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G = C3272- 1+4order 288 = 25·32

2nd semidirect product of C32 and 2- 1+4 acting via 2- 1+4/C2×Q8=C2

metabelian, supersoluble, monomial

Aliases: C3272- 1+4, C62.282C23, (C6×Q8)⋊11S3, (C3×Q8).69D6, (C2×C12).172D6, C6.63(S3×C23), (C3×C6).62C24, C12.26D69C2, C12.59D611C2, (C6×C12).171C22, C12.114(C22×S3), (C3×C12).133C23, C34(Q8.15D6), C3⋊Dic3.50C23, C327D4.4C22, C12⋊S3.34C22, (Q8×C32).33C22, C324Q8.36C22, (Q8×C3⋊S3)⋊9C2, (Q8×C3×C6)⋊14C2, (C2×Q8)⋊7(C3⋊S3), Q8.15(C2×C3⋊S3), C2.11(C23×C3⋊S3), C4.24(C22×C3⋊S3), (C4×C3⋊S3).48C22, (C2×C3⋊S3).54C23, C22.7(C22×C3⋊S3), (C2×C6).290(C22×S3), (C2×C4).23(C2×C3⋊S3), SmallGroup(288,1012)

Series: Derived Chief Lower central Upper central

C1C3×C6 — C3272- 1+4
C1C3C32C3×C6C2×C3⋊S3C4×C3⋊S3Q8×C3⋊S3 — C3272- 1+4
C32C3×C6 — C3272- 1+4
C1C2C2×Q8

Generators and relations for C3272- 1+4
 G = < a,b,c,d,e,f | a3=b3=c4=d2=1, e2=f2=c2, ab=ba, ac=ca, dad=eae-1=a-1, af=fa, bc=cb, dbd=ebe-1=b-1, bf=fb, dcd=c-1, ce=ec, cf=fc, de=ed, df=fd, fef-1=c2e >

Subgroups: 1412 in 438 conjugacy classes, 153 normal (9 characteristic)
C1, C2, C2 [×5], C3 [×4], C4 [×6], C4 [×4], C22, C22 [×4], S3 [×16], C6 [×4], C6 [×4], C2×C4 [×3], C2×C4 [×12], D4 [×10], Q8 [×4], Q8 [×6], C32, Dic3 [×16], C12 [×24], D6 [×16], C2×C6 [×4], C2×Q8, C2×Q8 [×4], C4○D4 [×10], C3⋊S3 [×4], C3×C6, C3×C6, Dic6 [×24], C4×S3 [×48], D12 [×24], C3⋊D4 [×16], C2×C12 [×12], C3×Q8 [×16], 2- 1+4, C3⋊Dic3 [×4], C3×C12 [×6], C2×C3⋊S3 [×4], C62, C4○D12 [×24], S3×Q8 [×16], Q83S3 [×16], C6×Q8 [×4], C324Q8 [×6], C4×C3⋊S3 [×12], C12⋊S3 [×6], C327D4 [×4], C6×C12 [×3], Q8×C32 [×4], Q8.15D6 [×4], C12.59D6 [×6], Q8×C3⋊S3 [×4], C12.26D6 [×4], Q8×C3×C6, C3272- 1+4
Quotients: C1, C2 [×15], C22 [×35], S3 [×4], C23 [×15], D6 [×28], C24, C3⋊S3, C22×S3 [×28], 2- 1+4, C2×C3⋊S3 [×7], S3×C23 [×4], C22×C3⋊S3 [×7], Q8.15D6 [×4], C23×C3⋊S3, C3272- 1+4

Smallest permutation representation of C3272- 1+4
On 144 points
Generators in S144
(1 32 76)(2 29 73)(3 30 74)(4 31 75)(5 90 102)(6 91 103)(7 92 104)(8 89 101)(9 55 126)(10 56 127)(11 53 128)(12 54 125)(13 100 142)(14 97 143)(15 98 144)(16 99 141)(17 140 112)(18 137 109)(19 138 110)(20 139 111)(21 44 121)(22 41 122)(23 42 123)(24 43 124)(25 114 86)(26 115 87)(27 116 88)(28 113 85)(33 81 63)(34 82 64)(35 83 61)(36 84 62)(37 95 129)(38 96 130)(39 93 131)(40 94 132)(45 65 105)(46 66 106)(47 67 107)(48 68 108)(49 57 136)(50 58 133)(51 59 134)(52 60 135)(69 117 77)(70 118 78)(71 119 79)(72 120 80)
(1 96 121)(2 93 122)(3 94 123)(4 95 124)(5 141 9)(6 142 10)(7 143 11)(8 144 12)(13 56 91)(14 53 92)(15 54 89)(16 55 90)(17 58 47)(18 59 48)(19 60 45)(20 57 46)(21 32 130)(22 29 131)(23 30 132)(24 31 129)(25 36 117)(26 33 118)(27 34 119)(28 35 120)(37 43 75)(38 44 76)(39 41 73)(40 42 74)(49 106 111)(50 107 112)(51 108 109)(52 105 110)(61 72 85)(62 69 86)(63 70 87)(64 71 88)(65 138 135)(66 139 136)(67 140 133)(68 137 134)(77 114 84)(78 115 81)(79 116 82)(80 113 83)(97 128 104)(98 125 101)(99 126 102)(100 127 103)
(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)
(1 4)(2 3)(5 101)(6 104)(7 103)(8 102)(9 98)(10 97)(11 100)(12 99)(13 53)(14 56)(15 55)(16 54)(17 46)(18 45)(19 48)(20 47)(21 37)(22 40)(23 39)(24 38)(25 63)(26 62)(27 61)(28 64)(29 74)(30 73)(31 76)(32 75)(33 86)(34 85)(35 88)(36 87)(41 132)(42 131)(43 130)(44 129)(49 133)(50 136)(51 135)(52 134)(57 58)(59 60)(65 109)(66 112)(67 111)(68 110)(69 118)(70 117)(71 120)(72 119)(77 78)(79 80)(81 114)(82 113)(83 116)(84 115)(89 90)(91 92)(93 123)(94 122)(95 121)(96 124)(105 137)(106 140)(107 139)(108 138)(125 141)(126 144)(127 143)(128 142)
(1 90 3 92)(2 91 4 89)(5 30 7 32)(6 31 8 29)(9 132 11 130)(10 129 12 131)(13 124 15 122)(14 121 16 123)(17 113 19 115)(18 114 20 116)(21 141 23 143)(22 142 24 144)(25 139 27 137)(26 140 28 138)(33 67 35 65)(34 68 36 66)(37 125 39 127)(38 126 40 128)(41 100 43 98)(42 97 44 99)(45 81 47 83)(46 82 48 84)(49 71 51 69)(50 72 52 70)(53 96 55 94)(54 93 56 95)(57 79 59 77)(58 80 60 78)(61 105 63 107)(62 106 64 108)(73 103 75 101)(74 104 76 102)(85 110 87 112)(86 111 88 109)(117 136 119 134)(118 133 120 135)
(1 78 3 80)(2 79 4 77)(5 52 7 50)(6 49 8 51)(9 110 11 112)(10 111 12 109)(13 46 15 48)(14 47 16 45)(17 55 19 53)(18 56 20 54)(21 63 23 61)(22 64 24 62)(25 39 27 37)(26 40 28 38)(29 71 31 69)(30 72 32 70)(33 42 35 44)(34 43 36 41)(57 89 59 91)(58 90 60 92)(65 97 67 99)(66 98 68 100)(73 119 75 117)(74 120 76 118)(81 123 83 121)(82 124 84 122)(85 130 87 132)(86 131 88 129)(93 116 95 114)(94 113 96 115)(101 134 103 136)(102 135 104 133)(105 143 107 141)(106 144 108 142)(125 137 127 139)(126 138 128 140)

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

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

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

57 conjugacy classes

class 1 2A2B2C2D2E2F3A3B3C3D4A···4F4G4H4I4J6A···6L12A···12X
order122222233334···444446···612···12
size1121818181822222···2181818182···24···4

57 irreducible representations

dim1111122244
type++++++++-
imageC1C2C2C2C2S3D6D62- 1+4Q8.15D6
kernelC3272- 1+4C12.59D6Q8×C3⋊S3C12.26D6Q8×C3×C6C6×Q8C2×C12C3×Q8C32C3
# reps164414121618

Matrix representation of C3272- 1+4 in GL6(𝔽13)

1210000
1200000
001000
000100
000010
000001
,
1210000
1200000
0012100
0012000
0000121
0000120
,
100000
010000
00111230
0011003
003721
00610123
,
0120000
1200000
001211108
0010153
0073110
001061112
,
0120000
1200000
009200
0011400
000292
0020114
,
1200000
0120000
0083712
00101116
0050510
000532

G:=sub<GL(6,GF(13))| [12,12,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[12,12,0,0,0,0,1,0,0,0,0,0,0,0,12,12,0,0,0,0,1,0,0,0,0,0,0,0,12,12,0,0,0,0,1,0],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,11,1,3,6,0,0,12,10,7,10,0,0,3,0,2,12,0,0,0,3,1,3],[0,12,0,0,0,0,12,0,0,0,0,0,0,0,12,10,7,10,0,0,11,1,3,6,0,0,10,5,1,11,0,0,8,3,10,12],[0,12,0,0,0,0,12,0,0,0,0,0,0,0,9,11,0,2,0,0,2,4,2,0,0,0,0,0,9,11,0,0,0,0,2,4],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,8,10,5,0,0,0,3,11,0,5,0,0,7,1,5,3,0,0,12,6,10,2] >;

C3272- 1+4 in GAP, Magma, Sage, TeX

C_3^2\rtimes_72_-^{1+4}
% in TeX

G:=Group("C3^2:7ES-(2,2)");
// GroupNames label

G:=SmallGroup(288,1012);
// by ID

G=gap.SmallGroup(288,1012);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-3,120,219,100,675,2693,9414]);
// Polycyclic

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

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