direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C22×D5⋊C8, Dic5.14C24, C5⋊C8⋊4C23, C5⋊1(C23×C8), D5⋊(C22×C8), D10⋊11(C2×C8), C10⋊1(C22×C8), (C22×D5)⋊7C8, C2.1(C23×F5), C10.1(C23×C4), C4.57(C22×F5), C23.64(C2×F5), (C22×C4).28F5, C20.97(C22×C4), (C22×C20).36C4, (C23×D5).17C4, (C4×D5).90C23, D10.43(C22×C4), C22.54(C22×F5), Dic5.43(C22×C4), (C2×Dic5).361C23, (C22×Dic5).281C22, (C2×C10)⋊4(C2×C8), (C2×C4×D5).47C4, (C22×C5⋊C8)⋊11C2, (C2×C5⋊C8)⋊14C22, (C4×D5).96(C2×C4), (C2×C4).172(C2×F5), (D5×C22×C4).36C2, (C2×C20).180(C2×C4), (C2×C4×D5).415C22, (C2×C10).95(C22×C4), (C22×C10).77(C2×C4), (C2×Dic5).197(C2×C4), (C22×D5).131(C2×C4), SmallGroup(320,1587)
Series: Derived ►Chief ►Lower central ►Upper central
| C5 — C22×D5⋊C8 |
Subgroups: 906 in 338 conjugacy classes, 196 normal (13 characteristic)
C1, C2, C2 [×6], C2 [×8], C4 [×4], C4 [×4], C22 [×7], C22 [×28], C5, C8 [×8], C2×C4 [×6], C2×C4 [×22], C23, C23 [×14], D5 [×8], C10, C10 [×6], C2×C8 [×28], C22×C4, C22×C4 [×13], C24, Dic5, Dic5 [×3], C20 [×4], D10 [×28], C2×C10 [×7], C22×C8 [×14], C23×C4, C5⋊C8 [×8], C4×D5 [×16], C2×Dic5 [×6], C2×C20 [×6], C22×D5 [×14], C22×C10, C23×C8, D5⋊C8 [×16], C2×C5⋊C8 [×12], C2×C4×D5 [×12], C22×Dic5, C22×C20, C23×D5, C2×D5⋊C8 [×12], C22×C5⋊C8 [×2], D5×C22×C4, C22×D5⋊C8
Quotients:
C1, C2 [×15], C4 [×8], C22 [×35], C8 [×8], C2×C4 [×28], C23 [×15], C2×C8 [×28], C22×C4 [×14], C24, F5, C22×C8 [×14], C23×C4, C2×F5 [×7], C23×C8, D5⋊C8 [×4], C22×F5 [×7], C2×D5⋊C8 [×6], C23×F5, C22×D5⋊C8
Generators and relations
G = < a,b,c,d,e | a2=b2=c5=d2=e8=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, dcd=c-1, ece-1=c3, ede-1=c2d >
►On 160 points
Generators in S160
(1 89)(2 90)(3 91)(4 92)(5 93)(6 94)(7 95)(8 96)(9 157)(10 158)(11 159)(12 160)(13 153)(14 154)(15 155)(16 156)(17 113)(18 114)(19 115)(20 116)(21 117)(22 118)(23 119)(24 120)(25 57)(26 58)(27 59)(28 60)(29 61)(30 62)(31 63)(32 64)(33 127)(34 128)(35 121)(36 122)(37 123)(38 124)(39 125)(40 126)(41 130)(42 131)(43 132)(44 133)(45 134)(46 135)(47 136)(48 129)(49 87)(50 88)(51 81)(52 82)(53 83)(54 84)(55 85)(56 86)(65 101)(66 102)(67 103)(68 104)(69 97)(70 98)(71 99)(72 100)(73 141)(74 142)(75 143)(76 144)(77 137)(78 138)(79 139)(80 140)(105 151)(106 152)(107 145)(108 146)(109 147)(110 148)(111 149)(112 150)
(1 137)(2 138)(3 139)(4 140)(5 141)(6 142)(7 143)(8 144)(9 19)(10 20)(11 21)(12 22)(13 23)(14 24)(15 17)(16 18)(25 135)(26 136)(27 129)(28 130)(29 131)(30 132)(31 133)(32 134)(33 109)(34 110)(35 111)(36 112)(37 105)(38 106)(39 107)(40 108)(41 60)(42 61)(43 62)(44 63)(45 64)(46 57)(47 58)(48 59)(49 67)(50 68)(51 69)(52 70)(53 71)(54 72)(55 65)(56 66)(73 93)(74 94)(75 95)(76 96)(77 89)(78 90)(79 91)(80 92)(81 97)(82 98)(83 99)(84 100)(85 101)(86 102)(87 103)(88 104)(113 155)(114 156)(115 157)(116 158)(117 159)(118 160)(119 153)(120 154)(121 149)(122 150)(123 151)(124 152)(125 145)(126 146)(127 147)(128 148)
(1 44 155 85 33)(2 86 45 34 156)(3 35 87 157 46)(4 158 36 47 88)(5 48 159 81 37)(6 82 41 38 160)(7 39 83 153 42)(8 154 40 43 84)(9 135 91 121 49)(10 122 136 50 92)(11 51 123 93 129)(12 94 52 130 124)(13 131 95 125 53)(14 126 132 54 96)(15 55 127 89 133)(16 90 56 134 128)(17 65 147 77 31)(18 78 66 32 148)(19 25 79 149 67)(20 150 26 68 80)(21 69 151 73 27)(22 74 70 28 152)(23 29 75 145 71)(24 146 30 72 76)(57 139 111 103 115)(58 104 140 116 112)(59 117 97 105 141)(60 106 118 142 98)(61 143 107 99 119)(62 100 144 120 108)(63 113 101 109 137)(64 110 114 138 102)
(1 33)(2 156)(3 46)(4 88)(5 37)(6 160)(7 42)(8 84)(9 121)(10 136)(12 94)(13 125)(14 132)(16 90)(18 78)(19 149)(20 26)(22 74)(23 145)(24 30)(25 79)(27 69)(29 75)(31 65)(34 86)(35 157)(38 82)(39 153)(43 154)(44 85)(47 158)(48 81)(50 92)(51 129)(52 124)(54 96)(55 133)(56 128)(57 139)(58 116)(59 97)(61 143)(62 120)(63 101)(66 148)(68 80)(70 152)(72 76)(73 151)(77 147)(89 127)(91 135)(93 123)(95 131)(98 106)(100 144)(102 110)(104 140)(105 141)(107 119)(109 137)(111 115)(114 138)(118 142)
(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)
G:=sub<Sym(160)| (1,89)(2,90)(3,91)(4,92)(5,93)(6,94)(7,95)(8,96)(9,157)(10,158)(11,159)(12,160)(13,153)(14,154)(15,155)(16,156)(17,113)(18,114)(19,115)(20,116)(21,117)(22,118)(23,119)(24,120)(25,57)(26,58)(27,59)(28,60)(29,61)(30,62)(31,63)(32,64)(33,127)(34,128)(35,121)(36,122)(37,123)(38,124)(39,125)(40,126)(41,130)(42,131)(43,132)(44,133)(45,134)(46,135)(47,136)(48,129)(49,87)(50,88)(51,81)(52,82)(53,83)(54,84)(55,85)(56,86)(65,101)(66,102)(67,103)(68,104)(69,97)(70,98)(71,99)(72,100)(73,141)(74,142)(75,143)(76,144)(77,137)(78,138)(79,139)(80,140)(105,151)(106,152)(107,145)(108,146)(109,147)(110,148)(111,149)(112,150), (1,137)(2,138)(3,139)(4,140)(5,141)(6,142)(7,143)(8,144)(9,19)(10,20)(11,21)(12,22)(13,23)(14,24)(15,17)(16,18)(25,135)(26,136)(27,129)(28,130)(29,131)(30,132)(31,133)(32,134)(33,109)(34,110)(35,111)(36,112)(37,105)(38,106)(39,107)(40,108)(41,60)(42,61)(43,62)(44,63)(45,64)(46,57)(47,58)(48,59)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72)(55,65)(56,66)(73,93)(74,94)(75,95)(76,96)(77,89)(78,90)(79,91)(80,92)(81,97)(82,98)(83,99)(84,100)(85,101)(86,102)(87,103)(88,104)(113,155)(114,156)(115,157)(116,158)(117,159)(118,160)(119,153)(120,154)(121,149)(122,150)(123,151)(124,152)(125,145)(126,146)(127,147)(128,148), (1,44,155,85,33)(2,86,45,34,156)(3,35,87,157,46)(4,158,36,47,88)(5,48,159,81,37)(6,82,41,38,160)(7,39,83,153,42)(8,154,40,43,84)(9,135,91,121,49)(10,122,136,50,92)(11,51,123,93,129)(12,94,52,130,124)(13,131,95,125,53)(14,126,132,54,96)(15,55,127,89,133)(16,90,56,134,128)(17,65,147,77,31)(18,78,66,32,148)(19,25,79,149,67)(20,150,26,68,80)(21,69,151,73,27)(22,74,70,28,152)(23,29,75,145,71)(24,146,30,72,76)(57,139,111,103,115)(58,104,140,116,112)(59,117,97,105,141)(60,106,118,142,98)(61,143,107,99,119)(62,100,144,120,108)(63,113,101,109,137)(64,110,114,138,102), (1,33)(2,156)(3,46)(4,88)(5,37)(6,160)(7,42)(8,84)(9,121)(10,136)(12,94)(13,125)(14,132)(16,90)(18,78)(19,149)(20,26)(22,74)(23,145)(24,30)(25,79)(27,69)(29,75)(31,65)(34,86)(35,157)(38,82)(39,153)(43,154)(44,85)(47,158)(48,81)(50,92)(51,129)(52,124)(54,96)(55,133)(56,128)(57,139)(58,116)(59,97)(61,143)(62,120)(63,101)(66,148)(68,80)(70,152)(72,76)(73,151)(77,147)(89,127)(91,135)(93,123)(95,131)(98,106)(100,144)(102,110)(104,140)(105,141)(107,119)(109,137)(111,115)(114,138)(118,142), (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)>;
G:=Group( (1,89)(2,90)(3,91)(4,92)(5,93)(6,94)(7,95)(8,96)(9,157)(10,158)(11,159)(12,160)(13,153)(14,154)(15,155)(16,156)(17,113)(18,114)(19,115)(20,116)(21,117)(22,118)(23,119)(24,120)(25,57)(26,58)(27,59)(28,60)(29,61)(30,62)(31,63)(32,64)(33,127)(34,128)(35,121)(36,122)(37,123)(38,124)(39,125)(40,126)(41,130)(42,131)(43,132)(44,133)(45,134)(46,135)(47,136)(48,129)(49,87)(50,88)(51,81)(52,82)(53,83)(54,84)(55,85)(56,86)(65,101)(66,102)(67,103)(68,104)(69,97)(70,98)(71,99)(72,100)(73,141)(74,142)(75,143)(76,144)(77,137)(78,138)(79,139)(80,140)(105,151)(106,152)(107,145)(108,146)(109,147)(110,148)(111,149)(112,150), (1,137)(2,138)(3,139)(4,140)(5,141)(6,142)(7,143)(8,144)(9,19)(10,20)(11,21)(12,22)(13,23)(14,24)(15,17)(16,18)(25,135)(26,136)(27,129)(28,130)(29,131)(30,132)(31,133)(32,134)(33,109)(34,110)(35,111)(36,112)(37,105)(38,106)(39,107)(40,108)(41,60)(42,61)(43,62)(44,63)(45,64)(46,57)(47,58)(48,59)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72)(55,65)(56,66)(73,93)(74,94)(75,95)(76,96)(77,89)(78,90)(79,91)(80,92)(81,97)(82,98)(83,99)(84,100)(85,101)(86,102)(87,103)(88,104)(113,155)(114,156)(115,157)(116,158)(117,159)(118,160)(119,153)(120,154)(121,149)(122,150)(123,151)(124,152)(125,145)(126,146)(127,147)(128,148), (1,44,155,85,33)(2,86,45,34,156)(3,35,87,157,46)(4,158,36,47,88)(5,48,159,81,37)(6,82,41,38,160)(7,39,83,153,42)(8,154,40,43,84)(9,135,91,121,49)(10,122,136,50,92)(11,51,123,93,129)(12,94,52,130,124)(13,131,95,125,53)(14,126,132,54,96)(15,55,127,89,133)(16,90,56,134,128)(17,65,147,77,31)(18,78,66,32,148)(19,25,79,149,67)(20,150,26,68,80)(21,69,151,73,27)(22,74,70,28,152)(23,29,75,145,71)(24,146,30,72,76)(57,139,111,103,115)(58,104,140,116,112)(59,117,97,105,141)(60,106,118,142,98)(61,143,107,99,119)(62,100,144,120,108)(63,113,101,109,137)(64,110,114,138,102), (1,33)(2,156)(3,46)(4,88)(5,37)(6,160)(7,42)(8,84)(9,121)(10,136)(12,94)(13,125)(14,132)(16,90)(18,78)(19,149)(20,26)(22,74)(23,145)(24,30)(25,79)(27,69)(29,75)(31,65)(34,86)(35,157)(38,82)(39,153)(43,154)(44,85)(47,158)(48,81)(50,92)(51,129)(52,124)(54,96)(55,133)(56,128)(57,139)(58,116)(59,97)(61,143)(62,120)(63,101)(66,148)(68,80)(70,152)(72,76)(73,151)(77,147)(89,127)(91,135)(93,123)(95,131)(98,106)(100,144)(102,110)(104,140)(105,141)(107,119)(109,137)(111,115)(114,138)(118,142), (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) );
G=PermutationGroup([(1,89),(2,90),(3,91),(4,92),(5,93),(6,94),(7,95),(8,96),(9,157),(10,158),(11,159),(12,160),(13,153),(14,154),(15,155),(16,156),(17,113),(18,114),(19,115),(20,116),(21,117),(22,118),(23,119),(24,120),(25,57),(26,58),(27,59),(28,60),(29,61),(30,62),(31,63),(32,64),(33,127),(34,128),(35,121),(36,122),(37,123),(38,124),(39,125),(40,126),(41,130),(42,131),(43,132),(44,133),(45,134),(46,135),(47,136),(48,129),(49,87),(50,88),(51,81),(52,82),(53,83),(54,84),(55,85),(56,86),(65,101),(66,102),(67,103),(68,104),(69,97),(70,98),(71,99),(72,100),(73,141),(74,142),(75,143),(76,144),(77,137),(78,138),(79,139),(80,140),(105,151),(106,152),(107,145),(108,146),(109,147),(110,148),(111,149),(112,150)], [(1,137),(2,138),(3,139),(4,140),(5,141),(6,142),(7,143),(8,144),(9,19),(10,20),(11,21),(12,22),(13,23),(14,24),(15,17),(16,18),(25,135),(26,136),(27,129),(28,130),(29,131),(30,132),(31,133),(32,134),(33,109),(34,110),(35,111),(36,112),(37,105),(38,106),(39,107),(40,108),(41,60),(42,61),(43,62),(44,63),(45,64),(46,57),(47,58),(48,59),(49,67),(50,68),(51,69),(52,70),(53,71),(54,72),(55,65),(56,66),(73,93),(74,94),(75,95),(76,96),(77,89),(78,90),(79,91),(80,92),(81,97),(82,98),(83,99),(84,100),(85,101),(86,102),(87,103),(88,104),(113,155),(114,156),(115,157),(116,158),(117,159),(118,160),(119,153),(120,154),(121,149),(122,150),(123,151),(124,152),(125,145),(126,146),(127,147),(128,148)], [(1,44,155,85,33),(2,86,45,34,156),(3,35,87,157,46),(4,158,36,47,88),(5,48,159,81,37),(6,82,41,38,160),(7,39,83,153,42),(8,154,40,43,84),(9,135,91,121,49),(10,122,136,50,92),(11,51,123,93,129),(12,94,52,130,124),(13,131,95,125,53),(14,126,132,54,96),(15,55,127,89,133),(16,90,56,134,128),(17,65,147,77,31),(18,78,66,32,148),(19,25,79,149,67),(20,150,26,68,80),(21,69,151,73,27),(22,74,70,28,152),(23,29,75,145,71),(24,146,30,72,76),(57,139,111,103,115),(58,104,140,116,112),(59,117,97,105,141),(60,106,118,142,98),(61,143,107,99,119),(62,100,144,120,108),(63,113,101,109,137),(64,110,114,138,102)], [(1,33),(2,156),(3,46),(4,88),(5,37),(6,160),(7,42),(8,84),(9,121),(10,136),(12,94),(13,125),(14,132),(16,90),(18,78),(19,149),(20,26),(22,74),(23,145),(24,30),(25,79),(27,69),(29,75),(31,65),(34,86),(35,157),(38,82),(39,153),(43,154),(44,85),(47,158),(48,81),(50,92),(51,129),(52,124),(54,96),(55,133),(56,128),(57,139),(58,116),(59,97),(61,143),(62,120),(63,101),(66,148),(68,80),(70,152),(72,76),(73,151),(77,147),(89,127),(91,135),(93,123),(95,131),(98,106),(100,144),(102,110),(104,140),(105,141),(107,119),(109,137),(111,115),(114,138),(118,142)], [(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)])
Matrix representation ►G ⊆ GL6(𝔽41)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 0 | 0 | 1 | 0 | 0 | 40 |
| 0 | 0 | 0 | 1 | 0 | 40 |
| 0 | 0 | 0 | 0 | 1 | 40 |
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 40 |
| 0 | 0 | 0 | 1 | 0 | 40 |
| 0 | 0 | 1 | 0 | 0 | 40 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 38 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 39 | 38 | 0 |
| 0 | 0 | 40 | 39 | 0 | 2 |
| 0 | 0 | 2 | 0 | 39 | 40 |
| 0 | 0 | 0 | 38 | 39 | 2 |
G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[40,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,40,40,40,40],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,40,40,40,40],[1,0,0,0,0,0,0,38,0,0,0,0,0,0,2,40,2,0,0,0,39,39,0,38,0,0,38,0,39,39,0,0,0,2,40,2] >;
80 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | ··· | 2O | 4A | ··· | 4H | 4I | ··· | 4P | 5 | 8A | ··· | 8AF | 10A | ··· | 10G | 20A | ··· | 20H |
| order | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 5 | 8 | ··· | 8 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | ··· | 1 | 5 | ··· | 5 | 1 | ··· | 1 | 5 | ··· | 5 | 4 | 5 | ··· | 5 | 4 | ··· | 4 | 4 | ··· | 4 |
80 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | |||||
| image | C1 | C2 | C2 | C2 | C4 | C4 | C4 | C8 | F5 | C2×F5 | C2×F5 | D5⋊C8 |
| kernel | C22×D5⋊C8 | C2×D5⋊C8 | C22×C5⋊C8 | D5×C22×C4 | C2×C4×D5 | C22×C20 | C23×D5 | C22×D5 | C22×C4 | C2×C4 | C23 | C22 |
| # reps | 1 | 12 | 2 | 1 | 12 | 2 | 2 | 32 | 1 | 6 | 1 | 8 |
In GAP, Magma, Sage, TeX
C_2^2\times D_5\rtimes C_8
% in TeX
G:=Group("C2^2xD5:C8"); // GroupNames label
G:=SmallGroup(320,1587);
// by ID
G=gap.SmallGroup(320,1587);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,136,102,6278,818]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^5=d^2=e^8=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,d*c*d=c^-1,e*c*e^-1=c^3,e*d*e^-1=c^2*d>;
// generators/relations
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