metabelian, supersoluble, monomial
Aliases: C33⋊8Q16, C32⋊5Dic12, C12.55S32, (C3×C6).40D12, (C3×C12).123D6, (C32×C6).40D4, C3⋊2(C32⋊5Q16), C33⋊8Q8.3C2, C32⋊4Q8.3S3, C32⋊9(C3⋊Q16), C3⋊1(C32⋊3Q16), C6.15(C12⋊S3), C2.7(C33⋊8D4), C6.11(C3⋊D12), (C32×C12).19C22, C3⋊C8.(C3⋊S3), C4.4(S3×C3⋊S3), (C3×C3⋊C8).3S3, C12.16(C2×C3⋊S3), (C32×C3⋊C8).1C2, (C3×C6).80(C3⋊D4), (C3×C32⋊4Q8).3C2, SmallGroup(432,447)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C33⋊8Q16
G = < a,b,c,d,e | a3=b3=c3=d8=1, e2=d4, ab=ba, ac=ca, ad=da, eae-1=a-1, bc=cb, bd=db, ebe-1=b-1, dcd-1=c-1, ce=ec, ede-1=d-1 >
Subgroups: 880 in 156 conjugacy classes, 46 normal (18 characteristic)
C1, C2, C3, C3, C3, C4, C4, C6, C6, C6, C8, Q8, C32, C32, C32, Dic3, C12, C12, C12, Q16, C3×C6, C3×C6, C3×C6, C3⋊C8, C24, Dic6, C3×Q8, C33, C3×Dic3, C3⋊Dic3, C3×C12, C3×C12, C3×C12, Dic12, C3⋊Q16, C32×C6, C3×C3⋊C8, C3×C24, C3×Dic6, C32⋊4Q8, C32⋊4Q8, C3×C3⋊Dic3, C33⋊5C4, C32×C12, C32⋊3Q16, C32⋊5Q16, C32×C3⋊C8, C3×C32⋊4Q8, C33⋊8Q8, C33⋊8Q16
Quotients: C1, C2, C22, S3, D4, D6, Q16, C3⋊S3, D12, C3⋊D4, S32, C2×C3⋊S3, Dic12, C3⋊Q16, C3⋊D12, C12⋊S3, S3×C3⋊S3, C32⋊3Q16, C32⋊5Q16, C33⋊8D4, C33⋊8Q16
►On 144 points
Generators in S144
(1 141 62)(2 142 63)(3 143 64)(4 144 57)(5 137 58)(6 138 59)(7 139 60)(8 140 61)(9 46 97)(10 47 98)(11 48 99)(12 41 100)(13 42 101)(14 43 102)(15 44 103)(16 45 104)(17 119 82)(18 120 83)(19 113 84)(20 114 85)(21 115 86)(22 116 87)(23 117 88)(24 118 81)(25 110 131)(26 111 132)(27 112 133)(28 105 134)(29 106 135)(30 107 136)(31 108 129)(32 109 130)(33 128 79)(34 121 80)(35 122 73)(36 123 74)(37 124 75)(38 125 76)(39 126 77)(40 127 78)(49 65 90)(50 66 91)(51 67 92)(52 68 93)(53 69 94)(54 70 95)(55 71 96)(56 72 89)
(1 49 38)(2 50 39)(3 51 40)(4 52 33)(5 53 34)(6 54 35)(7 55 36)(8 56 37)(9 29 87)(10 30 88)(11 31 81)(12 32 82)(13 25 83)(14 26 84)(15 27 85)(16 28 86)(17 41 109)(18 42 110)(19 43 111)(20 44 112)(21 45 105)(22 46 106)(23 47 107)(24 48 108)(57 93 79)(58 94 80)(59 95 73)(60 96 74)(61 89 75)(62 90 76)(63 91 77)(64 92 78)(65 125 141)(66 126 142)(67 127 143)(68 128 144)(69 121 137)(70 122 138)(71 123 139)(72 124 140)(97 135 116)(98 136 117)(99 129 118)(100 130 119)(101 131 120)(102 132 113)(103 133 114)(104 134 115)
(1 38 49)(2 50 39)(3 40 51)(4 52 33)(5 34 53)(6 54 35)(7 36 55)(8 56 37)(9 29 87)(10 88 30)(11 31 81)(12 82 32)(13 25 83)(14 84 26)(15 27 85)(16 86 28)(17 109 41)(18 42 110)(19 111 43)(20 44 112)(21 105 45)(22 46 106)(23 107 47)(24 48 108)(57 93 79)(58 80 94)(59 95 73)(60 74 96)(61 89 75)(62 76 90)(63 91 77)(64 78 92)(65 141 125)(66 126 142)(67 143 127)(68 128 144)(69 137 121)(70 122 138)(71 139 123)(72 124 140)(97 135 116)(98 117 136)(99 129 118)(100 119 130)(101 131 120)(102 113 132)(103 133 114)(104 115 134)
(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 81 5 85)(2 88 6 84)(3 87 7 83)(4 86 8 82)(9 36 13 40)(10 35 14 39)(11 34 15 38)(12 33 16 37)(17 57 21 61)(18 64 22 60)(19 63 23 59)(20 62 24 58)(25 51 29 55)(26 50 30 54)(27 49 31 53)(28 56 32 52)(41 79 45 75)(42 78 46 74)(43 77 47 73)(44 76 48 80)(65 129 69 133)(66 136 70 132)(67 135 71 131)(68 134 72 130)(89 109 93 105)(90 108 94 112)(91 107 95 111)(92 106 96 110)(97 123 101 127)(98 122 102 126)(99 121 103 125)(100 128 104 124)(113 142 117 138)(114 141 118 137)(115 140 119 144)(116 139 120 143)
G:=sub<Sym(144)| (1,141,62)(2,142,63)(3,143,64)(4,144,57)(5,137,58)(6,138,59)(7,139,60)(8,140,61)(9,46,97)(10,47,98)(11,48,99)(12,41,100)(13,42,101)(14,43,102)(15,44,103)(16,45,104)(17,119,82)(18,120,83)(19,113,84)(20,114,85)(21,115,86)(22,116,87)(23,117,88)(24,118,81)(25,110,131)(26,111,132)(27,112,133)(28,105,134)(29,106,135)(30,107,136)(31,108,129)(32,109,130)(33,128,79)(34,121,80)(35,122,73)(36,123,74)(37,124,75)(38,125,76)(39,126,77)(40,127,78)(49,65,90)(50,66,91)(51,67,92)(52,68,93)(53,69,94)(54,70,95)(55,71,96)(56,72,89), (1,49,38)(2,50,39)(3,51,40)(4,52,33)(5,53,34)(6,54,35)(7,55,36)(8,56,37)(9,29,87)(10,30,88)(11,31,81)(12,32,82)(13,25,83)(14,26,84)(15,27,85)(16,28,86)(17,41,109)(18,42,110)(19,43,111)(20,44,112)(21,45,105)(22,46,106)(23,47,107)(24,48,108)(57,93,79)(58,94,80)(59,95,73)(60,96,74)(61,89,75)(62,90,76)(63,91,77)(64,92,78)(65,125,141)(66,126,142)(67,127,143)(68,128,144)(69,121,137)(70,122,138)(71,123,139)(72,124,140)(97,135,116)(98,136,117)(99,129,118)(100,130,119)(101,131,120)(102,132,113)(103,133,114)(104,134,115), (1,38,49)(2,50,39)(3,40,51)(4,52,33)(5,34,53)(6,54,35)(7,36,55)(8,56,37)(9,29,87)(10,88,30)(11,31,81)(12,82,32)(13,25,83)(14,84,26)(15,27,85)(16,86,28)(17,109,41)(18,42,110)(19,111,43)(20,44,112)(21,105,45)(22,46,106)(23,107,47)(24,48,108)(57,93,79)(58,80,94)(59,95,73)(60,74,96)(61,89,75)(62,76,90)(63,91,77)(64,78,92)(65,141,125)(66,126,142)(67,143,127)(68,128,144)(69,137,121)(70,122,138)(71,139,123)(72,124,140)(97,135,116)(98,117,136)(99,129,118)(100,119,130)(101,131,120)(102,113,132)(103,133,114)(104,115,134), (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), (1,81,5,85)(2,88,6,84)(3,87,7,83)(4,86,8,82)(9,36,13,40)(10,35,14,39)(11,34,15,38)(12,33,16,37)(17,57,21,61)(18,64,22,60)(19,63,23,59)(20,62,24,58)(25,51,29,55)(26,50,30,54)(27,49,31,53)(28,56,32,52)(41,79,45,75)(42,78,46,74)(43,77,47,73)(44,76,48,80)(65,129,69,133)(66,136,70,132)(67,135,71,131)(68,134,72,130)(89,109,93,105)(90,108,94,112)(91,107,95,111)(92,106,96,110)(97,123,101,127)(98,122,102,126)(99,121,103,125)(100,128,104,124)(113,142,117,138)(114,141,118,137)(115,140,119,144)(116,139,120,143)>;
G:=Group( (1,141,62)(2,142,63)(3,143,64)(4,144,57)(5,137,58)(6,138,59)(7,139,60)(8,140,61)(9,46,97)(10,47,98)(11,48,99)(12,41,100)(13,42,101)(14,43,102)(15,44,103)(16,45,104)(17,119,82)(18,120,83)(19,113,84)(20,114,85)(21,115,86)(22,116,87)(23,117,88)(24,118,81)(25,110,131)(26,111,132)(27,112,133)(28,105,134)(29,106,135)(30,107,136)(31,108,129)(32,109,130)(33,128,79)(34,121,80)(35,122,73)(36,123,74)(37,124,75)(38,125,76)(39,126,77)(40,127,78)(49,65,90)(50,66,91)(51,67,92)(52,68,93)(53,69,94)(54,70,95)(55,71,96)(56,72,89), (1,49,38)(2,50,39)(3,51,40)(4,52,33)(5,53,34)(6,54,35)(7,55,36)(8,56,37)(9,29,87)(10,30,88)(11,31,81)(12,32,82)(13,25,83)(14,26,84)(15,27,85)(16,28,86)(17,41,109)(18,42,110)(19,43,111)(20,44,112)(21,45,105)(22,46,106)(23,47,107)(24,48,108)(57,93,79)(58,94,80)(59,95,73)(60,96,74)(61,89,75)(62,90,76)(63,91,77)(64,92,78)(65,125,141)(66,126,142)(67,127,143)(68,128,144)(69,121,137)(70,122,138)(71,123,139)(72,124,140)(97,135,116)(98,136,117)(99,129,118)(100,130,119)(101,131,120)(102,132,113)(103,133,114)(104,134,115), (1,38,49)(2,50,39)(3,40,51)(4,52,33)(5,34,53)(6,54,35)(7,36,55)(8,56,37)(9,29,87)(10,88,30)(11,31,81)(12,82,32)(13,25,83)(14,84,26)(15,27,85)(16,86,28)(17,109,41)(18,42,110)(19,111,43)(20,44,112)(21,105,45)(22,46,106)(23,107,47)(24,48,108)(57,93,79)(58,80,94)(59,95,73)(60,74,96)(61,89,75)(62,76,90)(63,91,77)(64,78,92)(65,141,125)(66,126,142)(67,143,127)(68,128,144)(69,137,121)(70,122,138)(71,139,123)(72,124,140)(97,135,116)(98,117,136)(99,129,118)(100,119,130)(101,131,120)(102,113,132)(103,133,114)(104,115,134), (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), (1,81,5,85)(2,88,6,84)(3,87,7,83)(4,86,8,82)(9,36,13,40)(10,35,14,39)(11,34,15,38)(12,33,16,37)(17,57,21,61)(18,64,22,60)(19,63,23,59)(20,62,24,58)(25,51,29,55)(26,50,30,54)(27,49,31,53)(28,56,32,52)(41,79,45,75)(42,78,46,74)(43,77,47,73)(44,76,48,80)(65,129,69,133)(66,136,70,132)(67,135,71,131)(68,134,72,130)(89,109,93,105)(90,108,94,112)(91,107,95,111)(92,106,96,110)(97,123,101,127)(98,122,102,126)(99,121,103,125)(100,128,104,124)(113,142,117,138)(114,141,118,137)(115,140,119,144)(116,139,120,143) );
G=PermutationGroup([[(1,141,62),(2,142,63),(3,143,64),(4,144,57),(5,137,58),(6,138,59),(7,139,60),(8,140,61),(9,46,97),(10,47,98),(11,48,99),(12,41,100),(13,42,101),(14,43,102),(15,44,103),(16,45,104),(17,119,82),(18,120,83),(19,113,84),(20,114,85),(21,115,86),(22,116,87),(23,117,88),(24,118,81),(25,110,131),(26,111,132),(27,112,133),(28,105,134),(29,106,135),(30,107,136),(31,108,129),(32,109,130),(33,128,79),(34,121,80),(35,122,73),(36,123,74),(37,124,75),(38,125,76),(39,126,77),(40,127,78),(49,65,90),(50,66,91),(51,67,92),(52,68,93),(53,69,94),(54,70,95),(55,71,96),(56,72,89)], [(1,49,38),(2,50,39),(3,51,40),(4,52,33),(5,53,34),(6,54,35),(7,55,36),(8,56,37),(9,29,87),(10,30,88),(11,31,81),(12,32,82),(13,25,83),(14,26,84),(15,27,85),(16,28,86),(17,41,109),(18,42,110),(19,43,111),(20,44,112),(21,45,105),(22,46,106),(23,47,107),(24,48,108),(57,93,79),(58,94,80),(59,95,73),(60,96,74),(61,89,75),(62,90,76),(63,91,77),(64,92,78),(65,125,141),(66,126,142),(67,127,143),(68,128,144),(69,121,137),(70,122,138),(71,123,139),(72,124,140),(97,135,116),(98,136,117),(99,129,118),(100,130,119),(101,131,120),(102,132,113),(103,133,114),(104,134,115)], [(1,38,49),(2,50,39),(3,40,51),(4,52,33),(5,34,53),(6,54,35),(7,36,55),(8,56,37),(9,29,87),(10,88,30),(11,31,81),(12,82,32),(13,25,83),(14,84,26),(15,27,85),(16,86,28),(17,109,41),(18,42,110),(19,111,43),(20,44,112),(21,105,45),(22,46,106),(23,107,47),(24,48,108),(57,93,79),(58,80,94),(59,95,73),(60,74,96),(61,89,75),(62,76,90),(63,91,77),(64,78,92),(65,141,125),(66,126,142),(67,143,127),(68,128,144),(69,137,121),(70,122,138),(71,139,123),(72,124,140),(97,135,116),(98,117,136),(99,129,118),(100,119,130),(101,131,120),(102,113,132),(103,133,114),(104,115,134)], [(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)], [(1,81,5,85),(2,88,6,84),(3,87,7,83),(4,86,8,82),(9,36,13,40),(10,35,14,39),(11,34,15,38),(12,33,16,37),(17,57,21,61),(18,64,22,60),(19,63,23,59),(20,62,24,58),(25,51,29,55),(26,50,30,54),(27,49,31,53),(28,56,32,52),(41,79,45,75),(42,78,46,74),(43,77,47,73),(44,76,48,80),(65,129,69,133),(66,136,70,132),(67,135,71,131),(68,134,72,130),(89,109,93,105),(90,108,94,112),(91,107,95,111),(92,106,96,110),(97,123,101,127),(98,122,102,126),(99,121,103,125),(100,128,104,124),(113,142,117,138),(114,141,118,137),(115,140,119,144),(116,139,120,143)]])
60 conjugacy classes
| class | 1 | 2 | 3A | ··· | 3E | 3F | 3G | 3H | 3I | 4A | 4B | 4C | 6A | ··· | 6E | 6F | 6G | 6H | 6I | 8A | 8B | 12A | ··· | 12H | 12I | ··· | 12Q | 12R | 12S | 24A | ··· | 24P |
| order | 1 | 2 | 3 | ··· | 3 | 3 | 3 | 3 | 3 | 4 | 4 | 4 | 6 | ··· | 6 | 6 | 6 | 6 | 6 | 8 | 8 | 12 | ··· | 12 | 12 | ··· | 12 | 12 | 12 | 24 | ··· | 24 |
| size | 1 | 1 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 2 | 36 | 108 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 6 | 6 | 2 | ··· | 2 | 4 | ··· | 4 | 36 | 36 | 6 | ··· | 6 |
60 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | + | - | + | - | + | - | |
| image | C1 | C2 | C2 | C2 | S3 | S3 | D4 | D6 | Q16 | D12 | C3⋊D4 | Dic12 | S32 | C3⋊Q16 | C3⋊D12 | C32⋊3Q16 |
| kernel | C33⋊8Q16 | C32×C3⋊C8 | C3×C32⋊4Q8 | C33⋊8Q8 | C3×C3⋊C8 | C32⋊4Q8 | C32×C6 | C3×C12 | C33 | C3×C6 | C3×C6 | C32 | C12 | C32 | C6 | C3 |
| # reps | 1 | 1 | 1 | 1 | 4 | 1 | 1 | 5 | 2 | 8 | 2 | 16 | 4 | 1 | 4 | 8 |
Matrix representation of C33⋊8Q16 ►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 | 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 |
| 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 |
| 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 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 41 | 32 | 0 | 0 | 0 | 0 | 0 | 0 |
| 57 | 0 | 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 | 1 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 24 | 34 | 0 | 0 | 0 | 0 | 0 | 0 |
| 41 | 49 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 22 | 41 | 0 | 0 | 0 | 0 |
| 0 | 0 | 63 | 51 | 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))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,72,72,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,72,72],[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],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,72,1,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[41,57,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,72,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[24,41,0,0,0,0,0,0,34,49,0,0,0,0,0,0,0,0,22,63,0,0,0,0,0,0,41,51,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0] >;
C33⋊8Q16 in GAP, Magma, Sage, TeX
C_3^3\rtimes_8Q_{16} % in TeX
G:=Group("C3^3:8Q16"); // GroupNames label
G:=SmallGroup(432,447);
// by ID
G=gap.SmallGroup(432,447);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,28,85,64,135,58,571,2028,14118]);
// Polycyclic
G:=Group<a,b,c,d,e|a^3=b^3=c^3=d^8=1,e^2=d^4,a*b=b*a,a*c=c*a,a*d=d*a,e*a*e^-1=a^-1,b*c=c*b,b*d=d*b,e*b*e^-1=b^-1,d*c*d^-1=c^-1,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations