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G = C32×C22.D4order 288 = 25·32

Direct product of C32 and C22.D4

direct product, metabelian, nilpotent (class 2), monomial

Aliases: C32×C22.D4, C62.98D4, C23.13C62, C62.292C23, C6.87(C6×D4), (C22×C12)⋊9C6, (C6×D4).23C6, (C2×C4).5C62, (C2×C62).2C22, C22.4(D4×C32), (C6×C12).270C22, C22.13(C2×C62), (C2×C6×C12)⋊7C2, C2.7(D4×C3×C6), C4⋊C44(C3×C6), (C3×C4⋊C4)⋊13C6, (D4×C3×C6).18C2, C22⋊C44(C3×C6), (C22×C4)⋊5(C3×C6), (C2×D4).4(C3×C6), C6.53(C3×C4○D4), (C2×C6).33(C3×D4), (C32×C4⋊C4)⋊22C2, (C3×C22⋊C4)⋊12C6, (C2×C12).98(C2×C6), (C3×C6).304(C2×D4), C2.6(C32×C4○D4), (C2×C6).98(C22×C6), (C22×C6).54(C2×C6), (C3×C6).170(C4○D4), (C32×C22⋊C4)⋊20C2, SmallGroup(288,820)

Series: Derived Chief Lower central Upper central

C1C22 — C32×C22.D4
C1C2C22C2×C6C62C2×C62D4×C3×C6 — C32×C22.D4
C1C22 — C32×C22.D4
C1C62 — C32×C22.D4

Generators and relations for C32×C22.D4
 G = < a,b,c,d,e,f | a3=b3=c2=d2=e4=f2=1, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, bd=db, be=eb, bf=fb, ece-1=fcf=cd=dc, de=ed, df=fd, fef=de-1 >

Subgroups: 348 in 234 conjugacy classes, 132 normal (20 characteristic)
C1, C2, C2 [×2], C2 [×3], C3 [×4], C4 [×5], C22, C22 [×2], C22 [×5], C6 [×12], C6 [×12], C2×C4, C2×C4 [×4], C2×C4 [×2], D4 [×2], C23 [×2], C32, C12 [×20], C2×C6 [×12], C2×C6 [×20], C22⋊C4, C22⋊C4 [×2], C4⋊C4 [×2], C22×C4, C2×D4, C3×C6, C3×C6 [×2], C3×C6 [×3], C2×C12 [×20], C2×C12 [×8], C3×D4 [×8], C22×C6 [×8], C22.D4, C3×C12 [×5], C62, C62 [×2], C62 [×5], C3×C22⋊C4 [×12], C3×C4⋊C4 [×8], C22×C12 [×4], C6×D4 [×4], C6×C12, C6×C12 [×4], C6×C12 [×2], D4×C32 [×2], C2×C62 [×2], C3×C22.D4 [×4], C32×C22⋊C4, C32×C22⋊C4 [×2], C32×C4⋊C4 [×2], C2×C6×C12, D4×C3×C6, C32×C22.D4
Quotients: C1, C2 [×7], C3 [×4], C22 [×7], C6 [×28], D4 [×2], C23, C32, C2×C6 [×28], C2×D4, C4○D4 [×2], C3×C6 [×7], C3×D4 [×8], C22×C6 [×4], C22.D4, C62 [×7], C6×D4 [×4], C3×C4○D4 [×8], D4×C32 [×2], C2×C62, C3×C22.D4 [×4], D4×C3×C6, C32×C4○D4 [×2], C32×C22.D4

Smallest permutation representation of C32×C22.D4
On 144 points
Generators in S144
(1 54 46)(2 55 47)(3 56 48)(4 53 45)(5 50 13)(6 51 14)(7 52 15)(8 49 16)(9 42 17)(10 43 18)(11 44 19)(12 41 20)(21 75 29)(22 76 30)(23 73 31)(24 74 32)(25 70 62)(26 71 63)(27 72 64)(28 69 61)(33 66 58)(34 67 59)(35 68 60)(36 65 57)(37 103 95)(38 104 96)(39 101 93)(40 102 94)(77 123 115)(78 124 116)(79 121 113)(80 122 114)(81 128 89)(82 125 90)(83 126 91)(84 127 92)(85 120 110)(86 117 111)(87 118 112)(88 119 109)(97 144 136)(98 141 133)(99 142 134)(100 143 135)(105 140 132)(106 137 129)(107 138 130)(108 139 131)
(1 42 5)(2 43 6)(3 44 7)(4 41 8)(9 13 46)(10 14 47)(11 15 48)(12 16 45)(17 50 54)(18 51 55)(19 52 56)(20 49 53)(21 25 58)(22 26 59)(23 27 60)(24 28 57)(29 62 66)(30 63 67)(31 64 68)(32 61 65)(33 75 70)(34 76 71)(35 73 72)(36 74 69)(37 142 107)(38 143 108)(39 144 105)(40 141 106)(77 109 127)(78 110 128)(79 111 125)(80 112 126)(81 116 120)(82 113 117)(83 114 118)(84 115 119)(85 89 124)(86 90 121)(87 91 122)(88 92 123)(93 97 132)(94 98 129)(95 99 130)(96 100 131)(101 136 140)(102 133 137)(103 134 138)(104 135 139)
(1 115)(2 93)(3 113)(4 95)(5 84)(6 132)(7 82)(8 130)(9 88)(10 136)(11 86)(12 134)(13 92)(14 140)(15 90)(16 138)(17 109)(18 144)(19 111)(20 142)(21 116)(22 94)(23 114)(24 96)(25 120)(26 98)(27 118)(28 100)(29 124)(30 102)(31 122)(32 104)(33 128)(34 106)(35 126)(36 108)(37 53)(38 74)(39 55)(40 76)(41 99)(42 119)(43 97)(44 117)(45 103)(46 123)(47 101)(48 121)(49 107)(50 127)(51 105)(52 125)(54 77)(56 79)(57 131)(58 81)(59 129)(60 83)(61 135)(62 85)(63 133)(64 87)(65 139)(66 89)(67 137)(68 91)(69 143)(70 110)(71 141)(72 112)(73 80)(75 78)
(1 24)(2 21)(3 22)(4 23)(5 57)(6 58)(7 59)(8 60)(9 61)(10 62)(11 63)(12 64)(13 65)(14 66)(15 67)(16 68)(17 69)(18 70)(19 71)(20 72)(25 43)(26 44)(27 41)(28 42)(29 47)(30 48)(31 45)(32 46)(33 51)(34 52)(35 49)(36 50)(37 80)(38 77)(39 78)(40 79)(53 73)(54 74)(55 75)(56 76)(81 132)(82 129)(83 130)(84 131)(85 136)(86 133)(87 134)(88 135)(89 140)(90 137)(91 138)(92 139)(93 116)(94 113)(95 114)(96 115)(97 120)(98 117)(99 118)(100 119)(101 124)(102 121)(103 122)(104 123)(105 128)(106 125)(107 126)(108 127)(109 143)(110 144)(111 141)(112 142)
(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)
(2 23)(4 21)(6 60)(8 58)(10 64)(12 62)(14 68)(16 66)(18 72)(20 70)(25 41)(27 43)(29 45)(31 47)(33 49)(35 51)(37 39)(38 77)(40 79)(53 75)(55 73)(78 80)(81 83)(82 129)(84 131)(85 87)(86 133)(88 135)(89 91)(90 137)(92 139)(93 95)(94 113)(96 115)(97 99)(98 117)(100 119)(101 103)(102 121)(104 123)(105 107)(106 125)(108 127)(109 143)(110 112)(111 141)(114 116)(118 120)(122 124)(126 128)(130 132)(134 136)(138 140)(142 144)

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

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

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

126 conjugacy classes

class 1 2A2B2C2D2E2F3A···3H4A4B4C4D4E4F4G6A···6X6Y···6AN6AO···6AV12A···12AF12AG···12BD
order12222223···344444446···66···66···612···1212···12
size11112241···122224441···12···24···42···24···4

126 irreducible representations

dim11111111112222
type++++++
imageC1C2C2C2C2C3C6C6C6C6D4C4○D4C3×D4C3×C4○D4
kernelC32×C22.D4C32×C22⋊C4C32×C4⋊C4C2×C6×C12D4×C3×C6C3×C22.D4C3×C22⋊C4C3×C4⋊C4C22×C12C6×D4C62C3×C6C2×C6C6
# reps132118241688241632

Matrix representation of C32×C22.D4 in GL5(𝔽13)

30000
01000
00100
00030
00003
,
30000
01000
00100
00090
00009
,
120000
01200
001200
00010
00001
,
10000
012000
001200
00010
00001
,
120000
05000
08800
000122
000121
,
120000
01000
0121200
00010
000112

G:=sub<GL(5,GF(13))| [3,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,3,0,0,0,0,0,3],[3,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,9,0,0,0,0,0,9],[12,0,0,0,0,0,1,0,0,0,0,2,12,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,12,0,0,0,0,0,12,0,0,0,0,0,1,0,0,0,0,0,1],[12,0,0,0,0,0,5,8,0,0,0,0,8,0,0,0,0,0,12,12,0,0,0,2,1],[12,0,0,0,0,0,1,12,0,0,0,0,12,0,0,0,0,0,1,1,0,0,0,0,12] >;

C32×C22.D4 in GAP, Magma, Sage, TeX

C_3^2\times C_2^2.D_4
% in TeX

G:=Group("C3^2xC2^2.D4");
// GroupNames label

G:=SmallGroup(288,820);
// by ID

G=gap.SmallGroup(288,820);
# by ID

G:=PCGroup([7,-2,-2,-2,-3,-3,-2,-2,1037,3110,394]);
// Polycyclic

G:=Group<a,b,c,d,e,f|a^3=b^3=c^2=d^2=e^4=f^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,e*c*e^-1=f*c*f=c*d=d*c,d*e=e*d,d*f=f*d,f*e*f=d*e^-1>;
// generators/relations

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