G = C32⋊92- 1+4 order 288 = 25·32
2nd semidirect product of C32 and 2- 1+4 acting via 2- 1+4/C4○D4=C2
metabelian, supersoluble, monomial
Aliases: C32⋊92- 1+4, C62.155C23, C3⋊5(Q8○D12), (C3×D4).45D6, (C3×Q8).70D6, (C2×C12).173D6, C6.66(S3×C23), (C3×C6).65C24, C12.D6⋊10C2, C12.59D6⋊14C2, (C3×C12).159C23, (C6×C12).172C22, C12.117(C22×S3), C3⋊Dic3.53C23, C32⋊7D4.3C22, C12⋊S3.35C22, (D4×C32).31C22, (Q8×C32).34C22, C32⋊4Q8.37C22, (C3×C4○D4)⋊9S3, (Q8×C3⋊S3)⋊10C2, C4○D4⋊6(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×C32⋊4Q8)⋊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
Generators and relations for C32⋊92- 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, C3, C4, C4, C4, C22, C22, S3, C6, C6, C2×C4, C2×C4, D4, D4, Q8, Q8, C32, Dic3, C12, D6, C2×C6, C2×Q8, C4○D4, C4○D4, C3⋊S3, C3×C6, C3×C6, Dic6, C4×S3, D12, C2×Dic3, C3⋊D4, C2×C12, C3×D4, C3×Q8, 2- 1+4, C3⋊Dic3, C3×C12, C3×C12, C2×C3⋊S3, C62, C2×Dic6, C4○D12, D4⋊2S3, S3×Q8, C3×C4○D4, C32⋊4Q8, C4×C3⋊S3, C12⋊S3, C2×C3⋊Dic3, C32⋊7D4, C6×C12, D4×C32, Q8×C32, Q8○D12, C2×C32⋊4Q8, C12.59D6, C12.D6, Q8×C3⋊S3, C32×C4○D4, C32⋊92- 1+4
Quotients: C1, C2, C22, S3, C23, D6, C24, C3⋊S3, C22×S3, 2- 1+4, C2×C3⋊S3, S3×C23, C22×C3⋊S3, Q8○D12, C23×C3⋊S3, C32⋊92- 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 | 2A | 2B | 2C | 2D | 2E | 2F | 3A | 3B | 3C | 3D | 4A | 4B | 4C | 4D | 4E | ··· | 4J | 6A | 6B | 6C | 6D | 6E | ··· | 6P | 12A | ··· | 12H | 12I | ··· | 12T |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 6 | 6 | 6 | 6 | 6 | ··· | 6 | 12 | ··· | 12 | 12 | ··· | 12 |
| size | 1 | 1 | 2 | 2 | 2 | 18 | 18 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 18 | ··· | 18 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
57 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | - |
| image | C1 | C2 | C2 | C2 | C2 | C2 | S3 | D6 | D6 | D6 | 2- 1+4 | Q8○D12 |
| kernel | C32⋊92- 1+4 | C2×C32⋊4Q8 | C12.59D6 | C12.D6 | Q8×C3⋊S3 | C32×C4○D4 | C3×C4○D4 | C2×C12 | C3×D4 | C3×Q8 | C32 | C3 |
| # reps | 1 | 3 | 3 | 6 | 2 | 1 | 4 | 12 | 12 | 4 | 1 | 8 |
Matrix representation of C32⋊92- 1+4 ►in GL6(𝔽13)
| 1 | 3 | 0 | 0 | 0 | 0 |
| 12 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 1 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 1 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 1 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 1 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 12 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 10 | 11 | 11 |
| 0 | 0 | 7 | 3 | 9 | 2 |
| 0 | 0 | 9 | 9 | 3 | 3 |
| 0 | 0 | 5 | 4 | 6 | 10 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 6 | 11 | 4 |
| 0 | 0 | 7 | 3 | 9 | 2 |
| 0 | 0 | 9 | 8 | 3 | 7 |
| 0 | 0 | 5 | 4 | 6 | 10 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 12 | 11 | 2 |
| 0 | 0 | 0 | 12 | 0 | 2 |
| 0 | 0 | 1 | 12 | 12 | 1 |
| 0 | 0 | 0 | 12 | 0 | 1 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 8 | 0 |
| 0 | 0 | 0 | 12 | 0 | 8 |
| 0 | 0 | 3 | 0 | 1 | 0 |
| 0 | 0 | 0 | 3 | 0 | 1 |
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] >;
C32⋊92- 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