195)(137 171)(138 172)(139 173)(140 174)(141 175)(142 176)(143 169)(144 170)(153 162)(154 163)(155 164)(156 165)(157 166)(158 167)(159 168)(160 161)
G:=sub<Sym(224)| (1,184,26,77,115,39,217)(2,218,40,116,78,27,177)(3,178,28,79,117,33,219)(4,220,34,118,80,29,179)(5,180,30,73,119,35,221)(6,222,36,120,74,31,181)(7,182,32,75,113,37,223)(8,224,38,114,76,25,183)(9,195,160,24,174,93,61)(10,62,94,175,17,153,196)(11,197,154,18,176,95,63)(12,64,96,169,19,155,198)(13,199,156,20,170,89,57)(14,58,90,171,21,157,200)(15,193,158,22,172,91,59)(16,60,92,173,23,159,194)(41,84,122,216,191,106,152)(42,145,107,192,209,123,85)(43,86,124,210,185,108,146)(44,147,109,186,211,125,87)(45,88,126,212,187,110,148)(46,149,111,188,213,127,81)(47,82,128,214,189,112,150)(48,151,105,190,215,121,83)(49,207,135,104,161,66,140)(50,141,67,162,97,136,208)(51,201,129,98,163,68,142)(52,143,69,164,99,130,202)(53,203,131,100,165,70,144)(54,137,71,166,101,132,204)(55,205,133,102,167,72,138)(56,139,65,168,103,134,206), (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), (1,156,47,165)(2,159,48,168)(3,154,41,163)(4,157,42,166)(5,160,43,161)(6,155,44,164)(7,158,45,167)(8,153,46,162)(9,108,135,35)(10,111,136,38)(11,106,129,33)(12,109,130,36)(13,112,131,39)(14,107,132,34)(15,110,133,37)(16,105,134,40)(17,81,67,183)(18,84,68,178)(19,87,69,181)(20,82,70,184)(21,85,71,179)(22,88,72,182)(23,83,65,177)(24,86,66,180)(25,175,127,141)(26,170,128,144)(27,173,121,139)(28,176,122,142)(29,171,123,137)(30,174,124,140)(31,169,125,143)(32,172,126,138)(49,73,93,210)(50,76,94,213)(51,79,95,216)(52,74,96,211)(53,77,89,214)(54,80,90,209)(55,75,91,212)(56,78,92,215)(57,189,203,115)(58,192,204,118)(59,187,205,113)(60,190,206,116)(61,185,207,119)(62,188,208,114)(63,191,201,117)(64,186,202,120)(97,224,196,149)(98,219,197,152)(99,222,198,147)(100,217,199,150)(101,220,200,145)(102,223,193,148)(103,218,194,151)(104,221,195,146), (9,135)(10,136)(11,129)(12,130)(13,131)(14,132)(15,133)(16,134)(17,67)(18,68)(19,69)(20,70)(21,71)(22,72)(23,65)(24,66)(49,93)(50,94)(51,95)(52,96)(53,89)(54,90)(55,91)(56,92)(57,203)(58,204)(59,205)(60,206)(61,207)(62,208)(63,201)(64,202)(97,196)(98,197)(99,198)(100,199)(101,200)(102,193)(103,194)(104,195)(137,171)(138,172)(139,173)(140,174)(141,175)(142,176)(143,169)(144,170)(153,162)(154,163)(155,164)(156,165)(157,166)(158,167)(159,168)(160,161)>;
G:=Group( (1,184,26,77,115,39,217)(2,218,40,116,78,27,177)(3,178,28,79,117,33,219)(4,220,34,118,80,29,179)(5,180,30,73,119,35,221)(6,222,36,120,74,31,181)(7,182,32,75,113,37,223)(8,224,38,114,76,25,183)(9,195,160,24,174,93,61)(10,62,94,175,17,153,196)(11,197,154,18,176,95,63)(12,64,96,169,19,155,198)(13,199,156,20,170,89,57)(14,58,90,171,21,157,200)(15,193,158,22,172,91,59)(16,60,92,173,23,159,194)(41,84,122,216,191,106,152)(42,145,107,192,209,123,85)(43,86,124,210,185,108,146)(44,147,109,186,211,125,87)(45,88,126,212,187,110,148)(46,149,111,188,213,127,81)(47,82,128,214,189,112,150)(48,151,105,190,215,121,83)(49,207,135,104,161,66,140)(50,141,67,162,97,136,208)(51,201,129,98,163,68,142)(52,143,69,164,99,130,202)(53,203,131,100,165,70,144)(54,137,71,166,101,132,204)(55,205,133,102,167,72,138)(56,139,65,168,103,134,206), (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), (1,156,47,165)(2,159,48,168)(3,154,41,163)(4,157,42,166)(5,160,43,161)(6,155,44,164)(7,158,45,167)(8,153,46,162)(9,108,135,35)(10,111,136,38)(11,106,129,33)(12,109,130,36)(13,112,131,39)(14,107,132,34)(15,110,133,37)(16,105,134,40)(17,81,67,183)(18,84,68,178)(19,87,69,181)(20,82,70,184)(21,85,71,179)(22,88,72,182)(23,83,65,177)(24,86,66,180)(25,175,127,141)(26,170,128,144)(27,173,121,139)(28,176,122,142)(29,171,123,137)(30,174,124,140)(31,169,125,143)(32,172,126,138)(49,73,93,210)(50,76,94,213)(51,79,95,216)(52,74,96,211)(53,77,89,214)(54,80,90,209)(55,75,91,212)(56,78,92,215)(57,189,203,115)(58,192,204,118)(59,187,205,113)(60,190,206,116)(61,185,207,119)(62,188,208,114)(63,191,201,117)(64,186,202,120)(97,224,196,149)(98,219,197,152)(99,222,198,147)(100,217,199,150)(101,220,200,145)(102,223,193,148)(103,218,194,151)(104,221,195,146), (9,135)(10,136)(11,129)(12,130)(13,131)(14,132)(15,133)(16,134)(17,67)(18,68)(19,69)(20,70)(21,71)(22,72)(23,65)(24,66)(49,93)(50,94)(51,95)(52,96)(53,89)(54,90)(55,91)(56,92)(57,203)(58,204)(59,205)(60,206)(61,207)(62,208)(63,201)(64,202)(97,196)(98,197)(99,198)(100,199)(101,200)(102,193)(103,194)(104,195)(137,171)(138,172)(139,173)(140,174)(141,175)(142,176)(143,169)(144,170)(153,162)(154,163)(155,164)(156,165)(157,166)(158,167)(159,168)(160,161) );
G=PermutationGroup([[(1,184,26,77,115,39,217),(2,218,40,116,78,27,177),(3,178,28,79,117,33,219),(4,220,34,118,80,29,179),(5,180,30,73,119,35,221),(6,222,36,120,74,31,181),(7,182,32,75,113,37,223),(8,224,38,114,76,25,183),(9,195,160,24,174,93,61),(10,62,94,175,17,153,196),(11,197,154,18,176,95,63),(12,64,96,169,19,155,198),(13,199,156,20,170,89,57),(14,58,90,171,21,157,200),(15,193,158,22,172,91,59),(16,60,92,173,23,159,194),(41,84,122,216,191,106,152),(42,145,107,192,209,123,85),(43,86,124,210,185,108,146),(44,147,109,186,211,125,87),(45,88,126,212,187,110,148),(46,149,111,188,213,127,81),(47,82,128,214,189,112,150),(48,151,105,190,215,121,83),(49,207,135,104,161,66,140),(50,141,67,162,97,136,208),(51,201,129,98,163,68,142),(52,143,69,164,99,130,202),(53,203,131,100,165,70,144),(54,137,71,166,101,132,204),(55,205,133,102,167,72,138),(56,139,65,168,103,134,206)], [(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)], [(1,156,47,165),(2,159,48,168),(3,154,41,163),(4,157,42,166),(5,160,43,161),(6,155,44,164),(7,158,45,167),(8,153,46,162),(9,108,135,35),(10,111,136,38),(11,106,129,33),(12,109,130,36),(13,112,131,39),(14,107,132,34),(15,110,133,37),(16,105,134,40),(17,81,67,183),(18,84,68,178),(19,87,69,181),(20,82,70,184),(21,85,71,179),(22,88,72,182),(23,83,65,177),(24,86,66,180),(25,175,127,141),(26,170,128,144),(27,173,121,139),(28,176,122,142),(29,171,123,137),(30,174,124,140),(31,169,125,143),(32,172,126,138),(49,73,93,210),(50,76,94,213),(51,79,95,216),(52,74,96,211),(53,77,89,214),(54,80,90,209),(55,75,91,212),(56,78,92,215),(57,189,203,115),(58,192,204,118),(59,187,205,113),(60,190,206,116),(61,185,207,119),(62,188,208,114),(63,191,201,117),(64,186,202,120),(97,224,196,149),(98,219,197,152),(99,222,198,147),(100,217,199,150),(101,220,200,145),(102,223,193,148),(103,218,194,151),(104,221,195,146)], [(9,135),(10,136),(11,129),(12,130),(13,131),(14,132),(15,133),(16,134),(17,67),(18,68),(19,69),(20,70),(21,71),(22,72),(23,65),(24,66),(49,93),(50,94),(51,95),(52,96),(53,89),(54,90),(55,91),(56,92),(57,203),(58,204),(59,205),(60,206),(61,207),(62,208),(63,201),(64,202),(97,196),(98,197),(99,198),(100,199),(101,200),(102,193),(103,194),(104,195),(137,171),(138,172),(139,173),(140,174),(141,175),(142,176),(143,169),(144,170),(153,162),(154,163),(155,164),(156,165),(157,166),(158,167),(159,168),(160,161)]])
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 | 14P | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28R |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 8 | 2 | 2 | 2 | 2 | 8 | 56 | 56 | 2 | 2 | 2 | 14 | ··· | 14 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 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 | D4.D7 | D4.8D14 |
| kernel | C7⋊C8⋊23D4 | C4.Dic14 | C14.Q16 | D4⋊Dic7 | C22×C7⋊C8 | C28.48D4 | C2×D4.D7 | C7×C4⋊D4 | C7⋊C8 | C2×C28 | C22×C14 | C4⋊D4 | C28 | C2×C14 | C4⋊C4 | C22×C4 | C2×D4 | 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⋊23D4 ►in GL6(𝔽113)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 88 | 112 | 0 | 0 |
| 0 | 0 | 2 | 104 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 95 | 0 | 0 | 0 | 0 | 0 |
| 30 | 44 | 0 | 0 | 0 | 0 |
| 0 | 0 | 48 | 59 | 0 | 0 |
| 0 | 0 | 28 | 65 | 0 | 0 |
| 0 | 0 | 0 | 0 | 15 | 0 |
| 0 | 0 | 0 | 0 | 105 | 98 |
| 7 | 22 | 0 | 0 | 0 | 0 |
| 8 | 106 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 36 | 22 |
| 0 | 0 | 0 | 0 | 90 | 77 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 61 | 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 | 7 | 112 |
G:=sub<GL(6,GF(113))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,88,2,0,0,0,0,112,104,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[95,30,0,0,0,0,0,44,0,0,0,0,0,0,48,28,0,0,0,0,59,65,0,0,0,0,0,0,15,105,0,0,0,0,0,98],[7,8,0,0,0,0,22,106,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,36,90,0,0,0,0,22,77],[1,61,0,0,0,0,0,112,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,7,0,0,0,0,0,112] >;
C7⋊C8⋊23D4 in GAP, Magma, Sage, TeX
C_7\rtimes C_8\rtimes_{23}D_4 % in TeX
G:=Group("C7:C8:23D4"); // GroupNames label
G:=SmallGroup(448,575);
// by ID
G=gap.SmallGroup(448,575);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,253,254,219,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^7=b^8=c^4=d^2=1,b*a*b^-1=a^-1,a*c=c*a,a*d=d*a,c*b*c^-1=b^3,b*d=d*b,d*c*d=c^-1>;
// generators/relations