metabelian, supersoluble, monomial
Aliases: C33⋊7M4(2), C12.70S32, (S3×C12).3S3, C33⋊7C8⋊9C2, D6.(C3⋊Dic3), C32⋊4C8⋊13S3, (C3×C12).165D6, (S3×C6).7Dic3, C6.29(S3×Dic3), Dic3.(C3⋊Dic3), C3⋊3(D6.Dic3), C32⋊14(C8⋊S3), C3⋊1(C12.58D6), (C3×Dic3).3Dic3, C32⋊5(C4.Dic3), (C32×Dic3).3C4, (C32×C12).67C22, (S3×C3×C6).6C4, C4.25(S3×C3⋊S3), (S3×C3×C12).1C2, C12.40(C2×C3⋊S3), (C3×C6).90(C4×S3), C2.3(S3×C3⋊Dic3), C6.2(C2×C3⋊Dic3), (C4×S3).2(C3⋊S3), (C3×C32⋊4C8)⋊11C2, (C32×C6).34(C2×C4), (C3×C6).36(C2×Dic3), SmallGroup(432,433)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C33⋊7M4(2)
G = < a,b,c,d,e | a3=b3=c3=d8=e2=1, ab=ba, ac=ca, dad-1=a-1, ae=ea, bc=cb, dbd-1=b-1, be=eb, dcd-1=ece=c-1, ede=d5 >
Subgroups: 520 in 152 conjugacy classes, 58 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×C6, C3×C6, C3×C6, C3⋊C8, C24, C4×S3, C2×C12, C33, C3×Dic3, C3×C12, C3×C12, C3×C12, S3×C6, C62, C8⋊S3, C4.Dic3, S3×C32, C32×C6, C3×C3⋊C8, C32⋊4C8, C32⋊4C8, S3×C12, C6×C12, C32×Dic3, C32×C12, S3×C3×C6, D6.Dic3, C12.58D6, C3×C32⋊4C8, C33⋊7C8, S3×C3×C12, C33⋊7M4(2)
Quotients: C1, C2, C4, C22, S3, C2×C4, Dic3, D6, M4(2), C3⋊S3, C4×S3, C2×Dic3, C3⋊Dic3, S32, C2×C3⋊S3, C8⋊S3, C4.Dic3, S3×Dic3, C2×C3⋊Dic3, S3×C3⋊S3, D6.Dic3, C12.58D6, S3×C3⋊Dic3, C33⋊7M4(2)
►On 144 points
Generators in S144
(1 18 84)(2 85 19)(3 20 86)(4 87 21)(5 22 88)(6 81 23)(7 24 82)(8 83 17)(9 70 50)(10 51 71)(11 72 52)(12 53 65)(13 66 54)(14 55 67)(15 68 56)(16 49 69)(25 143 59)(26 60 144)(27 137 61)(28 62 138)(29 139 63)(30 64 140)(31 141 57)(32 58 142)(33 41 113)(34 114 42)(35 43 115)(36 116 44)(37 45 117)(38 118 46)(39 47 119)(40 120 48)(73 93 104)(74 97 94)(75 95 98)(76 99 96)(77 89 100)(78 101 90)(79 91 102)(80 103 92)(105 125 136)(106 129 126)(107 127 130)(108 131 128)(109 121 132)(110 133 122)(111 123 134)(112 135 124)
(1 72 124)(2 125 65)(3 66 126)(4 127 67)(5 68 128)(6 121 69)(7 70 122)(8 123 71)(9 133 82)(10 83 134)(11 135 84)(12 85 136)(13 129 86)(14 87 130)(15 131 88)(16 81 132)(17 111 51)(18 52 112)(19 105 53)(20 54 106)(21 107 55)(22 56 108)(23 109 49)(24 50 110)(25 39 79)(26 80 40)(27 33 73)(28 74 34)(29 35 75)(30 76 36)(31 37 77)(32 78 38)(41 93 137)(42 138 94)(43 95 139)(44 140 96)(45 89 141)(46 142 90)(47 91 143)(48 144 92)(57 117 100)(58 101 118)(59 119 102)(60 103 120)(61 113 104)(62 97 114)(63 115 98)(64 99 116)
(1 11 112)(2 105 12)(3 13 106)(4 107 14)(5 15 108)(6 109 16)(7 9 110)(8 111 10)(17 134 71)(18 72 135)(19 136 65)(20 66 129)(21 130 67)(22 68 131)(23 132 69)(24 70 133)(25 91 119)(26 120 92)(27 93 113)(28 114 94)(29 95 115)(30 116 96)(31 89 117)(32 118 90)(33 137 104)(34 97 138)(35 139 98)(36 99 140)(37 141 100)(38 101 142)(39 143 102)(40 103 144)(41 61 73)(42 74 62)(43 63 75)(44 76 64)(45 57 77)(46 78 58)(47 59 79)(48 80 60)(49 81 121)(50 122 82)(51 83 123)(52 124 84)(53 85 125)(54 126 86)(55 87 127)(56 128 88)
(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 44)(2 41)(3 46)(4 43)(5 48)(6 45)(7 42)(8 47)(9 62)(10 59)(11 64)(12 61)(13 58)(14 63)(15 60)(16 57)(17 39)(18 36)(19 33)(20 38)(21 35)(22 40)(23 37)(24 34)(25 51)(26 56)(27 53)(28 50)(29 55)(30 52)(31 49)(32 54)(65 137)(66 142)(67 139)(68 144)(69 141)(70 138)(71 143)(72 140)(73 105)(74 110)(75 107)(76 112)(77 109)(78 106)(79 111)(80 108)(81 117)(82 114)(83 119)(84 116)(85 113)(86 118)(87 115)(88 120)(89 121)(90 126)(91 123)(92 128)(93 125)(94 122)(95 127)(96 124)(97 133)(98 130)(99 135)(100 132)(101 129)(102 134)(103 131)(104 136)
G:=sub<Sym(144)| (1,18,84)(2,85,19)(3,20,86)(4,87,21)(5,22,88)(6,81,23)(7,24,82)(8,83,17)(9,70,50)(10,51,71)(11,72,52)(12,53,65)(13,66,54)(14,55,67)(15,68,56)(16,49,69)(25,143,59)(26,60,144)(27,137,61)(28,62,138)(29,139,63)(30,64,140)(31,141,57)(32,58,142)(33,41,113)(34,114,42)(35,43,115)(36,116,44)(37,45,117)(38,118,46)(39,47,119)(40,120,48)(73,93,104)(74,97,94)(75,95,98)(76,99,96)(77,89,100)(78,101,90)(79,91,102)(80,103,92)(105,125,136)(106,129,126)(107,127,130)(108,131,128)(109,121,132)(110,133,122)(111,123,134)(112,135,124), (1,72,124)(2,125,65)(3,66,126)(4,127,67)(5,68,128)(6,121,69)(7,70,122)(8,123,71)(9,133,82)(10,83,134)(11,135,84)(12,85,136)(13,129,86)(14,87,130)(15,131,88)(16,81,132)(17,111,51)(18,52,112)(19,105,53)(20,54,106)(21,107,55)(22,56,108)(23,109,49)(24,50,110)(25,39,79)(26,80,40)(27,33,73)(28,74,34)(29,35,75)(30,76,36)(31,37,77)(32,78,38)(41,93,137)(42,138,94)(43,95,139)(44,140,96)(45,89,141)(46,142,90)(47,91,143)(48,144,92)(57,117,100)(58,101,118)(59,119,102)(60,103,120)(61,113,104)(62,97,114)(63,115,98)(64,99,116), (1,11,112)(2,105,12)(3,13,106)(4,107,14)(5,15,108)(6,109,16)(7,9,110)(8,111,10)(17,134,71)(18,72,135)(19,136,65)(20,66,129)(21,130,67)(22,68,131)(23,132,69)(24,70,133)(25,91,119)(26,120,92)(27,93,113)(28,114,94)(29,95,115)(30,116,96)(31,89,117)(32,118,90)(33,137,104)(34,97,138)(35,139,98)(36,99,140)(37,141,100)(38,101,142)(39,143,102)(40,103,144)(41,61,73)(42,74,62)(43,63,75)(44,76,64)(45,57,77)(46,78,58)(47,59,79)(48,80,60)(49,81,121)(50,122,82)(51,83,123)(52,124,84)(53,85,125)(54,126,86)(55,87,127)(56,128,88), (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), (1,44)(2,41)(3,46)(4,43)(5,48)(6,45)(7,42)(8,47)(9,62)(10,59)(11,64)(12,61)(13,58)(14,63)(15,60)(16,57)(17,39)(18,36)(19,33)(20,38)(21,35)(22,40)(23,37)(24,34)(25,51)(26,56)(27,53)(28,50)(29,55)(30,52)(31,49)(32,54)(65,137)(66,142)(67,139)(68,144)(69,141)(70,138)(71,143)(72,140)(73,105)(74,110)(75,107)(76,112)(77,109)(78,106)(79,111)(80,108)(81,117)(82,114)(83,119)(84,116)(85,113)(86,118)(87,115)(88,120)(89,121)(90,126)(91,123)(92,128)(93,125)(94,122)(95,127)(96,124)(97,133)(98,130)(99,135)(100,132)(101,129)(102,134)(103,131)(104,136)>;
G:=Group( (1,18,84)(2,85,19)(3,20,86)(4,87,21)(5,22,88)(6,81,23)(7,24,82)(8,83,17)(9,70,50)(10,51,71)(11,72,52)(12,53,65)(13,66,54)(14,55,67)(15,68,56)(16,49,69)(25,143,59)(26,60,144)(27,137,61)(28,62,138)(29,139,63)(30,64,140)(31,141,57)(32,58,142)(33,41,113)(34,114,42)(35,43,115)(36,116,44)(37,45,117)(38,118,46)(39,47,119)(40,120,48)(73,93,104)(74,97,94)(75,95,98)(76,99,96)(77,89,100)(78,101,90)(79,91,102)(80,103,92)(105,125,136)(106,129,126)(107,127,130)(108,131,128)(109,121,132)(110,133,122)(111,123,134)(112,135,124), (1,72,124)(2,125,65)(3,66,126)(4,127,67)(5,68,128)(6,121,69)(7,70,122)(8,123,71)(9,133,82)(10,83,134)(11,135,84)(12,85,136)(13,129,86)(14,87,130)(15,131,88)(16,81,132)(17,111,51)(18,52,112)(19,105,53)(20,54,106)(21,107,55)(22,56,108)(23,109,49)(24,50,110)(25,39,79)(26,80,40)(27,33,73)(28,74,34)(29,35,75)(30,76,36)(31,37,77)(32,78,38)(41,93,137)(42,138,94)(43,95,139)(44,140,96)(45,89,141)(46,142,90)(47,91,143)(48,144,92)(57,117,100)(58,101,118)(59,119,102)(60,103,120)(61,113,104)(62,97,114)(63,115,98)(64,99,116), (1,11,112)(2,105,12)(3,13,106)(4,107,14)(5,15,108)(6,109,16)(7,9,110)(8,111,10)(17,134,71)(18,72,135)(19,136,65)(20,66,129)(21,130,67)(22,68,131)(23,132,69)(24,70,133)(25,91,119)(26,120,92)(27,93,113)(28,114,94)(29,95,115)(30,116,96)(31,89,117)(32,118,90)(33,137,104)(34,97,138)(35,139,98)(36,99,140)(37,141,100)(38,101,142)(39,143,102)(40,103,144)(41,61,73)(42,74,62)(43,63,75)(44,76,64)(45,57,77)(46,78,58)(47,59,79)(48,80,60)(49,81,121)(50,122,82)(51,83,123)(52,124,84)(53,85,125)(54,126,86)(55,87,127)(56,128,88), (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), (1,44)(2,41)(3,46)(4,43)(5,48)(6,45)(7,42)(8,47)(9,62)(10,59)(11,64)(12,61)(13,58)(14,63)(15,60)(16,57)(17,39)(18,36)(19,33)(20,38)(21,35)(22,40)(23,37)(24,34)(25,51)(26,56)(27,53)(28,50)(29,55)(30,52)(31,49)(32,54)(65,137)(66,142)(67,139)(68,144)(69,141)(70,138)(71,143)(72,140)(73,105)(74,110)(75,107)(76,112)(77,109)(78,106)(79,111)(80,108)(81,117)(82,114)(83,119)(84,116)(85,113)(86,118)(87,115)(88,120)(89,121)(90,126)(91,123)(92,128)(93,125)(94,122)(95,127)(96,124)(97,133)(98,130)(99,135)(100,132)(101,129)(102,134)(103,131)(104,136) );
G=PermutationGroup([[(1,18,84),(2,85,19),(3,20,86),(4,87,21),(5,22,88),(6,81,23),(7,24,82),(8,83,17),(9,70,50),(10,51,71),(11,72,52),(12,53,65),(13,66,54),(14,55,67),(15,68,56),(16,49,69),(25,143,59),(26,60,144),(27,137,61),(28,62,138),(29,139,63),(30,64,140),(31,141,57),(32,58,142),(33,41,113),(34,114,42),(35,43,115),(36,116,44),(37,45,117),(38,118,46),(39,47,119),(40,120,48),(73,93,104),(74,97,94),(75,95,98),(76,99,96),(77,89,100),(78,101,90),(79,91,102),(80,103,92),(105,125,136),(106,129,126),(107,127,130),(108,131,128),(109,121,132),(110,133,122),(111,123,134),(112,135,124)], [(1,72,124),(2,125,65),(3,66,126),(4,127,67),(5,68,128),(6,121,69),(7,70,122),(8,123,71),(9,133,82),(10,83,134),(11,135,84),(12,85,136),(13,129,86),(14,87,130),(15,131,88),(16,81,132),(17,111,51),(18,52,112),(19,105,53),(20,54,106),(21,107,55),(22,56,108),(23,109,49),(24,50,110),(25,39,79),(26,80,40),(27,33,73),(28,74,34),(29,35,75),(30,76,36),(31,37,77),(32,78,38),(41,93,137),(42,138,94),(43,95,139),(44,140,96),(45,89,141),(46,142,90),(47,91,143),(48,144,92),(57,117,100),(58,101,118),(59,119,102),(60,103,120),(61,113,104),(62,97,114),(63,115,98),(64,99,116)], [(1,11,112),(2,105,12),(3,13,106),(4,107,14),(5,15,108),(6,109,16),(7,9,110),(8,111,10),(17,134,71),(18,72,135),(19,136,65),(20,66,129),(21,130,67),(22,68,131),(23,132,69),(24,70,133),(25,91,119),(26,120,92),(27,93,113),(28,114,94),(29,95,115),(30,116,96),(31,89,117),(32,118,90),(33,137,104),(34,97,138),(35,139,98),(36,99,140),(37,141,100),(38,101,142),(39,143,102),(40,103,144),(41,61,73),(42,74,62),(43,63,75),(44,76,64),(45,57,77),(46,78,58),(47,59,79),(48,80,60),(49,81,121),(50,122,82),(51,83,123),(52,124,84),(53,85,125),(54,126,86),(55,87,127),(56,128,88)], [(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)], [(1,44),(2,41),(3,46),(4,43),(5,48),(6,45),(7,42),(8,47),(9,62),(10,59),(11,64),(12,61),(13,58),(14,63),(15,60),(16,57),(17,39),(18,36),(19,33),(20,38),(21,35),(22,40),(23,37),(24,34),(25,51),(26,56),(27,53),(28,50),(29,55),(30,52),(31,49),(32,54),(65,137),(66,142),(67,139),(68,144),(69,141),(70,138),(71,143),(72,140),(73,105),(74,110),(75,107),(76,112),(77,109),(78,106),(79,111),(80,108),(81,117),(82,114),(83,119),(84,116),(85,113),(86,118),(87,115),(88,120),(89,121),(90,126),(91,123),(92,128),(93,125),(94,122),(95,127),(96,124),(97,133),(98,130),(99,135),(100,132),(101,129),(102,134),(103,131),(104,136)]])
66 conjugacy classes
| class | 1 | 2A | 2B | 3A | ··· | 3E | 3F | 3G | 3H | 3I | 4A | 4B | 4C | 6A | ··· | 6E | 6F | 6G | 6H | 6I | 6J | ··· | 6Q | 8A | 8B | 8C | 8D | 12A | ··· | 12J | 12K | ··· | 12R | 12S | ··· | 12Z | 24A | 24B | 24C | 24D |
| 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 | 24 | 24 |
| size | 1 | 1 | 6 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 1 | 1 | 6 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 18 | 18 | 54 | 54 | 2 | ··· | 2 | 4 | ··· | 4 | 6 | ··· | 6 | 18 | 18 | 18 | 18 |
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⋊7M4(2) | C3×C32⋊4C8 | C33⋊7C8 | S3×C3×C12 | C32×Dic3 | S3×C3×C6 | C32⋊4C8 | S3×C12 | C3×Dic3 | C3×C12 | S3×C6 | C33 | C3×C6 | C32 | C32 | C12 | C6 | C3 |
| # reps | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 4 | 4 | 5 | 4 | 2 | 2 | 4 | 16 | 4 | 4 | 8 |
Matrix representation of C33⋊7M4(2) ►in GL8(𝔽73)
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 64 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 8 | 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 | 64 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 8 | 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 | 0 | 72 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 72 |
| 15 | 56 | 0 | 0 | 0 | 0 | 0 | 0 |
| 32 | 58 | 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 | 0 | 27 | 0 | 0 |
| 0 | 0 | 0 | 0 | 27 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 51 | 20 | 0 | 0 | 0 | 0 | 0 | 0 |
| 16 | 22 | 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 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 72 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
G:=sub<GL(8,GF(73))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,72,72,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,72,72],[15,32,0,0,0,0,0,0,56,58,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,27,0,0,0,0,0,0,27,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0],[51,16,0,0,0,0,0,0,20,22,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0] >;
C33⋊7M4(2) in GAP, Magma, Sage, TeX
C_3^3\rtimes_7M_4(2)
% in TeX
G:=Group("C3^3:7M4(2)"); // GroupNames label
G:=SmallGroup(432,433);
// by ID
G=gap.SmallGroup(432,433);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,141,36,58,571,2028,14118]);
// 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=a^-1,a*e=e*a,b*c=c*b,d*b*d^-1=b^-1,b*e=e*b,d*c*d^-1=e*c*e=c^-1,e*d*e=d^5>;
// generators/relations