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G = C24.14D10order 320 = 26·5

14th non-split extension by C24 of D10 acting via D10/C5=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C24.14D10, (C2×Dic5)⋊4D4, C10.39C22≀C2, (C22×D5).39D4, C22.241(D4×D5), (C22×C10).69D4, (C22×C4).34D10, C2.7(C23⋊D10), C10.32(C4⋊D4), C23.18(C5⋊D4), C52(C23.10D4), C2.33(D10⋊D4), C10.35(C4.4D4), C22.99(C4○D20), (C22×C20).27C22, (C23×C10).42C22, (C23×D5).15C22, C23.371(C22×D5), C10.10C4217C2, C2.10(Dic5⋊D4), C22.97(D42D5), (C22×C10).333C23, C2.22(D10.12D4), C2.22(Dic5.5D4), C10.34(C22.D4), C2.7(C23.23D10), (C22×Dic5).45C22, (C2×C22⋊C4)⋊6D5, (C10×C22⋊C4)⋊4C2, (C2×C23.D5)⋊5C2, (C2×D10⋊C4)⋊7C2, (C2×C10).434(C2×D4), (C22×C5⋊D4).5C2, (C2×C10.D4)⋊12C2, C22.127(C2×C5⋊D4), (C2×C10).148(C4○D4), SmallGroup(320,586)

Series: Derived Chief Lower central Upper central

C1C22×C10 — C24.14D10
C1C5C10C2×C10C22×C10C23×D5C22×C5⋊D4 — C24.14D10
C5C22×C10 — C24.14D10
C1C23C2×C22⋊C4

Generators and relations for C24.14D10
 G = < a,b,c,d,e,f | a2=b2=c2=d2=1, e10=c, f2=cb=bc, ab=ba, ac=ca, eae-1=ad=da, faf-1=acd, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=be9 >

Subgroups: 998 in 238 conjugacy classes, 61 normal (51 characteristic)
C1, C2 [×7], C2 [×4], C4 [×7], C22 [×7], C22 [×20], C5, C2×C4 [×17], D4 [×8], C23, C23 [×2], C23 [×14], D5 [×2], C10 [×7], C10 [×2], C22⋊C4 [×8], C4⋊C4 [×2], C22×C4 [×2], C22×C4 [×3], C2×D4 [×6], C24, C24, Dic5 [×5], C20 [×2], D10 [×10], C2×C10 [×7], C2×C10 [×10], C2.C42, C2×C22⋊C4, C2×C22⋊C4 [×3], C2×C4⋊C4, C22×D4, C2×Dic5 [×4], C2×Dic5 [×7], C5⋊D4 [×8], C2×C20 [×6], C22×D5 [×2], C22×D5 [×6], C22×C10, C22×C10 [×2], C22×C10 [×6], C23.10D4, C10.D4 [×2], D10⋊C4 [×4], C23.D5 [×2], C5×C22⋊C4 [×2], C22×Dic5 [×3], C2×C5⋊D4 [×6], C22×C20 [×2], C23×D5, C23×C10, C10.10C42, C2×C10.D4, C2×D10⋊C4 [×2], C2×C23.D5, C10×C22⋊C4, C22×C5⋊D4, C24.14D10
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 [×2], C22×D5, C23.10D4, C4○D20 [×2], D4×D5 [×3], D42D5, C2×C5⋊D4, D10.12D4, D10⋊D4 [×2], Dic5.5D4, C23.23D10, C23⋊D10, Dic5⋊D4, C24.14D10

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

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

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

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

62 conjugacy classes

class 1 2A···2G2H2I2J2K4A4B4C4D4E···4J5A5B10A···10N10O···10V20A···20P
order12···2222244444···45510···1010···1020···20
size11···1442020444420···20222···24···44···4

62 irreducible representations

dim111111122222222244
type++++++++++++++-
imageC1C2C2C2C2C2C2D4D4D4D5C4○D4D10D10C5⋊D4C4○D20D4×D5D42D5
kernelC24.14D10C10.10C42C2×C10.D4C2×D10⋊C4C2×C23.D5C10×C22⋊C4C22×C5⋊D4C2×Dic5C22×D5C22×C10C2×C22⋊C4C2×C10C22×C4C24C23C22C22C22
# reps1112111422264281662

Matrix representation of C24.14D10 in GL6(𝔽41)

2360000
35180000
001000
000100
00003221
000049
,
4000000
0400000
0040000
0004000
0000400
0000040
,
4000000
0400000
001000
000100
0000400
0000040
,
100000
010000
001000
000100
0000400
0000040
,
25160000
25390000
00202100
00202300
00003221
000009
,
16250000
39250000
00202100
00182100
0000920
00003732

G:=sub<GL(6,GF(41))| [23,35,0,0,0,0,6,18,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,32,4,0,0,0,0,21,9],[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],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[25,25,0,0,0,0,16,39,0,0,0,0,0,0,20,20,0,0,0,0,21,23,0,0,0,0,0,0,32,0,0,0,0,0,21,9],[16,39,0,0,0,0,25,25,0,0,0,0,0,0,20,18,0,0,0,0,21,21,0,0,0,0,0,0,9,37,0,0,0,0,20,32] >;

C24.14D10 in GAP, Magma, Sage, TeX

C_2^4._{14}D_{10}
% in TeX

G:=Group("C2^4.14D10");
// GroupNames label

G:=SmallGroup(320,586);
// by ID

G=gap.SmallGroup(320,586);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,253,254,387,100,12550]);
// Polycyclic

G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=1,e^10=c,f^2=c*b=b*c,a*b=b*a,a*c=c*a,e*a*e^-1=a*d=d*a,f*a*f^-1=a*c*d,b*d=d*b,b*e=e*b,b*f=f*b,c*d=d*c,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,f*e*f^-1=b*e^9>;
// generators/relations

׿
×
𝔽