metabelian, supersoluble, monomial
Aliases: C33⋊8M4(2), C12.71S32, C3⋊3(C24⋊S3), C6.7(S3×Dic3), C33⋊7C8⋊10C2, (C3×C12).166D6, C32⋊6(C8⋊S3), C3⋊Dic3.4Dic3, C3⋊1(D6.Dic3), C32⋊9(C4.Dic3), (C32×C12).68C22, (C3×C3⋊C8)⋊7S3, C3⋊C8⋊4(C3⋊S3), (C6×C3⋊S3).6C4, (C4×C3⋊S3).6S3, C4.26(S3×C3⋊S3), C6.18(C4×C3⋊S3), (C12×C3⋊S3).1C2, C12.41(C2×C3⋊S3), (C32×C3⋊C8)⋊12C2, (C3×C6).46(C4×S3), C2.3(Dic3×C3⋊S3), (C2×C3⋊S3).4Dic3, (C3×C3⋊Dic3).5C4, (C32×C6).35(C2×C4), (C3×C6).51(C2×Dic3), SmallGroup(432,434)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C33⋊8M4(2)
G = < a,b,c,d,e | a3=b3=c3=d8=e2=1, ab=ba, ac=ca, dad-1=eae=a-1, bc=cb, dbd-1=ebe=b-1, dcd-1=c-1, ce=ec, ede=d5 >
Subgroups: 600 in 152 conjugacy classes, 50 normal (22 characteristic)
C1, C2, C2, C3, C3, C3, C4, C4, C22, S3, C6, C6, C6, C8, C2×C4, C32, C32, C32, Dic3, C12, C12, C12, D6, C2×C6, M4(2), C3×S3, C3⋊S3, C3×C6, C3×C6, C3×C6, C3⋊C8, C3⋊C8, C24, C4×S3, C2×C12, C33, C3×Dic3, C3⋊Dic3, C3×C12, C3×C12, C3×C12, S3×C6, C2×C3⋊S3, C8⋊S3, C4.Dic3, C3×C3⋊S3, C32×C6, C3×C3⋊C8, C32⋊4C8, C3×C24, S3×C12, C4×C3⋊S3, C3×C3⋊Dic3, C32×C12, C6×C3⋊S3, D6.Dic3, C24⋊S3, C32×C3⋊C8, C33⋊7C8, C12×C3⋊S3, C33⋊8M4(2)
Quotients: C1, C2, C4, C22, S3, C2×C4, Dic3, D6, M4(2), C3⋊S3, C4×S3, C2×Dic3, S32, C2×C3⋊S3, C8⋊S3, C4.Dic3, S3×Dic3, C4×C3⋊S3, S3×C3⋊S3, D6.Dic3, C24⋊S3, Dic3×C3⋊S3, C33⋊8M4(2)
►On 144 points
Generators in S144
(1 52 84)(2 85 53)(3 54 86)(4 87 55)(5 56 88)(6 81 49)(7 50 82)(8 83 51)(9 135 63)(10 64 136)(11 129 57)(12 58 130)(13 131 59)(14 60 132)(15 133 61)(16 62 134)(17 125 120)(18 113 126)(19 127 114)(20 115 128)(21 121 116)(22 117 122)(23 123 118)(24 119 124)(25 143 47)(26 48 144)(27 137 41)(28 42 138)(29 139 43)(30 44 140)(31 141 45)(32 46 142)(33 66 112)(34 105 67)(35 68 106)(36 107 69)(37 70 108)(38 109 71)(39 72 110)(40 111 65)(73 93 104)(74 97 94)(75 95 98)(76 99 96)(77 89 100)(78 101 90)(79 91 102)(80 103 92)
(1 133 22)(2 23 134)(3 135 24)(4 17 136)(5 129 18)(6 19 130)(7 131 20)(8 21 132)(9 124 86)(10 87 125)(11 126 88)(12 81 127)(13 128 82)(14 83 121)(15 122 84)(16 85 123)(25 39 77)(26 78 40)(27 33 79)(28 80 34)(29 35 73)(30 74 36)(31 37 75)(32 76 38)(41 112 102)(42 103 105)(43 106 104)(44 97 107)(45 108 98)(46 99 109)(47 110 100)(48 101 111)(49 114 58)(50 59 115)(51 116 60)(52 61 117)(53 118 62)(54 63 119)(55 120 64)(56 57 113)(65 144 90)(66 91 137)(67 138 92)(68 93 139)(69 140 94)(70 95 141)(71 142 96)(72 89 143)
(1 15 117)(2 118 16)(3 9 119)(4 120 10)(5 11 113)(6 114 12)(7 13 115)(8 116 14)(17 64 87)(18 88 57)(19 58 81)(20 82 59)(21 60 83)(22 84 61)(23 62 85)(24 86 63)(25 89 110)(26 111 90)(27 91 112)(28 105 92)(29 93 106)(30 107 94)(31 95 108)(32 109 96)(33 137 102)(34 103 138)(35 139 104)(36 97 140)(37 141 98)(38 99 142)(39 143 100)(40 101 144)(41 79 66)(42 67 80)(43 73 68)(44 69 74)(45 75 70)(46 71 76)(47 77 72)(48 65 78)(49 127 130)(50 131 128)(51 121 132)(52 133 122)(53 123 134)(54 135 124)(55 125 136)(56 129 126)
(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 70)(2 67)(3 72)(4 69)(5 66)(6 71)(7 68)(8 65)(9 47)(10 44)(11 41)(12 46)(13 43)(14 48)(15 45)(16 42)(17 94)(18 91)(19 96)(20 93)(21 90)(22 95)(23 92)(24 89)(25 63)(26 60)(27 57)(28 62)(29 59)(30 64)(31 61)(32 58)(33 56)(34 53)(35 50)(36 55)(37 52)(38 49)(39 54)(40 51)(73 115)(74 120)(75 117)(76 114)(77 119)(78 116)(79 113)(80 118)(81 109)(82 106)(83 111)(84 108)(85 105)(86 110)(87 107)(88 112)(97 125)(98 122)(99 127)(100 124)(101 121)(102 126)(103 123)(104 128)(129 137)(130 142)(131 139)(132 144)(133 141)(134 138)(135 143)(136 140)
G:=sub<Sym(144)| (1,52,84)(2,85,53)(3,54,86)(4,87,55)(5,56,88)(6,81,49)(7,50,82)(8,83,51)(9,135,63)(10,64,136)(11,129,57)(12,58,130)(13,131,59)(14,60,132)(15,133,61)(16,62,134)(17,125,120)(18,113,126)(19,127,114)(20,115,128)(21,121,116)(22,117,122)(23,123,118)(24,119,124)(25,143,47)(26,48,144)(27,137,41)(28,42,138)(29,139,43)(30,44,140)(31,141,45)(32,46,142)(33,66,112)(34,105,67)(35,68,106)(36,107,69)(37,70,108)(38,109,71)(39,72,110)(40,111,65)(73,93,104)(74,97,94)(75,95,98)(76,99,96)(77,89,100)(78,101,90)(79,91,102)(80,103,92), (1,133,22)(2,23,134)(3,135,24)(4,17,136)(5,129,18)(6,19,130)(7,131,20)(8,21,132)(9,124,86)(10,87,125)(11,126,88)(12,81,127)(13,128,82)(14,83,121)(15,122,84)(16,85,123)(25,39,77)(26,78,40)(27,33,79)(28,80,34)(29,35,73)(30,74,36)(31,37,75)(32,76,38)(41,112,102)(42,103,105)(43,106,104)(44,97,107)(45,108,98)(46,99,109)(47,110,100)(48,101,111)(49,114,58)(50,59,115)(51,116,60)(52,61,117)(53,118,62)(54,63,119)(55,120,64)(56,57,113)(65,144,90)(66,91,137)(67,138,92)(68,93,139)(69,140,94)(70,95,141)(71,142,96)(72,89,143), (1,15,117)(2,118,16)(3,9,119)(4,120,10)(5,11,113)(6,114,12)(7,13,115)(8,116,14)(17,64,87)(18,88,57)(19,58,81)(20,82,59)(21,60,83)(22,84,61)(23,62,85)(24,86,63)(25,89,110)(26,111,90)(27,91,112)(28,105,92)(29,93,106)(30,107,94)(31,95,108)(32,109,96)(33,137,102)(34,103,138)(35,139,104)(36,97,140)(37,141,98)(38,99,142)(39,143,100)(40,101,144)(41,79,66)(42,67,80)(43,73,68)(44,69,74)(45,75,70)(46,71,76)(47,77,72)(48,65,78)(49,127,130)(50,131,128)(51,121,132)(52,133,122)(53,123,134)(54,135,124)(55,125,136)(56,129,126), (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), (1,70)(2,67)(3,72)(4,69)(5,66)(6,71)(7,68)(8,65)(9,47)(10,44)(11,41)(12,46)(13,43)(14,48)(15,45)(16,42)(17,94)(18,91)(19,96)(20,93)(21,90)(22,95)(23,92)(24,89)(25,63)(26,60)(27,57)(28,62)(29,59)(30,64)(31,61)(32,58)(33,56)(34,53)(35,50)(36,55)(37,52)(38,49)(39,54)(40,51)(73,115)(74,120)(75,117)(76,114)(77,119)(78,116)(79,113)(80,118)(81,109)(82,106)(83,111)(84,108)(85,105)(86,110)(87,107)(88,112)(97,125)(98,122)(99,127)(100,124)(101,121)(102,126)(103,123)(104,128)(129,137)(130,142)(131,139)(132,144)(133,141)(134,138)(135,143)(136,140)>;
G:=Group( (1,52,84)(2,85,53)(3,54,86)(4,87,55)(5,56,88)(6,81,49)(7,50,82)(8,83,51)(9,135,63)(10,64,136)(11,129,57)(12,58,130)(13,131,59)(14,60,132)(15,133,61)(16,62,134)(17,125,120)(18,113,126)(19,127,114)(20,115,128)(21,121,116)(22,117,122)(23,123,118)(24,119,124)(25,143,47)(26,48,144)(27,137,41)(28,42,138)(29,139,43)(30,44,140)(31,141,45)(32,46,142)(33,66,112)(34,105,67)(35,68,106)(36,107,69)(37,70,108)(38,109,71)(39,72,110)(40,111,65)(73,93,104)(74,97,94)(75,95,98)(76,99,96)(77,89,100)(78,101,90)(79,91,102)(80,103,92), (1,133,22)(2,23,134)(3,135,24)(4,17,136)(5,129,18)(6,19,130)(7,131,20)(8,21,132)(9,124,86)(10,87,125)(11,126,88)(12,81,127)(13,128,82)(14,83,121)(15,122,84)(16,85,123)(25,39,77)(26,78,40)(27,33,79)(28,80,34)(29,35,73)(30,74,36)(31,37,75)(32,76,38)(41,112,102)(42,103,105)(43,106,104)(44,97,107)(45,108,98)(46,99,109)(47,110,100)(48,101,111)(49,114,58)(50,59,115)(51,116,60)(52,61,117)(53,118,62)(54,63,119)(55,120,64)(56,57,113)(65,144,90)(66,91,137)(67,138,92)(68,93,139)(69,140,94)(70,95,141)(71,142,96)(72,89,143), (1,15,117)(2,118,16)(3,9,119)(4,120,10)(5,11,113)(6,114,12)(7,13,115)(8,116,14)(17,64,87)(18,88,57)(19,58,81)(20,82,59)(21,60,83)(22,84,61)(23,62,85)(24,86,63)(25,89,110)(26,111,90)(27,91,112)(28,105,92)(29,93,106)(30,107,94)(31,95,108)(32,109,96)(33,137,102)(34,103,138)(35,139,104)(36,97,140)(37,141,98)(38,99,142)(39,143,100)(40,101,144)(41,79,66)(42,67,80)(43,73,68)(44,69,74)(45,75,70)(46,71,76)(47,77,72)(48,65,78)(49,127,130)(50,131,128)(51,121,132)(52,133,122)(53,123,134)(54,135,124)(55,125,136)(56,129,126), (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), (1,70)(2,67)(3,72)(4,69)(5,66)(6,71)(7,68)(8,65)(9,47)(10,44)(11,41)(12,46)(13,43)(14,48)(15,45)(16,42)(17,94)(18,91)(19,96)(20,93)(21,90)(22,95)(23,92)(24,89)(25,63)(26,60)(27,57)(28,62)(29,59)(30,64)(31,61)(32,58)(33,56)(34,53)(35,50)(36,55)(37,52)(38,49)(39,54)(40,51)(73,115)(74,120)(75,117)(76,114)(77,119)(78,116)(79,113)(80,118)(81,109)(82,106)(83,111)(84,108)(85,105)(86,110)(87,107)(88,112)(97,125)(98,122)(99,127)(100,124)(101,121)(102,126)(103,123)(104,128)(129,137)(130,142)(131,139)(132,144)(133,141)(134,138)(135,143)(136,140) );
G=PermutationGroup([[(1,52,84),(2,85,53),(3,54,86),(4,87,55),(5,56,88),(6,81,49),(7,50,82),(8,83,51),(9,135,63),(10,64,136),(11,129,57),(12,58,130),(13,131,59),(14,60,132),(15,133,61),(16,62,134),(17,125,120),(18,113,126),(19,127,114),(20,115,128),(21,121,116),(22,117,122),(23,123,118),(24,119,124),(25,143,47),(26,48,144),(27,137,41),(28,42,138),(29,139,43),(30,44,140),(31,141,45),(32,46,142),(33,66,112),(34,105,67),(35,68,106),(36,107,69),(37,70,108),(38,109,71),(39,72,110),(40,111,65),(73,93,104),(74,97,94),(75,95,98),(76,99,96),(77,89,100),(78,101,90),(79,91,102),(80,103,92)], [(1,133,22),(2,23,134),(3,135,24),(4,17,136),(5,129,18),(6,19,130),(7,131,20),(8,21,132),(9,124,86),(10,87,125),(11,126,88),(12,81,127),(13,128,82),(14,83,121),(15,122,84),(16,85,123),(25,39,77),(26,78,40),(27,33,79),(28,80,34),(29,35,73),(30,74,36),(31,37,75),(32,76,38),(41,112,102),(42,103,105),(43,106,104),(44,97,107),(45,108,98),(46,99,109),(47,110,100),(48,101,111),(49,114,58),(50,59,115),(51,116,60),(52,61,117),(53,118,62),(54,63,119),(55,120,64),(56,57,113),(65,144,90),(66,91,137),(67,138,92),(68,93,139),(69,140,94),(70,95,141),(71,142,96),(72,89,143)], [(1,15,117),(2,118,16),(3,9,119),(4,120,10),(5,11,113),(6,114,12),(7,13,115),(8,116,14),(17,64,87),(18,88,57),(19,58,81),(20,82,59),(21,60,83),(22,84,61),(23,62,85),(24,86,63),(25,89,110),(26,111,90),(27,91,112),(28,105,92),(29,93,106),(30,107,94),(31,95,108),(32,109,96),(33,137,102),(34,103,138),(35,139,104),(36,97,140),(37,141,98),(38,99,142),(39,143,100),(40,101,144),(41,79,66),(42,67,80),(43,73,68),(44,69,74),(45,75,70),(46,71,76),(47,77,72),(48,65,78),(49,127,130),(50,131,128),(51,121,132),(52,133,122),(53,123,134),(54,135,124),(55,125,136),(56,129,126)], [(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)], [(1,70),(2,67),(3,72),(4,69),(5,66),(6,71),(7,68),(8,65),(9,47),(10,44),(11,41),(12,46),(13,43),(14,48),(15,45),(16,42),(17,94),(18,91),(19,96),(20,93),(21,90),(22,95),(23,92),(24,89),(25,63),(26,60),(27,57),(28,62),(29,59),(30,64),(31,61),(32,58),(33,56),(34,53),(35,50),(36,55),(37,52),(38,49),(39,54),(40,51),(73,115),(74,120),(75,117),(76,114),(77,119),(78,116),(79,113),(80,118),(81,109),(82,106),(83,111),(84,108),(85,105),(86,110),(87,107),(88,112),(97,125),(98,122),(99,127),(100,124),(101,121),(102,126),(103,123),(104,128),(129,137),(130,142),(131,139),(132,144),(133,141),(134,138),(135,143),(136,140)]])
66 conjugacy classes
| class | 1 | 2A | 2B | 3A | ··· | 3E | 3F | 3G | 3H | 3I | 4A | 4B | 4C | 6A | ··· | 6E | 6F | 6G | 6H | 6I | 6J | 6K | 8A | 8B | 8C | 8D | 12A | ··· | 12J | 12K | ··· | 12R | 12S | 12T | 24A | ··· | 24P |
| order | 1 | 2 | 2 | 3 | ··· | 3 | 3 | 3 | 3 | 3 | 4 | 4 | 4 | 6 | ··· | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 8 | 8 | 8 | 8 | 12 | ··· | 12 | 12 | ··· | 12 | 12 | 12 | 24 | ··· | 24 |
| size | 1 | 1 | 18 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 1 | 1 | 18 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 18 | 18 | 6 | 6 | 54 | 54 | 2 | ··· | 2 | 4 | ··· | 4 | 18 | 18 | 6 | ··· | 6 |
66 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | - | + | - | + | - | |||||||
| image | C1 | C2 | C2 | C2 | C4 | C4 | S3 | S3 | Dic3 | D6 | Dic3 | M4(2) | C4×S3 | C8⋊S3 | C4.Dic3 | S32 | S3×Dic3 | D6.Dic3 |
| kernel | C33⋊8M4(2) | C32×C3⋊C8 | C33⋊7C8 | C12×C3⋊S3 | C3×C3⋊Dic3 | C6×C3⋊S3 | C3×C3⋊C8 | C4×C3⋊S3 | C3⋊Dic3 | C3×C12 | C2×C3⋊S3 | C33 | C3×C6 | C32 | C32 | C12 | C6 | C3 |
| # reps | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 1 | 1 | 5 | 1 | 2 | 8 | 16 | 4 | 4 | 4 | 8 |
Matrix representation of C33⋊8M4(2) ►in GL8(𝔽73)
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 72 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 72 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 72 | 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 | 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 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 72 | 72 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 67 | 3 | 0 | 0 | 0 | 0 | 0 | 0 |
| 70 | 6 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 54 | 48 | 0 | 0 | 0 | 0 |
| 0 | 0 | 29 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 72 | 0 | 0 |
| 0 | 0 | 0 | 0 | 72 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 72 | 72 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 54 | 48 | 0 | 0 | 0 | 0 |
| 0 | 0 | 29 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 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 |
G:=sub<GL(8,GF(73))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,72,72,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,72,72,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,72,72,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,72,1,0,0,0,0,0,0,72,0],[67,70,0,0,0,0,0,0,3,6,0,0,0,0,0,0,0,0,54,29,0,0,0,0,0,0,48,19,0,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,0,1,72,0,0,0,0,0,0,0,72],[0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,54,29,0,0,0,0,0,0,48,19,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1] >;
C33⋊8M4(2) in GAP, Magma, Sage, TeX
C_3^3\rtimes_8M_4(2)
% in TeX
G:=Group("C3^3:8M4(2)"); // GroupNames label
G:=SmallGroup(432,434);
// by ID
G=gap.SmallGroup(432,434);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,28,141,58,571,2028,14118]);
// Polycyclic
G:=Group<a,b,c,d,e|a^3=b^3=c^3=d^8=e^2=1,a*b=b*a,a*c=c*a,d*a*d^-1=e*a*e=a^-1,b*c=c*b,d*b*d^-1=e*b*e=b^-1,d*c*d^-1=c^-1,c*e=e*c,e*d*e=d^5>;
// generators/relations