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## G = (C2×C28)⋊5D4order 448 = 26·7

### 1st semidirect product of C2×C28 and D4 acting via D4/C2=C22

Series: Derived Chief Lower central Upper central

 Derived series C1 — C22×C14 — (C2×C28)⋊5D4
 Chief series C1 — C7 — C14 — C2×C14 — C22×C14 — C23×D7 — C22×D28 — (C2×C28)⋊5D4
 Lower central C7 — C22×C14 — (C2×C28)⋊5D4
 Upper central C1 — C23 — C2.C42

Generators and relations for (C2×C28)⋊5D4
G = < a,b,c,d | a2=b4=c28=d2=1, cbc-1=ab=ba, ac=ca, ad=da, dbd=ab-1, dcd=c-1 >

Subgroups: 2236 in 322 conjugacy classes, 69 normal (12 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C22⋊C4, C22×C4, C22×C4, C2×D4, C24, Dic7, C28, D14, C2×C14, C2×C14, C2.C42, C2×C22⋊C4, C22×D4, D28, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C232D4, D14⋊C4, C2×D28, C22×Dic7, C22×C28, C23×D7, C7×C2.C42, C2×D14⋊C4, C22×D28, (C2×C28)⋊5D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C22≀C2, C4⋊D4, C41D4, D28, C22×D7, C232D4, C2×D28, D4×D7, Q82D7, C284D4, C22⋊D28, C4⋊D28, (C2×C28)⋊5D4

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

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

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

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

82 conjugacy classes

 class 1 2A ··· 2G 2H ··· 2M 4A ··· 4F 4G 4H 7A 7B 7C 14A ··· 14U 28A ··· 28AJ order 1 2 ··· 2 2 ··· 2 4 ··· 4 4 4 7 7 7 14 ··· 14 28 ··· 28 size 1 1 ··· 1 28 ··· 28 4 ··· 4 28 28 2 2 2 2 ··· 2 4 ··· 4

82 irreducible representations

 dim 1 1 1 1 2 2 2 2 2 2 4 4 type + + + + + + + + + + + image C1 C2 C2 C2 D4 D4 D7 C4○D4 D14 D28 D4×D7 Q8⋊2D7 kernel (C2×C28)⋊5D4 C7×C2.C42 C2×D14⋊C4 C22×D28 C2×C28 C22×D7 C2.C42 C2×C14 C22×C4 C2×C4 C22 C22 # reps 1 1 3 3 6 6 3 2 9 36 9 3

Matrix representation of (C2×C28)⋊5D4 in GL6(𝔽29)

 1 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 28 0 0 0 0 0 0 28
,
 28 0 0 0 0 0 0 28 0 0 0 0 0 0 21 23 0 0 0 0 6 8 0 0 0 0 0 0 0 1 0 0 0 0 28 0
,
 20 25 0 0 0 0 4 21 0 0 0 0 0 0 9 4 0 0 0 0 25 8 0 0 0 0 0 0 21 16 0 0 0 0 16 8
,
 10 7 0 0 0 0 19 19 0 0 0 0 0 0 19 22 0 0 0 0 10 10 0 0 0 0 0 0 28 0 0 0 0 0 0 28

G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,21,6,0,0,0,0,23,8,0,0,0,0,0,0,0,28,0,0,0,0,1,0],[20,4,0,0,0,0,25,21,0,0,0,0,0,0,9,25,0,0,0,0,4,8,0,0,0,0,0,0,21,16,0,0,0,0,16,8],[10,19,0,0,0,0,7,19,0,0,0,0,0,0,19,10,0,0,0,0,22,10,0,0,0,0,0,0,28,0,0,0,0,0,0,28] >;

(C2×C28)⋊5D4 in GAP, Magma, Sage, TeX

(C_2\times C_{28})\rtimes_5D_4
% in TeX

G:=Group("(C2xC28):5D4");
// GroupNames label

G:=SmallGroup(448,205);
// by ID

G=gap.SmallGroup(448,205);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,120,254,387,58,18822]);
// Polycyclic

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

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