Copied to
clipboard

G = C24.20D10order 320 = 26·5

20th non-split extension by C24 of D10 acting via D10/C5=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C24.20D10, (C2×Dic5)⋊6D4, (C2×C20).302D4, (C22×D4).8D5, C10.73C22≀C2, C22.283(D4×D5), C2.25(C202D4), (C22×C10).110D4, (C22×C4).152D10, C2.6(C242D5), C55(C23.10D4), C23.30(C5⋊D4), C10.130(C4⋊D4), C10.48(C4.4D4), (C23×C10).48C22, C23.384(C22×D5), C10.10C4245C2, C2.34(Dic5⋊D4), C2.14(C20.17D4), (C22×C20).395C22, (C22×C10).367C23, C22.106(D42D5), C10.84(C22.D4), (C22×Dic5).68C22, C2.17(C23.18D10), (D4×C2×C10).12C2, (C2×C10).556(C2×D4), (C2×C4).85(C5⋊D4), (C2×C23.D5)⋊11C2, (C2×C10.D4)⋊43C2, C22.218(C2×C5⋊D4), (C2×C10).163(C4○D4), SmallGroup(320,849)

Series: Derived Chief Lower central Upper central

C1C22×C10 — C24.20D10
C1C5C10C2×C10C22×C10C22×Dic5C2×C23.D5 — C24.20D10
C5C22×C10 — C24.20D10
C1C23C22×D4

Generators and relations for C24.20D10
 G = < a,b,c,d,e,f | a2=b2=c2=d2=e10=1, f2=dc=cd, ab=ba, ac=ca, eae-1=ad=da, faf-1=abd, bc=cb, bd=db, be=eb, bf=fb, ce=ec, cf=fc, de=ed, df=fd, fef-1=ce-1 >

Subgroups: 742 in 238 conjugacy classes, 65 normal (25 characteristic)
C1, C2 [×3], C2 [×4], C2 [×4], C4 [×7], C22 [×3], C22 [×4], C22 [×20], C5, C2×C4 [×2], C2×C4 [×15], D4 [×8], C23, C23 [×4], C23 [×12], C10 [×3], C10 [×4], C10 [×4], C22⋊C4 [×8], C4⋊C4 [×2], C22×C4, C22×C4 [×4], C2×D4 [×6], C24 [×2], Dic5 [×5], C20 [×2], C2×C10 [×3], C2×C10 [×4], C2×C10 [×20], C2.C42, C2×C22⋊C4 [×4], C2×C4⋊C4, C22×D4, C2×Dic5 [×2], C2×Dic5 [×11], C2×C20 [×2], C2×C20 [×2], C5×D4 [×8], C22×C10, C22×C10 [×4], C22×C10 [×12], C23.10D4, C10.D4 [×2], C23.D5 [×8], C22×Dic5 [×2], C22×Dic5 [×2], C22×C20, D4×C10 [×6], C23×C10 [×2], C10.10C42, C2×C10.D4, C2×C23.D5 [×4], D4×C2×C10, C24.20D10
Quotients: C1, C2 [×7], C22 [×7], D4 [×8], C23, D5, C2×D4 [×4], C4○D4 [×3], D10 [×3], C22≀C2, C4⋊D4 [×3], C22.D4 [×2], C4.4D4, C5⋊D4 [×6], C22×D5, C23.10D4, D4×D5, D42D5 [×3], C2×C5⋊D4 [×3], C23.18D10 [×2], C20.17D4, C202D4, Dic5⋊D4 [×2], C242D5, C24.20D10

Smallest permutation representation of C24.20D10
On 160 points
Generators in S160
(2 64)(4 66)(6 68)(8 70)(10 62)(11 100)(13 92)(15 94)(17 96)(19 98)(21 72)(23 74)(25 76)(27 78)(29 80)(31 56)(33 58)(35 60)(37 52)(39 54)(41 114)(42 107)(43 116)(44 109)(45 118)(46 101)(47 120)(48 103)(49 112)(50 105)(81 160)(82 139)(83 152)(84 131)(85 154)(86 133)(87 156)(88 135)(89 158)(90 137)(102 127)(104 129)(106 121)(108 123)(110 125)(111 128)(113 130)(115 122)(117 124)(119 126)(132 144)(134 146)(136 148)(138 150)(140 142)(141 151)(143 153)(145 155)(147 157)(149 159)
(1 22)(2 23)(3 24)(4 25)(5 26)(6 27)(7 28)(8 29)(9 30)(10 21)(11 54)(12 55)(13 56)(14 57)(15 58)(16 59)(17 60)(18 51)(19 52)(20 53)(31 92)(32 93)(33 94)(34 95)(35 96)(36 97)(37 98)(38 99)(39 100)(40 91)(41 106)(42 107)(43 108)(44 109)(45 110)(46 101)(47 102)(48 103)(49 104)(50 105)(61 71)(62 72)(63 73)(64 74)(65 75)(66 76)(67 77)(68 78)(69 79)(70 80)(81 138)(82 139)(83 140)(84 131)(85 132)(86 133)(87 134)(88 135)(89 136)(90 137)(111 128)(112 129)(113 130)(114 121)(115 122)(116 123)(117 124)(118 125)(119 126)(120 127)(141 151)(142 152)(143 153)(144 154)(145 155)(146 156)(147 157)(148 158)(149 159)(150 160)
(1 55)(2 56)(3 57)(4 58)(5 59)(6 60)(7 51)(8 52)(9 53)(10 54)(11 21)(12 22)(13 23)(14 24)(15 25)(16 26)(17 27)(18 28)(19 29)(20 30)(31 64)(32 65)(33 66)(34 67)(35 68)(36 69)(37 70)(38 61)(39 62)(40 63)(41 158)(42 159)(43 160)(44 151)(45 152)(46 153)(47 154)(48 155)(49 156)(50 157)(71 99)(72 100)(73 91)(74 92)(75 93)(76 94)(77 95)(78 96)(79 97)(80 98)(81 116)(82 117)(83 118)(84 119)(85 120)(86 111)(87 112)(88 113)(89 114)(90 115)(101 143)(102 144)(103 145)(104 146)(105 147)(106 148)(107 149)(108 150)(109 141)(110 142)(121 136)(122 137)(123 138)(124 139)(125 140)(126 131)(127 132)(128 133)(129 134)(130 135)
(1 63)(2 64)(3 65)(4 66)(5 67)(6 68)(7 69)(8 70)(9 61)(10 62)(11 100)(12 91)(13 92)(14 93)(15 94)(16 95)(17 96)(18 97)(19 98)(20 99)(21 72)(22 73)(23 74)(24 75)(25 76)(26 77)(27 78)(28 79)(29 80)(30 71)(31 56)(32 57)(33 58)(34 59)(35 60)(36 51)(37 52)(38 53)(39 54)(40 55)(41 121)(42 122)(43 123)(44 124)(45 125)(46 126)(47 127)(48 128)(49 129)(50 130)(81 150)(82 141)(83 142)(84 143)(85 144)(86 145)(87 146)(88 147)(89 148)(90 149)(101 119)(102 120)(103 111)(104 112)(105 113)(106 114)(107 115)(108 116)(109 117)(110 118)(131 153)(132 154)(133 155)(134 156)(135 157)(136 158)(137 159)(138 160)(139 151)(140 152)
(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)
(1 104 40 87)(2 145 31 111)(3 102 32 85)(4 143 33 119)(5 110 34 83)(6 141 35 117)(7 108 36 81)(8 149 37 115)(9 106 38 89)(10 147 39 113)(11 50 72 135)(12 156 73 129)(13 48 74 133)(14 154 75 127)(15 46 76 131)(16 152 77 125)(17 44 78 139)(18 160 79 123)(19 42 80 137)(20 158 71 121)(21 157 100 130)(22 49 91 134)(23 155 92 128)(24 47 93 132)(25 153 94 126)(26 45 95 140)(27 151 96 124)(28 43 97 138)(29 159 98 122)(30 41 99 136)(51 150 69 116)(52 107 70 90)(53 148 61 114)(54 105 62 88)(55 146 63 112)(56 103 64 86)(57 144 65 120)(58 101 66 84)(59 142 67 118)(60 109 68 82)

G:=sub<Sym(160)| (2,64)(4,66)(6,68)(8,70)(10,62)(11,100)(13,92)(15,94)(17,96)(19,98)(21,72)(23,74)(25,76)(27,78)(29,80)(31,56)(33,58)(35,60)(37,52)(39,54)(41,114)(42,107)(43,116)(44,109)(45,118)(46,101)(47,120)(48,103)(49,112)(50,105)(81,160)(82,139)(83,152)(84,131)(85,154)(86,133)(87,156)(88,135)(89,158)(90,137)(102,127)(104,129)(106,121)(108,123)(110,125)(111,128)(113,130)(115,122)(117,124)(119,126)(132,144)(134,146)(136,148)(138,150)(140,142)(141,151)(143,153)(145,155)(147,157)(149,159), (1,22)(2,23)(3,24)(4,25)(5,26)(6,27)(7,28)(8,29)(9,30)(10,21)(11,54)(12,55)(13,56)(14,57)(15,58)(16,59)(17,60)(18,51)(19,52)(20,53)(31,92)(32,93)(33,94)(34,95)(35,96)(36,97)(37,98)(38,99)(39,100)(40,91)(41,106)(42,107)(43,108)(44,109)(45,110)(46,101)(47,102)(48,103)(49,104)(50,105)(61,71)(62,72)(63,73)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(81,138)(82,139)(83,140)(84,131)(85,132)(86,133)(87,134)(88,135)(89,136)(90,137)(111,128)(112,129)(113,130)(114,121)(115,122)(116,123)(117,124)(118,125)(119,126)(120,127)(141,151)(142,152)(143,153)(144,154)(145,155)(146,156)(147,157)(148,158)(149,159)(150,160), (1,55)(2,56)(3,57)(4,58)(5,59)(6,60)(7,51)(8,52)(9,53)(10,54)(11,21)(12,22)(13,23)(14,24)(15,25)(16,26)(17,27)(18,28)(19,29)(20,30)(31,64)(32,65)(33,66)(34,67)(35,68)(36,69)(37,70)(38,61)(39,62)(40,63)(41,158)(42,159)(43,160)(44,151)(45,152)(46,153)(47,154)(48,155)(49,156)(50,157)(71,99)(72,100)(73,91)(74,92)(75,93)(76,94)(77,95)(78,96)(79,97)(80,98)(81,116)(82,117)(83,118)(84,119)(85,120)(86,111)(87,112)(88,113)(89,114)(90,115)(101,143)(102,144)(103,145)(104,146)(105,147)(106,148)(107,149)(108,150)(109,141)(110,142)(121,136)(122,137)(123,138)(124,139)(125,140)(126,131)(127,132)(128,133)(129,134)(130,135), (1,63)(2,64)(3,65)(4,66)(5,67)(6,68)(7,69)(8,70)(9,61)(10,62)(11,100)(12,91)(13,92)(14,93)(15,94)(16,95)(17,96)(18,97)(19,98)(20,99)(21,72)(22,73)(23,74)(24,75)(25,76)(26,77)(27,78)(28,79)(29,80)(30,71)(31,56)(32,57)(33,58)(34,59)(35,60)(36,51)(37,52)(38,53)(39,54)(40,55)(41,121)(42,122)(43,123)(44,124)(45,125)(46,126)(47,127)(48,128)(49,129)(50,130)(81,150)(82,141)(83,142)(84,143)(85,144)(86,145)(87,146)(88,147)(89,148)(90,149)(101,119)(102,120)(103,111)(104,112)(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(131,153)(132,154)(133,155)(134,156)(135,157)(136,158)(137,159)(138,160)(139,151)(140,152), (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), (1,104,40,87)(2,145,31,111)(3,102,32,85)(4,143,33,119)(5,110,34,83)(6,141,35,117)(7,108,36,81)(8,149,37,115)(9,106,38,89)(10,147,39,113)(11,50,72,135)(12,156,73,129)(13,48,74,133)(14,154,75,127)(15,46,76,131)(16,152,77,125)(17,44,78,139)(18,160,79,123)(19,42,80,137)(20,158,71,121)(21,157,100,130)(22,49,91,134)(23,155,92,128)(24,47,93,132)(25,153,94,126)(26,45,95,140)(27,151,96,124)(28,43,97,138)(29,159,98,122)(30,41,99,136)(51,150,69,116)(52,107,70,90)(53,148,61,114)(54,105,62,88)(55,146,63,112)(56,103,64,86)(57,144,65,120)(58,101,66,84)(59,142,67,118)(60,109,68,82)>;

G:=Group( (2,64)(4,66)(6,68)(8,70)(10,62)(11,100)(13,92)(15,94)(17,96)(19,98)(21,72)(23,74)(25,76)(27,78)(29,80)(31,56)(33,58)(35,60)(37,52)(39,54)(41,114)(42,107)(43,116)(44,109)(45,118)(46,101)(47,120)(48,103)(49,112)(50,105)(81,160)(82,139)(83,152)(84,131)(85,154)(86,133)(87,156)(88,135)(89,158)(90,137)(102,127)(104,129)(106,121)(108,123)(110,125)(111,128)(113,130)(115,122)(117,124)(119,126)(132,144)(134,146)(136,148)(138,150)(140,142)(141,151)(143,153)(145,155)(147,157)(149,159), (1,22)(2,23)(3,24)(4,25)(5,26)(6,27)(7,28)(8,29)(9,30)(10,21)(11,54)(12,55)(13,56)(14,57)(15,58)(16,59)(17,60)(18,51)(19,52)(20,53)(31,92)(32,93)(33,94)(34,95)(35,96)(36,97)(37,98)(38,99)(39,100)(40,91)(41,106)(42,107)(43,108)(44,109)(45,110)(46,101)(47,102)(48,103)(49,104)(50,105)(61,71)(62,72)(63,73)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(81,138)(82,139)(83,140)(84,131)(85,132)(86,133)(87,134)(88,135)(89,136)(90,137)(111,128)(112,129)(113,130)(114,121)(115,122)(116,123)(117,124)(118,125)(119,126)(120,127)(141,151)(142,152)(143,153)(144,154)(145,155)(146,156)(147,157)(148,158)(149,159)(150,160), (1,55)(2,56)(3,57)(4,58)(5,59)(6,60)(7,51)(8,52)(9,53)(10,54)(11,21)(12,22)(13,23)(14,24)(15,25)(16,26)(17,27)(18,28)(19,29)(20,30)(31,64)(32,65)(33,66)(34,67)(35,68)(36,69)(37,70)(38,61)(39,62)(40,63)(41,158)(42,159)(43,160)(44,151)(45,152)(46,153)(47,154)(48,155)(49,156)(50,157)(71,99)(72,100)(73,91)(74,92)(75,93)(76,94)(77,95)(78,96)(79,97)(80,98)(81,116)(82,117)(83,118)(84,119)(85,120)(86,111)(87,112)(88,113)(89,114)(90,115)(101,143)(102,144)(103,145)(104,146)(105,147)(106,148)(107,149)(108,150)(109,141)(110,142)(121,136)(122,137)(123,138)(124,139)(125,140)(126,131)(127,132)(128,133)(129,134)(130,135), (1,63)(2,64)(3,65)(4,66)(5,67)(6,68)(7,69)(8,70)(9,61)(10,62)(11,100)(12,91)(13,92)(14,93)(15,94)(16,95)(17,96)(18,97)(19,98)(20,99)(21,72)(22,73)(23,74)(24,75)(25,76)(26,77)(27,78)(28,79)(29,80)(30,71)(31,56)(32,57)(33,58)(34,59)(35,60)(36,51)(37,52)(38,53)(39,54)(40,55)(41,121)(42,122)(43,123)(44,124)(45,125)(46,126)(47,127)(48,128)(49,129)(50,130)(81,150)(82,141)(83,142)(84,143)(85,144)(86,145)(87,146)(88,147)(89,148)(90,149)(101,119)(102,120)(103,111)(104,112)(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(131,153)(132,154)(133,155)(134,156)(135,157)(136,158)(137,159)(138,160)(139,151)(140,152), (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), (1,104,40,87)(2,145,31,111)(3,102,32,85)(4,143,33,119)(5,110,34,83)(6,141,35,117)(7,108,36,81)(8,149,37,115)(9,106,38,89)(10,147,39,113)(11,50,72,135)(12,156,73,129)(13,48,74,133)(14,154,75,127)(15,46,76,131)(16,152,77,125)(17,44,78,139)(18,160,79,123)(19,42,80,137)(20,158,71,121)(21,157,100,130)(22,49,91,134)(23,155,92,128)(24,47,93,132)(25,153,94,126)(26,45,95,140)(27,151,96,124)(28,43,97,138)(29,159,98,122)(30,41,99,136)(51,150,69,116)(52,107,70,90)(53,148,61,114)(54,105,62,88)(55,146,63,112)(56,103,64,86)(57,144,65,120)(58,101,66,84)(59,142,67,118)(60,109,68,82) );

G=PermutationGroup([(2,64),(4,66),(6,68),(8,70),(10,62),(11,100),(13,92),(15,94),(17,96),(19,98),(21,72),(23,74),(25,76),(27,78),(29,80),(31,56),(33,58),(35,60),(37,52),(39,54),(41,114),(42,107),(43,116),(44,109),(45,118),(46,101),(47,120),(48,103),(49,112),(50,105),(81,160),(82,139),(83,152),(84,131),(85,154),(86,133),(87,156),(88,135),(89,158),(90,137),(102,127),(104,129),(106,121),(108,123),(110,125),(111,128),(113,130),(115,122),(117,124),(119,126),(132,144),(134,146),(136,148),(138,150),(140,142),(141,151),(143,153),(145,155),(147,157),(149,159)], [(1,22),(2,23),(3,24),(4,25),(5,26),(6,27),(7,28),(8,29),(9,30),(10,21),(11,54),(12,55),(13,56),(14,57),(15,58),(16,59),(17,60),(18,51),(19,52),(20,53),(31,92),(32,93),(33,94),(34,95),(35,96),(36,97),(37,98),(38,99),(39,100),(40,91),(41,106),(42,107),(43,108),(44,109),(45,110),(46,101),(47,102),(48,103),(49,104),(50,105),(61,71),(62,72),(63,73),(64,74),(65,75),(66,76),(67,77),(68,78),(69,79),(70,80),(81,138),(82,139),(83,140),(84,131),(85,132),(86,133),(87,134),(88,135),(89,136),(90,137),(111,128),(112,129),(113,130),(114,121),(115,122),(116,123),(117,124),(118,125),(119,126),(120,127),(141,151),(142,152),(143,153),(144,154),(145,155),(146,156),(147,157),(148,158),(149,159),(150,160)], [(1,55),(2,56),(3,57),(4,58),(5,59),(6,60),(7,51),(8,52),(9,53),(10,54),(11,21),(12,22),(13,23),(14,24),(15,25),(16,26),(17,27),(18,28),(19,29),(20,30),(31,64),(32,65),(33,66),(34,67),(35,68),(36,69),(37,70),(38,61),(39,62),(40,63),(41,158),(42,159),(43,160),(44,151),(45,152),(46,153),(47,154),(48,155),(49,156),(50,157),(71,99),(72,100),(73,91),(74,92),(75,93),(76,94),(77,95),(78,96),(79,97),(80,98),(81,116),(82,117),(83,118),(84,119),(85,120),(86,111),(87,112),(88,113),(89,114),(90,115),(101,143),(102,144),(103,145),(104,146),(105,147),(106,148),(107,149),(108,150),(109,141),(110,142),(121,136),(122,137),(123,138),(124,139),(125,140),(126,131),(127,132),(128,133),(129,134),(130,135)], [(1,63),(2,64),(3,65),(4,66),(5,67),(6,68),(7,69),(8,70),(9,61),(10,62),(11,100),(12,91),(13,92),(14,93),(15,94),(16,95),(17,96),(18,97),(19,98),(20,99),(21,72),(22,73),(23,74),(24,75),(25,76),(26,77),(27,78),(28,79),(29,80),(30,71),(31,56),(32,57),(33,58),(34,59),(35,60),(36,51),(37,52),(38,53),(39,54),(40,55),(41,121),(42,122),(43,123),(44,124),(45,125),(46,126),(47,127),(48,128),(49,129),(50,130),(81,150),(82,141),(83,142),(84,143),(85,144),(86,145),(87,146),(88,147),(89,148),(90,149),(101,119),(102,120),(103,111),(104,112),(105,113),(106,114),(107,115),(108,116),(109,117),(110,118),(131,153),(132,154),(133,155),(134,156),(135,157),(136,158),(137,159),(138,160),(139,151),(140,152)], [(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)], [(1,104,40,87),(2,145,31,111),(3,102,32,85),(4,143,33,119),(5,110,34,83),(6,141,35,117),(7,108,36,81),(8,149,37,115),(9,106,38,89),(10,147,39,113),(11,50,72,135),(12,156,73,129),(13,48,74,133),(14,154,75,127),(15,46,76,131),(16,152,77,125),(17,44,78,139),(18,160,79,123),(19,42,80,137),(20,158,71,121),(21,157,100,130),(22,49,91,134),(23,155,92,128),(24,47,93,132),(25,153,94,126),(26,45,95,140),(27,151,96,124),(28,43,97,138),(29,159,98,122),(30,41,99,136),(51,150,69,116),(52,107,70,90),(53,148,61,114),(54,105,62,88),(55,146,63,112),(56,103,64,86),(57,144,65,120),(58,101,66,84),(59,142,67,118),(60,109,68,82)])

62 conjugacy classes

class 1 2A···2G2H2I2J2K4A4B4C···4J5A5B10A···10N10O···10AD20A···20H
order12···22222444···45510···1010···1020···20
size11···144444420···20222···24···44···4

62 irreducible representations

dim1111122222222244
type++++++++++++-
imageC1C2C2C2C2D4D4D4D5C4○D4D10D10C5⋊D4C5⋊D4D4×D5D42D5
kernelC24.20D10C10.10C42C2×C10.D4C2×C23.D5D4×C2×C10C2×Dic5C2×C20C22×C10C22×D4C2×C10C22×C4C24C2×C4C23C22C22
# reps11141224262481626

Matrix representation of C24.20D10 in GL6(𝔽41)

100000
0400000
001000
0004000
000010
00002340
,
4000000
0400000
0040000
0004000
0000400
0000040
,
100000
010000
0040000
0004000
0000400
0000040
,
4000000
0400000
0040000
0004000
000010
000001
,
010000
100000
000100
001000
0000370
00002831
,
3200000
0320000
001000
0004000
00002521
00001916

G:=sub<GL(6,GF(41))| [1,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,1,23,0,0,0,0,0,40],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,37,28,0,0,0,0,0,31],[32,0,0,0,0,0,0,32,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,25,19,0,0,0,0,21,16] >;

C24.20D10 in GAP, Magma, Sage, TeX

C_2^4._{20}D_{10}
% in TeX

G:=Group("C2^4.20D10");
// GroupNames label

G:=SmallGroup(320,849);
// by ID

G=gap.SmallGroup(320,849);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,253,254,387,12550]);
// Polycyclic

G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=e^10=1,f^2=d*c=c*d,a*b=b*a,a*c=c*a,e*a*e^-1=a*d=d*a,f*a*f^-1=a*b*d,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,f*e*f^-1=c*e^-1>;
// generators/relations

׿
×
𝔽