metabelian, supersoluble, monomial
Aliases: C33⋊6D8, C12.25S32, (C3×D12)⋊2S3, C12⋊S3⋊8S3, D12⋊2(C3⋊S3), C33⋊7C8⋊1C2, (C3×C12).112D6, (C32×D12)⋊3C2, C3⋊2(C32⋊2D8), C3⋊2(C32⋊7D8), (C32×C6).29D4, C32⋊11(D4⋊S3), C2.4(C33⋊6D4), C6.8(C32⋊7D4), C6.20(D6⋊S3), (C32×C12).8C22, C12.9(C2×C3⋊S3), C4.15(S3×C3⋊S3), (C3×C12⋊S3)⋊2C2, (C3×C6).86(C3⋊D4), SmallGroup(432,436)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C33⋊6D8
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=d-1 >
Subgroups: 832 in 164 conjugacy classes, 46 normal (18 characteristic)
C1, C2, C2, C3, C3, C3, C4, C22, S3, C6, C6, C6, C8, D4, C32, C32, C32, C12, C12, C12, D6, C2×C6, D8, C3×S3, C3⋊S3, C3×C6, C3×C6, C3×C6, C3⋊C8, D12, D12, C3×D4, C33, C3×C12, C3×C12, C3×C12, S3×C6, C2×C3⋊S3, C62, D4⋊S3, S3×C32, C3×C3⋊S3, C32×C6, C32⋊4C8, C3×D12, C3×D12, C12⋊S3, D4×C32, C32×C12, S3×C3×C6, C6×C3⋊S3, C32⋊2D8, C32⋊7D8, C33⋊7C8, C32×D12, C3×C12⋊S3, C33⋊6D8
Quotients: C1, C2, C22, S3, D4, D6, D8, C3⋊S3, C3⋊D4, S32, C2×C3⋊S3, D4⋊S3, D6⋊S3, C32⋊7D4, S3×C3⋊S3, C32⋊2D8, C32⋊7D8, C33⋊6D4, C33⋊6D8
►On 144 points
Generators in S144
(1 45 15)(2 16 46)(3 47 9)(4 10 48)(5 41 11)(6 12 42)(7 43 13)(8 14 44)(17 28 121)(18 122 29)(19 30 123)(20 124 31)(21 32 125)(22 126 25)(23 26 127)(24 128 27)(33 70 108)(34 109 71)(35 72 110)(36 111 65)(37 66 112)(38 105 67)(39 68 106)(40 107 69)(49 99 92)(50 93 100)(51 101 94)(52 95 102)(53 103 96)(54 89 104)(55 97 90)(56 91 98)(57 118 76)(58 77 119)(59 120 78)(60 79 113)(61 114 80)(62 73 115)(63 116 74)(64 75 117)(81 140 134)(82 135 141)(83 142 136)(84 129 143)(85 144 130)(86 131 137)(87 138 132)(88 133 139)
(1 60 29)(2 30 61)(3 62 31)(4 32 63)(5 64 25)(6 26 57)(7 58 27)(8 28 59)(9 115 124)(10 125 116)(11 117 126)(12 127 118)(13 119 128)(14 121 120)(15 113 122)(16 123 114)(17 78 44)(18 45 79)(19 80 46)(20 47 73)(21 74 48)(22 41 75)(23 76 42)(24 43 77)(33 56 131)(34 132 49)(35 50 133)(36 134 51)(37 52 135)(38 136 53)(39 54 129)(40 130 55)(65 140 94)(66 95 141)(67 142 96)(68 89 143)(69 144 90)(70 91 137)(71 138 92)(72 93 139)(81 101 111)(82 112 102)(83 103 105)(84 106 104)(85 97 107)(86 108 98)(87 99 109)(88 110 100)
(1 113 18)(2 19 114)(3 115 20)(4 21 116)(5 117 22)(6 23 118)(7 119 24)(8 17 120)(9 73 31)(10 32 74)(11 75 25)(12 26 76)(13 77 27)(14 28 78)(15 79 29)(16 30 80)(33 137 98)(34 99 138)(35 139 100)(36 101 140)(37 141 102)(38 103 142)(39 143 104)(40 97 144)(41 64 126)(42 127 57)(43 58 128)(44 121 59)(45 60 122)(46 123 61)(47 62 124)(48 125 63)(49 87 71)(50 72 88)(51 81 65)(52 66 82)(53 83 67)(54 68 84)(55 85 69)(56 70 86)(89 106 129)(90 130 107)(91 108 131)(92 132 109)(93 110 133)(94 134 111)(95 112 135)(96 136 105)
(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 65)(2 72)(3 71)(4 70)(5 69)(6 68)(7 67)(8 66)(9 109)(10 108)(11 107)(12 106)(13 105)(14 112)(15 111)(16 110)(17 52)(18 51)(19 50)(20 49)(21 56)(22 55)(23 54)(24 53)(25 90)(26 89)(27 96)(28 95)(29 94)(30 93)(31 92)(32 91)(33 48)(34 47)(35 46)(36 45)(37 44)(38 43)(39 42)(40 41)(57 143)(58 142)(59 141)(60 140)(61 139)(62 138)(63 137)(64 144)(73 132)(74 131)(75 130)(76 129)(77 136)(78 135)(79 134)(80 133)(81 113)(82 120)(83 119)(84 118)(85 117)(86 116)(87 115)(88 114)(97 126)(98 125)(99 124)(100 123)(101 122)(102 121)(103 128)(104 127)
G:=sub<Sym(144)| (1,45,15)(2,16,46)(3,47,9)(4,10,48)(5,41,11)(6,12,42)(7,43,13)(8,14,44)(17,28,121)(18,122,29)(19,30,123)(20,124,31)(21,32,125)(22,126,25)(23,26,127)(24,128,27)(33,70,108)(34,109,71)(35,72,110)(36,111,65)(37,66,112)(38,105,67)(39,68,106)(40,107,69)(49,99,92)(50,93,100)(51,101,94)(52,95,102)(53,103,96)(54,89,104)(55,97,90)(56,91,98)(57,118,76)(58,77,119)(59,120,78)(60,79,113)(61,114,80)(62,73,115)(63,116,74)(64,75,117)(81,140,134)(82,135,141)(83,142,136)(84,129,143)(85,144,130)(86,131,137)(87,138,132)(88,133,139), (1,60,29)(2,30,61)(3,62,31)(4,32,63)(5,64,25)(6,26,57)(7,58,27)(8,28,59)(9,115,124)(10,125,116)(11,117,126)(12,127,118)(13,119,128)(14,121,120)(15,113,122)(16,123,114)(17,78,44)(18,45,79)(19,80,46)(20,47,73)(21,74,48)(22,41,75)(23,76,42)(24,43,77)(33,56,131)(34,132,49)(35,50,133)(36,134,51)(37,52,135)(38,136,53)(39,54,129)(40,130,55)(65,140,94)(66,95,141)(67,142,96)(68,89,143)(69,144,90)(70,91,137)(71,138,92)(72,93,139)(81,101,111)(82,112,102)(83,103,105)(84,106,104)(85,97,107)(86,108,98)(87,99,109)(88,110,100), (1,113,18)(2,19,114)(3,115,20)(4,21,116)(5,117,22)(6,23,118)(7,119,24)(8,17,120)(9,73,31)(10,32,74)(11,75,25)(12,26,76)(13,77,27)(14,28,78)(15,79,29)(16,30,80)(33,137,98)(34,99,138)(35,139,100)(36,101,140)(37,141,102)(38,103,142)(39,143,104)(40,97,144)(41,64,126)(42,127,57)(43,58,128)(44,121,59)(45,60,122)(46,123,61)(47,62,124)(48,125,63)(49,87,71)(50,72,88)(51,81,65)(52,66,82)(53,83,67)(54,68,84)(55,85,69)(56,70,86)(89,106,129)(90,130,107)(91,108,131)(92,132,109)(93,110,133)(94,134,111)(95,112,135)(96,136,105), (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), (1,65)(2,72)(3,71)(4,70)(5,69)(6,68)(7,67)(8,66)(9,109)(10,108)(11,107)(12,106)(13,105)(14,112)(15,111)(16,110)(17,52)(18,51)(19,50)(20,49)(21,56)(22,55)(23,54)(24,53)(25,90)(26,89)(27,96)(28,95)(29,94)(30,93)(31,92)(32,91)(33,48)(34,47)(35,46)(36,45)(37,44)(38,43)(39,42)(40,41)(57,143)(58,142)(59,141)(60,140)(61,139)(62,138)(63,137)(64,144)(73,132)(74,131)(75,130)(76,129)(77,136)(78,135)(79,134)(80,133)(81,113)(82,120)(83,119)(84,118)(85,117)(86,116)(87,115)(88,114)(97,126)(98,125)(99,124)(100,123)(101,122)(102,121)(103,128)(104,127)>;
G:=Group( (1,45,15)(2,16,46)(3,47,9)(4,10,48)(5,41,11)(6,12,42)(7,43,13)(8,14,44)(17,28,121)(18,122,29)(19,30,123)(20,124,31)(21,32,125)(22,126,25)(23,26,127)(24,128,27)(33,70,108)(34,109,71)(35,72,110)(36,111,65)(37,66,112)(38,105,67)(39,68,106)(40,107,69)(49,99,92)(50,93,100)(51,101,94)(52,95,102)(53,103,96)(54,89,104)(55,97,90)(56,91,98)(57,118,76)(58,77,119)(59,120,78)(60,79,113)(61,114,80)(62,73,115)(63,116,74)(64,75,117)(81,140,134)(82,135,141)(83,142,136)(84,129,143)(85,144,130)(86,131,137)(87,138,132)(88,133,139), (1,60,29)(2,30,61)(3,62,31)(4,32,63)(5,64,25)(6,26,57)(7,58,27)(8,28,59)(9,115,124)(10,125,116)(11,117,126)(12,127,118)(13,119,128)(14,121,120)(15,113,122)(16,123,114)(17,78,44)(18,45,79)(19,80,46)(20,47,73)(21,74,48)(22,41,75)(23,76,42)(24,43,77)(33,56,131)(34,132,49)(35,50,133)(36,134,51)(37,52,135)(38,136,53)(39,54,129)(40,130,55)(65,140,94)(66,95,141)(67,142,96)(68,89,143)(69,144,90)(70,91,137)(71,138,92)(72,93,139)(81,101,111)(82,112,102)(83,103,105)(84,106,104)(85,97,107)(86,108,98)(87,99,109)(88,110,100), (1,113,18)(2,19,114)(3,115,20)(4,21,116)(5,117,22)(6,23,118)(7,119,24)(8,17,120)(9,73,31)(10,32,74)(11,75,25)(12,26,76)(13,77,27)(14,28,78)(15,79,29)(16,30,80)(33,137,98)(34,99,138)(35,139,100)(36,101,140)(37,141,102)(38,103,142)(39,143,104)(40,97,144)(41,64,126)(42,127,57)(43,58,128)(44,121,59)(45,60,122)(46,123,61)(47,62,124)(48,125,63)(49,87,71)(50,72,88)(51,81,65)(52,66,82)(53,83,67)(54,68,84)(55,85,69)(56,70,86)(89,106,129)(90,130,107)(91,108,131)(92,132,109)(93,110,133)(94,134,111)(95,112,135)(96,136,105), (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), (1,65)(2,72)(3,71)(4,70)(5,69)(6,68)(7,67)(8,66)(9,109)(10,108)(11,107)(12,106)(13,105)(14,112)(15,111)(16,110)(17,52)(18,51)(19,50)(20,49)(21,56)(22,55)(23,54)(24,53)(25,90)(26,89)(27,96)(28,95)(29,94)(30,93)(31,92)(32,91)(33,48)(34,47)(35,46)(36,45)(37,44)(38,43)(39,42)(40,41)(57,143)(58,142)(59,141)(60,140)(61,139)(62,138)(63,137)(64,144)(73,132)(74,131)(75,130)(76,129)(77,136)(78,135)(79,134)(80,133)(81,113)(82,120)(83,119)(84,118)(85,117)(86,116)(87,115)(88,114)(97,126)(98,125)(99,124)(100,123)(101,122)(102,121)(103,128)(104,127) );
G=PermutationGroup([[(1,45,15),(2,16,46),(3,47,9),(4,10,48),(5,41,11),(6,12,42),(7,43,13),(8,14,44),(17,28,121),(18,122,29),(19,30,123),(20,124,31),(21,32,125),(22,126,25),(23,26,127),(24,128,27),(33,70,108),(34,109,71),(35,72,110),(36,111,65),(37,66,112),(38,105,67),(39,68,106),(40,107,69),(49,99,92),(50,93,100),(51,101,94),(52,95,102),(53,103,96),(54,89,104),(55,97,90),(56,91,98),(57,118,76),(58,77,119),(59,120,78),(60,79,113),(61,114,80),(62,73,115),(63,116,74),(64,75,117),(81,140,134),(82,135,141),(83,142,136),(84,129,143),(85,144,130),(86,131,137),(87,138,132),(88,133,139)], [(1,60,29),(2,30,61),(3,62,31),(4,32,63),(5,64,25),(6,26,57),(7,58,27),(8,28,59),(9,115,124),(10,125,116),(11,117,126),(12,127,118),(13,119,128),(14,121,120),(15,113,122),(16,123,114),(17,78,44),(18,45,79),(19,80,46),(20,47,73),(21,74,48),(22,41,75),(23,76,42),(24,43,77),(33,56,131),(34,132,49),(35,50,133),(36,134,51),(37,52,135),(38,136,53),(39,54,129),(40,130,55),(65,140,94),(66,95,141),(67,142,96),(68,89,143),(69,144,90),(70,91,137),(71,138,92),(72,93,139),(81,101,111),(82,112,102),(83,103,105),(84,106,104),(85,97,107),(86,108,98),(87,99,109),(88,110,100)], [(1,113,18),(2,19,114),(3,115,20),(4,21,116),(5,117,22),(6,23,118),(7,119,24),(8,17,120),(9,73,31),(10,32,74),(11,75,25),(12,26,76),(13,77,27),(14,28,78),(15,79,29),(16,30,80),(33,137,98),(34,99,138),(35,139,100),(36,101,140),(37,141,102),(38,103,142),(39,143,104),(40,97,144),(41,64,126),(42,127,57),(43,58,128),(44,121,59),(45,60,122),(46,123,61),(47,62,124),(48,125,63),(49,87,71),(50,72,88),(51,81,65),(52,66,82),(53,83,67),(54,68,84),(55,85,69),(56,70,86),(89,106,129),(90,130,107),(91,108,131),(92,132,109),(93,110,133),(94,134,111),(95,112,135),(96,136,105)], [(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)], [(1,65),(2,72),(3,71),(4,70),(5,69),(6,68),(7,67),(8,66),(9,109),(10,108),(11,107),(12,106),(13,105),(14,112),(15,111),(16,110),(17,52),(18,51),(19,50),(20,49),(21,56),(22,55),(23,54),(24,53),(25,90),(26,89),(27,96),(28,95),(29,94),(30,93),(31,92),(32,91),(33,48),(34,47),(35,46),(36,45),(37,44),(38,43),(39,42),(40,41),(57,143),(58,142),(59,141),(60,140),(61,139),(62,138),(63,137),(64,144),(73,132),(74,131),(75,130),(76,129),(77,136),(78,135),(79,134),(80,133),(81,113),(82,120),(83,119),(84,118),(85,117),(86,116),(87,115),(88,114),(97,126),(98,125),(99,124),(100,123),(101,122),(102,121),(103,128),(104,127)]])
48 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | ··· | 3E | 3F | 3G | 3H | 3I | 4 | 6A | ··· | 6E | 6F | 6G | 6H | 6I | 6J | ··· | 6Q | 6R | 6S | 8A | 8B | 12A | ··· | 12M |
| order | 1 | 2 | 2 | 2 | 3 | ··· | 3 | 3 | 3 | 3 | 3 | 4 | 6 | ··· | 6 | 6 | 6 | 6 | 6 | 6 | ··· | 6 | 6 | 6 | 8 | 8 | 12 | ··· | 12 |
| size | 1 | 1 | 12 | 36 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 2 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 12 | ··· | 12 | 36 | 36 | 54 | 54 | 4 | ··· | 4 |
48 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | S3 | S3 | D4 | D6 | D8 | C3⋊D4 | S32 | D4⋊S3 | D6⋊S3 | C32⋊2D8 |
| kernel | C33⋊6D8 | C33⋊7C8 | C32×D12 | C3×C12⋊S3 | C3×D12 | C12⋊S3 | C32×C6 | C3×C12 | C33 | C3×C6 | C12 | C32 | C6 | C3 |
| # reps | 1 | 1 | 1 | 1 | 4 | 1 | 1 | 5 | 2 | 10 | 4 | 5 | 4 | 8 |
Matrix representation of C33⋊6D8 ►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 |
| 0 | 25 | 0 | 0 | 0 | 0 | 0 | 0 |
| 35 | 32 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 29 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 48 | 44 | 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 | 72 | 72 |
| 62 | 35 | 0 | 0 | 0 | 0 | 0 | 0 |
| 7 | 11 | 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 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 72 | 72 |
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],[0,35,0,0,0,0,0,0,25,32,0,0,0,0,0,0,0,0,29,48,0,0,0,0,0,0,19,44,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,72,0,0,0,0,0,0,0,72],[62,7,0,0,0,0,0,0,35,11,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,1,72,0,0,0,0,0,0,0,72] >;
C33⋊6D8 in GAP, Magma, Sage, TeX
C_3^3\rtimes_6D_8
% in TeX
G:=Group("C3^3:6D8"); // GroupNames label
G:=SmallGroup(432,436);
// by ID
G=gap.SmallGroup(432,436);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,85,254,135,58,571,2028,14118]);
// 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^-1>;
// generators/relations