Copied to
clipboard

## G = C2×C28⋊D4order 448 = 26·7

### Direct product of C2 and C28⋊D4

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C14 — C2×C28⋊D4
 Chief series C1 — C7 — C14 — C2×C14 — C22×D7 — C23×D7 — C22×D28 — C2×C28⋊D4
 Lower central C7 — C2×C14 — C2×C28⋊D4
 Upper central C1 — C23 — C22×D4

Generators and relations for C2×C28⋊D4
G = < a,b,c,d | a2=b28=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=b13, dbd=b-1, dcd=c-1 >

Subgroups: 2580 in 498 conjugacy classes, 143 normal (15 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, C23, C23, C23, D7, C14, C14, C14, C42, C22×C4, C22×C4, C2×D4, C2×D4, C24, C24, Dic7, C28, D14, C2×C14, C2×C14, C2×C14, C2×C42, C41D4, C22×D4, C22×D4, D28, C2×Dic7, C7⋊D4, C2×C28, C7×D4, C22×D7, C22×D7, C22×C14, C22×C14, C22×C14, C2×C41D4, C4×Dic7, C2×D28, C2×D28, C22×Dic7, C2×C7⋊D4, C2×C7⋊D4, C22×C28, D4×C14, D4×C14, C23×D7, C23×C14, C2×C4×Dic7, C28⋊D4, C22×D28, C22×C7⋊D4, D4×C2×C14, C2×C28⋊D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C24, D14, C41D4, C22×D4, C7⋊D4, C22×D7, C2×C41D4, D4×D7, C2×C7⋊D4, C23×D7, C28⋊D4, C2×D4×D7, C22×C7⋊D4, C2×C28⋊D4

Smallest permutation representation of C2×C28⋊D4
On 224 points
Generators in S224
(1 108)(2 109)(3 110)(4 111)(5 112)(6 85)(7 86)(8 87)(9 88)(10 89)(11 90)(12 91)(13 92)(14 93)(15 94)(16 95)(17 96)(18 97)(19 98)(20 99)(21 100)(22 101)(23 102)(24 103)(25 104)(26 105)(27 106)(28 107)(29 177)(30 178)(31 179)(32 180)(33 181)(34 182)(35 183)(36 184)(37 185)(38 186)(39 187)(40 188)(41 189)(42 190)(43 191)(44 192)(45 193)(46 194)(47 195)(48 196)(49 169)(50 170)(51 171)(52 172)(53 173)(54 174)(55 175)(56 176)(57 120)(58 121)(59 122)(60 123)(61 124)(62 125)(63 126)(64 127)(65 128)(66 129)(67 130)(68 131)(69 132)(70 133)(71 134)(72 135)(73 136)(74 137)(75 138)(76 139)(77 140)(78 113)(79 114)(80 115)(81 116)(82 117)(83 118)(84 119)(141 216)(142 217)(143 218)(144 219)(145 220)(146 221)(147 222)(148 223)(149 224)(150 197)(151 198)(152 199)(153 200)(154 201)(155 202)(156 203)(157 204)(158 205)(159 206)(160 207)(161 208)(162 209)(163 210)(164 211)(165 212)(166 213)(167 214)(168 215)
(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)
(1 206 130 41)(2 219 131 54)(3 204 132 39)(4 217 133 52)(5 202 134 37)(6 215 135 50)(7 200 136 35)(8 213 137 48)(9 198 138 33)(10 211 139 46)(11 224 140 31)(12 209 113 44)(13 222 114 29)(14 207 115 42)(15 220 116 55)(16 205 117 40)(17 218 118 53)(18 203 119 38)(19 216 120 51)(20 201 121 36)(21 214 122 49)(22 199 123 34)(23 212 124 47)(24 197 125 32)(25 210 126 45)(26 223 127 30)(27 208 128 43)(28 221 129 56)(57 171 98 141)(58 184 99 154)(59 169 100 167)(60 182 101 152)(61 195 102 165)(62 180 103 150)(63 193 104 163)(64 178 105 148)(65 191 106 161)(66 176 107 146)(67 189 108 159)(68 174 109 144)(69 187 110 157)(70 172 111 142)(71 185 112 155)(72 170 85 168)(73 183 86 153)(74 196 87 166)(75 181 88 151)(76 194 89 164)(77 179 90 149)(78 192 91 162)(79 177 92 147)(80 190 93 160)(81 175 94 145)(82 188 95 158)(83 173 96 143)(84 186 97 156)
(1 22)(2 21)(3 20)(4 19)(5 18)(6 17)(7 16)(8 15)(9 14)(10 13)(11 12)(23 28)(24 27)(25 26)(29 211)(30 210)(31 209)(32 208)(33 207)(34 206)(35 205)(36 204)(37 203)(38 202)(39 201)(40 200)(41 199)(42 198)(43 197)(44 224)(45 223)(46 222)(47 221)(48 220)(49 219)(50 218)(51 217)(52 216)(53 215)(54 214)(55 213)(56 212)(57 70)(58 69)(59 68)(60 67)(61 66)(62 65)(63 64)(71 84)(72 83)(73 82)(74 81)(75 80)(76 79)(77 78)(85 96)(86 95)(87 94)(88 93)(89 92)(90 91)(97 112)(98 111)(99 110)(100 109)(101 108)(102 107)(103 106)(104 105)(113 140)(114 139)(115 138)(116 137)(117 136)(118 135)(119 134)(120 133)(121 132)(122 131)(123 130)(124 129)(125 128)(126 127)(141 172)(142 171)(143 170)(144 169)(145 196)(146 195)(147 194)(148 193)(149 192)(150 191)(151 190)(152 189)(153 188)(154 187)(155 186)(156 185)(157 184)(158 183)(159 182)(160 181)(161 180)(162 179)(163 178)(164 177)(165 176)(166 175)(167 174)(168 173)

G:=sub<Sym(224)| (1,108)(2,109)(3,110)(4,111)(5,112)(6,85)(7,86)(8,87)(9,88)(10,89)(11,90)(12,91)(13,92)(14,93)(15,94)(16,95)(17,96)(18,97)(19,98)(20,99)(21,100)(22,101)(23,102)(24,103)(25,104)(26,105)(27,106)(28,107)(29,177)(30,178)(31,179)(32,180)(33,181)(34,182)(35,183)(36,184)(37,185)(38,186)(39,187)(40,188)(41,189)(42,190)(43,191)(44,192)(45,193)(46,194)(47,195)(48,196)(49,169)(50,170)(51,171)(52,172)(53,173)(54,174)(55,175)(56,176)(57,120)(58,121)(59,122)(60,123)(61,124)(62,125)(63,126)(64,127)(65,128)(66,129)(67,130)(68,131)(69,132)(70,133)(71,134)(72,135)(73,136)(74,137)(75,138)(76,139)(77,140)(78,113)(79,114)(80,115)(81,116)(82,117)(83,118)(84,119)(141,216)(142,217)(143,218)(144,219)(145,220)(146,221)(147,222)(148,223)(149,224)(150,197)(151,198)(152,199)(153,200)(154,201)(155,202)(156,203)(157,204)(158,205)(159,206)(160,207)(161,208)(162,209)(163,210)(164,211)(165,212)(166,213)(167,214)(168,215), (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), (1,206,130,41)(2,219,131,54)(3,204,132,39)(4,217,133,52)(5,202,134,37)(6,215,135,50)(7,200,136,35)(8,213,137,48)(9,198,138,33)(10,211,139,46)(11,224,140,31)(12,209,113,44)(13,222,114,29)(14,207,115,42)(15,220,116,55)(16,205,117,40)(17,218,118,53)(18,203,119,38)(19,216,120,51)(20,201,121,36)(21,214,122,49)(22,199,123,34)(23,212,124,47)(24,197,125,32)(25,210,126,45)(26,223,127,30)(27,208,128,43)(28,221,129,56)(57,171,98,141)(58,184,99,154)(59,169,100,167)(60,182,101,152)(61,195,102,165)(62,180,103,150)(63,193,104,163)(64,178,105,148)(65,191,106,161)(66,176,107,146)(67,189,108,159)(68,174,109,144)(69,187,110,157)(70,172,111,142)(71,185,112,155)(72,170,85,168)(73,183,86,153)(74,196,87,166)(75,181,88,151)(76,194,89,164)(77,179,90,149)(78,192,91,162)(79,177,92,147)(80,190,93,160)(81,175,94,145)(82,188,95,158)(83,173,96,143)(84,186,97,156), (1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)(23,28)(24,27)(25,26)(29,211)(30,210)(31,209)(32,208)(33,207)(34,206)(35,205)(36,204)(37,203)(38,202)(39,201)(40,200)(41,199)(42,198)(43,197)(44,224)(45,223)(46,222)(47,221)(48,220)(49,219)(50,218)(51,217)(52,216)(53,215)(54,214)(55,213)(56,212)(57,70)(58,69)(59,68)(60,67)(61,66)(62,65)(63,64)(71,84)(72,83)(73,82)(74,81)(75,80)(76,79)(77,78)(85,96)(86,95)(87,94)(88,93)(89,92)(90,91)(97,112)(98,111)(99,110)(100,109)(101,108)(102,107)(103,106)(104,105)(113,140)(114,139)(115,138)(116,137)(117,136)(118,135)(119,134)(120,133)(121,132)(122,131)(123,130)(124,129)(125,128)(126,127)(141,172)(142,171)(143,170)(144,169)(145,196)(146,195)(147,194)(148,193)(149,192)(150,191)(151,190)(152,189)(153,188)(154,187)(155,186)(156,185)(157,184)(158,183)(159,182)(160,181)(161,180)(162,179)(163,178)(164,177)(165,176)(166,175)(167,174)(168,173)>;

G:=Group( (1,108)(2,109)(3,110)(4,111)(5,112)(6,85)(7,86)(8,87)(9,88)(10,89)(11,90)(12,91)(13,92)(14,93)(15,94)(16,95)(17,96)(18,97)(19,98)(20,99)(21,100)(22,101)(23,102)(24,103)(25,104)(26,105)(27,106)(28,107)(29,177)(30,178)(31,179)(32,180)(33,181)(34,182)(35,183)(36,184)(37,185)(38,186)(39,187)(40,188)(41,189)(42,190)(43,191)(44,192)(45,193)(46,194)(47,195)(48,196)(49,169)(50,170)(51,171)(52,172)(53,173)(54,174)(55,175)(56,176)(57,120)(58,121)(59,122)(60,123)(61,124)(62,125)(63,126)(64,127)(65,128)(66,129)(67,130)(68,131)(69,132)(70,133)(71,134)(72,135)(73,136)(74,137)(75,138)(76,139)(77,140)(78,113)(79,114)(80,115)(81,116)(82,117)(83,118)(84,119)(141,216)(142,217)(143,218)(144,219)(145,220)(146,221)(147,222)(148,223)(149,224)(150,197)(151,198)(152,199)(153,200)(154,201)(155,202)(156,203)(157,204)(158,205)(159,206)(160,207)(161,208)(162,209)(163,210)(164,211)(165,212)(166,213)(167,214)(168,215), (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), (1,206,130,41)(2,219,131,54)(3,204,132,39)(4,217,133,52)(5,202,134,37)(6,215,135,50)(7,200,136,35)(8,213,137,48)(9,198,138,33)(10,211,139,46)(11,224,140,31)(12,209,113,44)(13,222,114,29)(14,207,115,42)(15,220,116,55)(16,205,117,40)(17,218,118,53)(18,203,119,38)(19,216,120,51)(20,201,121,36)(21,214,122,49)(22,199,123,34)(23,212,124,47)(24,197,125,32)(25,210,126,45)(26,223,127,30)(27,208,128,43)(28,221,129,56)(57,171,98,141)(58,184,99,154)(59,169,100,167)(60,182,101,152)(61,195,102,165)(62,180,103,150)(63,193,104,163)(64,178,105,148)(65,191,106,161)(66,176,107,146)(67,189,108,159)(68,174,109,144)(69,187,110,157)(70,172,111,142)(71,185,112,155)(72,170,85,168)(73,183,86,153)(74,196,87,166)(75,181,88,151)(76,194,89,164)(77,179,90,149)(78,192,91,162)(79,177,92,147)(80,190,93,160)(81,175,94,145)(82,188,95,158)(83,173,96,143)(84,186,97,156), (1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)(23,28)(24,27)(25,26)(29,211)(30,210)(31,209)(32,208)(33,207)(34,206)(35,205)(36,204)(37,203)(38,202)(39,201)(40,200)(41,199)(42,198)(43,197)(44,224)(45,223)(46,222)(47,221)(48,220)(49,219)(50,218)(51,217)(52,216)(53,215)(54,214)(55,213)(56,212)(57,70)(58,69)(59,68)(60,67)(61,66)(62,65)(63,64)(71,84)(72,83)(73,82)(74,81)(75,80)(76,79)(77,78)(85,96)(86,95)(87,94)(88,93)(89,92)(90,91)(97,112)(98,111)(99,110)(100,109)(101,108)(102,107)(103,106)(104,105)(113,140)(114,139)(115,138)(116,137)(117,136)(118,135)(119,134)(120,133)(121,132)(122,131)(123,130)(124,129)(125,128)(126,127)(141,172)(142,171)(143,170)(144,169)(145,196)(146,195)(147,194)(148,193)(149,192)(150,191)(151,190)(152,189)(153,188)(154,187)(155,186)(156,185)(157,184)(158,183)(159,182)(160,181)(161,180)(162,179)(163,178)(164,177)(165,176)(166,175)(167,174)(168,173) );

G=PermutationGroup([[(1,108),(2,109),(3,110),(4,111),(5,112),(6,85),(7,86),(8,87),(9,88),(10,89),(11,90),(12,91),(13,92),(14,93),(15,94),(16,95),(17,96),(18,97),(19,98),(20,99),(21,100),(22,101),(23,102),(24,103),(25,104),(26,105),(27,106),(28,107),(29,177),(30,178),(31,179),(32,180),(33,181),(34,182),(35,183),(36,184),(37,185),(38,186),(39,187),(40,188),(41,189),(42,190),(43,191),(44,192),(45,193),(46,194),(47,195),(48,196),(49,169),(50,170),(51,171),(52,172),(53,173),(54,174),(55,175),(56,176),(57,120),(58,121),(59,122),(60,123),(61,124),(62,125),(63,126),(64,127),(65,128),(66,129),(67,130),(68,131),(69,132),(70,133),(71,134),(72,135),(73,136),(74,137),(75,138),(76,139),(77,140),(78,113),(79,114),(80,115),(81,116),(82,117),(83,118),(84,119),(141,216),(142,217),(143,218),(144,219),(145,220),(146,221),(147,222),(148,223),(149,224),(150,197),(151,198),(152,199),(153,200),(154,201),(155,202),(156,203),(157,204),(158,205),(159,206),(160,207),(161,208),(162,209),(163,210),(164,211),(165,212),(166,213),(167,214),(168,215)], [(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)], [(1,206,130,41),(2,219,131,54),(3,204,132,39),(4,217,133,52),(5,202,134,37),(6,215,135,50),(7,200,136,35),(8,213,137,48),(9,198,138,33),(10,211,139,46),(11,224,140,31),(12,209,113,44),(13,222,114,29),(14,207,115,42),(15,220,116,55),(16,205,117,40),(17,218,118,53),(18,203,119,38),(19,216,120,51),(20,201,121,36),(21,214,122,49),(22,199,123,34),(23,212,124,47),(24,197,125,32),(25,210,126,45),(26,223,127,30),(27,208,128,43),(28,221,129,56),(57,171,98,141),(58,184,99,154),(59,169,100,167),(60,182,101,152),(61,195,102,165),(62,180,103,150),(63,193,104,163),(64,178,105,148),(65,191,106,161),(66,176,107,146),(67,189,108,159),(68,174,109,144),(69,187,110,157),(70,172,111,142),(71,185,112,155),(72,170,85,168),(73,183,86,153),(74,196,87,166),(75,181,88,151),(76,194,89,164),(77,179,90,149),(78,192,91,162),(79,177,92,147),(80,190,93,160),(81,175,94,145),(82,188,95,158),(83,173,96,143),(84,186,97,156)], [(1,22),(2,21),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,13),(11,12),(23,28),(24,27),(25,26),(29,211),(30,210),(31,209),(32,208),(33,207),(34,206),(35,205),(36,204),(37,203),(38,202),(39,201),(40,200),(41,199),(42,198),(43,197),(44,224),(45,223),(46,222),(47,221),(48,220),(49,219),(50,218),(51,217),(52,216),(53,215),(54,214),(55,213),(56,212),(57,70),(58,69),(59,68),(60,67),(61,66),(62,65),(63,64),(71,84),(72,83),(73,82),(74,81),(75,80),(76,79),(77,78),(85,96),(86,95),(87,94),(88,93),(89,92),(90,91),(97,112),(98,111),(99,110),(100,109),(101,108),(102,107),(103,106),(104,105),(113,140),(114,139),(115,138),(116,137),(117,136),(118,135),(119,134),(120,133),(121,132),(122,131),(123,130),(124,129),(125,128),(126,127),(141,172),(142,171),(143,170),(144,169),(145,196),(146,195),(147,194),(148,193),(149,192),(150,191),(151,190),(152,189),(153,188),(154,187),(155,186),(156,185),(157,184),(158,183),(159,182),(160,181),(161,180),(162,179),(163,178),(164,177),(165,176),(166,175),(167,174),(168,173)]])

88 conjugacy classes

 class 1 2A ··· 2G 2H 2I 2J 2K 2L 2M 2N 2O 4A 4B 4C 4D 4E ··· 4L 7A 7B 7C 14A ··· 14U 14V ··· 14AS 28A ··· 28L order 1 2 ··· 2 2 2 2 2 2 2 2 2 4 4 4 4 4 ··· 4 7 7 7 14 ··· 14 14 ··· 14 28 ··· 28 size 1 1 ··· 1 4 4 4 4 28 28 28 28 2 2 2 2 14 ··· 14 2 2 2 2 ··· 2 4 ··· 4 4 ··· 4

88 irreducible representations

 dim 1 1 1 1 1 1 2 2 2 2 2 2 2 4 type + + + + + + + + + + + + + image C1 C2 C2 C2 C2 C2 D4 D4 D7 D14 D14 D14 C7⋊D4 D4×D7 kernel C2×C28⋊D4 C2×C4×Dic7 C28⋊D4 C22×D28 C22×C7⋊D4 D4×C2×C14 C2×Dic7 C2×C28 C22×D4 C22×C4 C2×D4 C24 C2×C4 C22 # reps 1 1 8 1 4 1 8 4 3 3 12 6 24 12

Matrix representation of C2×C28⋊D4 in GL5(𝔽29)

 28 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 28 0 0 0 0 0 28
,
 28 0 0 0 0 0 10 17 0 0 0 18 22 0 0 0 0 0 1 10 0 0 0 23 28
,
 1 0 0 0 0 0 8 27 0 0 0 18 21 0 0 0 0 0 1 0 0 0 0 0 1
,
 1 0 0 0 0 0 10 17 0 0 0 1 19 0 0 0 0 0 28 19 0 0 0 0 1

G:=sub<GL(5,GF(29))| [28,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,28,0,0,0,0,0,28],[28,0,0,0,0,0,10,18,0,0,0,17,22,0,0,0,0,0,1,23,0,0,0,10,28],[1,0,0,0,0,0,8,18,0,0,0,27,21,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,10,1,0,0,0,17,19,0,0,0,0,0,28,0,0,0,0,19,1] >;

C2×C28⋊D4 in GAP, Magma, Sage, TeX

C_2\times C_{28}\rtimes D_4
% in TeX

G:=Group("C2xC28:D4");
// GroupNames label

G:=SmallGroup(448,1256);
// by ID

G=gap.SmallGroup(448,1256);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,758,184,675,297,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^28=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^13,d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations

׿
×
𝔽