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G = C4⋊D4⋊D5order 320 = 26·5

4th semidirect product of C4⋊D4 and D5 acting via D5/C5=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C52C84D4, C4⋊D44D5, C53(C82D4), C4⋊C4.59D10, (C2×C20).72D4, C4.171(D4×D5), C207D424C2, (C2×D4).39D10, C20.148(C2×D4), D206C436C2, D4⋊Dic516C2, C20.Q835C2, (C22×C10).85D4, C20.184(C4○D4), C4.60(D42D5), C10.94(C4⋊D4), C10.91(C8⋊C22), (C2×C20).358C23, (D4×C10).55C22, (C22×C4).121D10, C23.24(C5⋊D4), C2.13(D4⋊D10), (C2×D20).102C22, C4⋊Dic5.143C22, C2.15(Dic5⋊D4), C2.12(D4.D10), (C22×C20).162C22, (C2×D4⋊D5)⋊11C2, (C5×C4⋊D4)⋊4C2, (C2×C10).489(C2×D4), (C2×C4).50(C5⋊D4), (C2×C4.Dic5)⋊11C2, (C5×C4⋊C4).106C22, (C2×C4).458(C22×D5), C22.164(C2×C5⋊D4), (C2×C52C8).109C22, SmallGroup(320,666)

Series: Derived Chief Lower central Upper central

C1C2×C20 — C4⋊D4⋊D5
C1C5C10C20C2×C20C2×D20C207D4 — C4⋊D4⋊D5
C5C10C2×C20 — C4⋊D4⋊D5
C1C22C22×C4C4⋊D4

Generators and relations for C4⋊D4⋊D5
 G = < a,b,c,d,e | a4=b4=c2=d5=e2=1, bab-1=cac=eae=a-1, ad=da, cbc=b-1, bd=db, ebe=ab-1, cd=dc, ece=a-1c, ede=d-1 >

Subgroups: 550 in 130 conjugacy classes, 41 normal (39 characteristic)
C1, C2 [×3], C2 [×3], C4 [×2], C4 [×3], C22, C22 [×9], C5, C8 [×3], C2×C4 [×2], C2×C4 [×4], D4 [×8], C23, C23 [×2], D5, C10 [×3], C10 [×2], C22⋊C4 [×2], C4⋊C4, C4⋊C4, C2×C8 [×2], M4(2) [×2], D8 [×2], C22×C4, C2×D4, C2×D4 [×3], Dic5, C20 [×2], C20 [×2], D10 [×3], C2×C10, C2×C10 [×6], D4⋊C4 [×2], C4.Q8, C4⋊D4, C4⋊D4, C2×M4(2), C2×D8, C52C8 [×2], C52C8, D20 [×2], C2×Dic5, C5⋊D4 [×2], C2×C20 [×2], C2×C20 [×3], C5×D4 [×4], C22×D5, C22×C10, C22×C10, C82D4, C2×C52C8 [×2], C4.Dic5 [×2], C4⋊Dic5, D10⋊C4, D4⋊D5 [×2], C5×C22⋊C4, C5×C4⋊C4, C2×D20, C2×C5⋊D4, C22×C20, D4×C10, D4×C10, C20.Q8, D206C4, D4⋊Dic5, C2×C4.Dic5, C207D4, C2×D4⋊D5, C5×C4⋊D4, C4⋊D4⋊D5
Quotients: C1, C2 [×7], C22 [×7], D4 [×4], C23, D5, C2×D4 [×2], C4○D4, D10 [×3], C4⋊D4, C8⋊C22 [×2], C5⋊D4 [×2], C22×D5, C82D4, D4×D5, D42D5, C2×C5⋊D4, D4.D10, Dic5⋊D4, D4⋊D10, C4⋊D4⋊D5

Smallest permutation representation of C4⋊D4⋊D5
On 160 points
Generators in S160
(1 29 9 24)(2 30 10 25)(3 26 6 21)(4 27 7 22)(5 28 8 23)(11 36 16 31)(12 37 17 32)(13 38 18 33)(14 39 19 34)(15 40 20 35)(41 61 46 66)(42 62 47 67)(43 63 48 68)(44 64 49 69)(45 65 50 70)(51 71 56 76)(52 72 57 77)(53 73 58 78)(54 74 59 79)(55 75 60 80)(81 106 86 101)(82 107 87 102)(83 108 88 103)(84 109 89 104)(85 110 90 105)(91 116 96 111)(92 117 97 112)(93 118 98 113)(94 119 99 114)(95 120 100 115)(121 141 126 146)(122 142 127 147)(123 143 128 148)(124 144 129 149)(125 145 130 150)(131 151 136 156)(132 152 137 157)(133 153 138 158)(134 154 139 159)(135 155 140 160)
(1 124 19 139)(2 125 20 140)(3 121 16 136)(4 122 17 137)(5 123 18 138)(6 126 11 131)(7 127 12 132)(8 128 13 133)(9 129 14 134)(10 130 15 135)(21 141 36 156)(22 142 37 157)(23 143 38 158)(24 144 39 159)(25 145 40 160)(26 146 31 151)(27 147 32 152)(28 148 33 153)(29 149 34 154)(30 150 35 155)(41 81 56 96)(42 82 57 97)(43 83 58 98)(44 84 59 99)(45 85 60 100)(46 86 51 91)(47 87 52 92)(48 88 53 93)(49 89 54 94)(50 90 55 95)(61 101 76 116)(62 102 77 117)(63 103 78 118)(64 104 79 119)(65 105 80 120)(66 106 71 111)(67 107 72 112)(68 108 73 113)(69 109 74 114)(70 110 75 115)
(1 44)(2 45)(3 41)(4 42)(5 43)(6 46)(7 47)(8 48)(9 49)(10 50)(11 51)(12 52)(13 53)(14 54)(15 55)(16 56)(17 57)(18 58)(19 59)(20 60)(21 61)(22 62)(23 63)(24 64)(25 65)(26 66)(27 67)(28 68)(29 69)(30 70)(31 71)(32 72)(33 73)(34 74)(35 75)(36 76)(37 77)(38 78)(39 79)(40 80)(81 136)(82 137)(83 138)(84 139)(85 140)(86 131)(87 132)(88 133)(89 134)(90 135)(91 126)(92 127)(93 128)(94 129)(95 130)(96 121)(97 122)(98 123)(99 124)(100 125)(101 156)(102 157)(103 158)(104 159)(105 160)(106 151)(107 152)(108 153)(109 154)(110 155)(111 146)(112 147)(113 148)(114 149)(115 150)(116 141)(117 142)(118 143)(119 144)(120 145)
(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 5)(2 4)(7 10)(8 9)(12 15)(13 14)(17 20)(18 19)(21 26)(22 30)(23 29)(24 28)(25 27)(31 36)(32 40)(33 39)(34 38)(35 37)(41 61)(42 65)(43 64)(44 63)(45 62)(46 66)(47 70)(48 69)(49 68)(50 67)(51 71)(52 75)(53 74)(54 73)(55 72)(56 76)(57 80)(58 79)(59 78)(60 77)(81 91)(82 95)(83 94)(84 93)(85 92)(86 96)(87 100)(88 99)(89 98)(90 97)(101 116)(102 120)(103 119)(104 118)(105 117)(106 111)(107 115)(108 114)(109 113)(110 112)(121 151)(122 155)(123 154)(124 153)(125 152)(126 156)(127 160)(128 159)(129 158)(130 157)(131 141)(132 145)(133 144)(134 143)(135 142)(136 146)(137 150)(138 149)(139 148)(140 147)

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

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

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

44 conjugacy classes

class 1 2A2B2C2D2E2F4A4B4C4D4E5A5B8A8B8C8D10A···10F10G10H10I10J10K10L10M10N20A···20H20I20J20K20L
order12222224444455888810···10101010101010101020···2020202020
size1111484022484022202020202···2444488884···48888

44 irreducible representations

dim11111111222222222244444
type+++++++++++++++++-+
imageC1C2C2C2C2C2C2C2D4D4D4D5C4○D4D10D10D10C5⋊D4C5⋊D4C8⋊C22D4×D5D42D5D4.D10D4⋊D10
kernelC4⋊D4⋊D5C20.Q8D206C4D4⋊Dic5C2×C4.Dic5C207D4C2×D4⋊D5C5×C4⋊D4C52C8C2×C20C22×C10C4⋊D4C20C4⋊C4C22×C4C2×D4C2×C4C23C10C4C4C2C2
# reps11111111211222224422244

Matrix representation of C4⋊D4⋊D5 in GL8(𝔽41)

10000000
01000000
00100000
00010000
00000100
000040000
000000040
00000010
,
3225000000
09000000
004000000
000400000
0000113006
00003030350
0000061130
00003503030
,
400000000
371000000
004000000
000400000
00000010
00000001
00001000
00000100
,
10000000
01000000
003410000
004000000
00001000
00000100
00000010
00000001
,
10000000
440000000
001340000
000400000
00001000
000004000
00000001
00000010

G:=sub<GL(8,GF(41))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0],[32,0,0,0,0,0,0,0,25,9,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,11,30,0,35,0,0,0,0,30,30,6,0,0,0,0,0,0,35,11,30,0,0,0,0,6,0,30,30],[40,37,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,34,40,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,4,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,34,40,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0] >;

C4⋊D4⋊D5 in GAP, Magma, Sage, TeX

C_4\rtimes D_4\rtimes D_5
% in TeX

G:=Group("C4:D4:D5");
// GroupNames label

G:=SmallGroup(320,666);
// by ID

G=gap.SmallGroup(320,666);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,253,254,555,1123,297,136,12550]);
// Polycyclic

G:=Group<a,b,c,d,e|a^4=b^4=c^2=d^5=e^2=1,b*a*b^-1=c*a*c=e*a*e=a^-1,a*d=d*a,c*b*c=b^-1,b*d=d*b,e*b*e=a*b^-1,c*d=d*c,e*c*e=a^-1*c,e*d*e=d^-1>;
// generators/relations

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