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G = C3292- 1+4order 288 = 25·32

2nd semidirect product of C32 and 2- 1+4 acting via 2- 1+4/C4○D4=C2

metabelian, supersoluble, monomial

Aliases: C3292- 1+4, C62.155C23, C35(Q8○D12), (C3×D4).45D6, (C3×Q8).70D6, (C2×C12).173D6, C6.66(S3×C23), (C3×C6).65C24, C12.D610C2, C12.59D614C2, (C3×C12).159C23, (C6×C12).172C22, C12.117(C22×S3), C3⋊Dic3.53C23, C327D4.3C22, C12⋊S3.35C22, (D4×C32).31C22, (Q8×C32).34C22, C324Q8.37C22, (C3×C4○D4)⋊9S3, (Q8×C3⋊S3)⋊10C2, C4○D46(C3⋊S3), D4.10(C2×C3⋊S3), Q8.16(C2×C3⋊S3), C4.34(C22×C3⋊S3), C2.14(C23×C3⋊S3), (C32×C4○D4)⋊10C2, (C2×C3⋊S3).57C23, (C4×C3⋊S3).49C22, (C2×C6).19(C22×S3), (C2×C324Q8)⋊23C2, C22.4(C22×C3⋊S3), (C2×C3⋊Dic3).106C22, (C2×C4).24(C2×C3⋊S3), SmallGroup(288,1015)

Series: Derived Chief Lower central Upper central

C1C3×C6 — C3292- 1+4
C1C3C32C3×C6C2×C3⋊S3C4×C3⋊S3Q8×C3⋊S3 — C3292- 1+4
C32C3×C6 — C3292- 1+4
C1C2C4○D4

Generators and relations for C3292- 1+4
 G = < a,b,c,d,e,f | a3=b3=c4=d2=1, e2=f2=c2, ab=ba, cac-1=eae-1=a-1, ad=da, af=fa, cbc-1=ebe-1=b-1, bd=db, bf=fb, dcd=c-1, ce=ec, cf=fc, de=ed, df=fd, fef-1=c2e >

Subgroups: 1348 in 438 conjugacy classes, 153 normal (12 characteristic)
C1, C2, C2 [×5], C3 [×4], C4, C4 [×3], C4 [×6], C22 [×3], C22 [×2], S3 [×8], C6 [×4], C6 [×12], C2×C4 [×3], C2×C4 [×12], D4 [×3], D4 [×7], Q8, Q8 [×9], C32, Dic3 [×24], C12 [×16], D6 [×8], C2×C6 [×12], C2×Q8 [×5], C4○D4, C4○D4 [×9], C3⋊S3 [×2], C3×C6, C3×C6 [×3], Dic6 [×36], C4×S3 [×24], D12 [×4], C2×Dic3 [×24], C3⋊D4 [×24], C2×C12 [×12], C3×D4 [×12], C3×Q8 [×4], 2- 1+4, C3⋊Dic3 [×6], C3×C12, C3×C12 [×3], C2×C3⋊S3 [×2], C62 [×3], C2×Dic6 [×12], C4○D12 [×12], D42S3 [×24], S3×Q8 [×8], C3×C4○D4 [×4], C324Q8 [×9], C4×C3⋊S3 [×6], C12⋊S3, C2×C3⋊Dic3 [×6], C327D4 [×6], C6×C12 [×3], D4×C32 [×3], Q8×C32, Q8○D12 [×4], C2×C324Q8 [×3], C12.59D6 [×3], C12.D6 [×6], Q8×C3⋊S3 [×2], C32×C4○D4, C3292- 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○D12 [×4], C23×C3⋊S3, C3292- 1+4

Smallest permutation representation of C3292- 1+4
On 144 points
Generators in S144
(1 73 35)(2 36 74)(3 75 33)(4 34 76)(5 56 124)(6 121 53)(7 54 122)(8 123 55)(9 28 42)(10 43 25)(11 26 44)(12 41 27)(13 98 19)(14 20 99)(15 100 17)(16 18 97)(21 81 113)(22 114 82)(23 83 115)(24 116 84)(29 88 68)(30 65 85)(31 86 66)(32 67 87)(37 104 50)(38 51 101)(39 102 52)(40 49 103)(45 64 133)(46 134 61)(47 62 135)(48 136 63)(57 79 117)(58 118 80)(59 77 119)(60 120 78)(69 129 127)(70 128 130)(71 131 125)(72 126 132)(89 144 93)(90 94 141)(91 142 95)(92 96 143)(105 140 110)(106 111 137)(107 138 112)(108 109 139)
(1 123 72)(2 69 124)(3 121 70)(4 71 122)(5 36 129)(6 130 33)(7 34 131)(8 132 35)(9 141 14)(10 15 142)(11 143 16)(12 13 144)(17 91 25)(18 26 92)(19 89 27)(20 28 90)(21 67 60)(22 57 68)(23 65 58)(24 59 66)(29 114 79)(30 80 115)(31 116 77)(32 78 113)(37 138 135)(38 136 139)(39 140 133)(40 134 137)(41 98 93)(42 94 99)(43 100 95)(44 96 97)(45 102 110)(46 111 103)(47 104 112)(48 109 101)(49 61 106)(50 107 62)(51 63 108)(52 105 64)(53 128 75)(54 76 125)(55 126 73)(56 74 127)(81 87 120)(82 117 88)(83 85 118)(84 119 86)
(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)(5 128)(6 127)(7 126)(8 125)(9 89)(10 92)(11 91)(12 90)(13 20)(14 19)(15 18)(16 17)(21 86)(22 85)(23 88)(24 87)(25 143)(26 142)(27 141)(28 144)(29 115)(30 114)(31 113)(32 116)(33 74)(34 73)(35 76)(36 75)(37 111)(38 110)(39 109)(40 112)(41 94)(42 93)(43 96)(44 95)(45 136)(46 135)(47 134)(48 133)(49 107)(50 106)(51 105)(52 108)(53 129)(54 132)(55 131)(56 130)(57 118)(58 117)(59 120)(60 119)(61 62)(63 64)(65 82)(66 81)(67 84)(68 83)(69 121)(70 124)(71 123)(72 122)(77 78)(79 80)(97 100)(98 99)(101 140)(102 139)(103 138)(104 137)
(1 97 3 99)(2 98 4 100)(5 144 7 142)(6 141 8 143)(9 132 11 130)(10 129 12 131)(13 34 15 36)(14 35 16 33)(17 74 19 76)(18 75 20 73)(21 112 23 110)(22 109 24 111)(25 127 27 125)(26 128 28 126)(29 51 31 49)(30 52 32 50)(37 85 39 87)(38 86 40 88)(41 71 43 69)(42 72 44 70)(45 60 47 58)(46 57 48 59)(53 90 55 92)(54 91 56 89)(61 79 63 77)(62 80 64 78)(65 102 67 104)(66 103 68 101)(81 138 83 140)(82 139 84 137)(93 122 95 124)(94 123 96 121)(105 113 107 115)(106 114 108 116)(117 136 119 134)(118 133 120 135)
(1 80 3 78)(2 77 4 79)(5 84 7 82)(6 81 8 83)(9 39 11 37)(10 40 12 38)(13 136 15 134)(14 133 16 135)(17 46 19 48)(18 47 20 45)(21 55 23 53)(22 56 24 54)(25 103 27 101)(26 104 28 102)(29 69 31 71)(30 70 32 72)(33 120 35 118)(34 117 36 119)(41 51 43 49)(42 52 44 50)(57 74 59 76)(58 75 60 73)(61 98 63 100)(62 99 64 97)(65 128 67 126)(66 125 68 127)(85 130 87 132)(86 131 88 129)(89 109 91 111)(90 110 92 112)(93 108 95 106)(94 105 96 107)(113 123 115 121)(114 124 116 122)(137 144 139 142)(138 141 140 143)

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

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

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

57 conjugacy classes

class 1 2A2B2C2D2E2F3A3B3C3D4A4B4C4D4E···4J6A6B6C6D6E···6P12A···12H12I···12T
order1222222333344444···466666···612···1212···12
size1122218182222222218···1822224···42···24···4

57 irreducible representations

dim111111222244
type++++++++++--
imageC1C2C2C2C2C2S3D6D6D62- 1+4Q8○D12
kernelC3292- 1+4C2×C324Q8C12.59D6C12.D6Q8×C3⋊S3C32×C4○D4C3×C4○D4C2×C12C3×D4C3×Q8C32C3
# reps13362141212418

Matrix representation of C3292- 1+4 in GL6(𝔽13)

130000
12110000
0012100
0012000
0000121
0000120
,
100000
010000
0012100
0012000
0000121
0000120
,
100000
12120000
0010101111
007392
009933
0054610
,
100000
010000
00106114
007392
009837
0054610
,
1200000
110000
00112112
0001202
00112121
0001201
,
1200000
0120000
0012080
0001208
003010
000301

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

C3292- 1+4 in GAP, Magma, Sage, TeX

C_3^2\rtimes_92_-^{1+4}
% in TeX

G:=Group("C3^2:9ES-(2,2)");
// GroupNames label

G:=SmallGroup(288,1015);
// by ID

G=gap.SmallGroup(288,1015);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-3,120,219,100,675,80,2693,9414]);
// 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,c*a*c^-1=e*a*e^-1=a^-1,a*d=d*a,a*f=f*a,c*b*c^-1=e*b*e^-1=b^-1,b*d=d*b,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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