metabelian, supersoluble, monomial
Aliases: C33⋊6Q16, C12.31S32, (C3×C12).121D6, C33⋊7C8.1C2, (C32×C6).38D4, C32⋊4Q8.4S3, Dic6.2(C3⋊S3), (C3×Dic6).10S3, C3⋊2(C32⋊7Q16), C3⋊2(C32⋊2Q16), C2.7(C33⋊6D4), C6.23(D6⋊S3), C32⋊11(C3⋊Q16), C6.11(C32⋊7D4), (C32×Dic6).3C2, (C32×C12).17C22, C4.18(S3×C3⋊S3), C12.15(C2×C3⋊S3), (C3×C6).89(C3⋊D4), (C3×C32⋊4Q8).2C2, SmallGroup(432,445)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C33⋊6Q16
G = < a,b,c,d,e | a3=b3=c3=d8=1, e2=d4, ab=ba, ac=ca, dad-1=eae-1=a-1, bc=cb, dbd-1=ebe-1=b-1, dcd-1=c-1, ce=ec, ede-1=d-1 >
Subgroups: 560 in 140 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, Dic6, Dic6, C3×Q8, C33, C3×Dic3, C3⋊Dic3, C3×C12, C3×C12, C3×C12, C3⋊Q16, C32×C6, C32⋊4C8, C3×Dic6, C3×Dic6, C32⋊4Q8, Q8×C32, C32×Dic3, C3×C3⋊Dic3, C32×C12, C32⋊2Q16, C32⋊7Q16, C33⋊7C8, C32×Dic6, C3×C32⋊4Q8, C33⋊6Q16
Quotients: C1, C2, C22, S3, D4, D6, Q16, C3⋊S3, C3⋊D4, S32, C2×C3⋊S3, C3⋊Q16, D6⋊S3, C32⋊7D4, S3×C3⋊S3, C32⋊2Q16, C32⋊7Q16, C33⋊6D4, C33⋊6Q16
►On 144 points
Generators in S144
(1 42 24)(2 17 43)(3 44 18)(4 19 45)(5 46 20)(6 21 47)(7 48 22)(8 23 41)(9 29 128)(10 121 30)(11 31 122)(12 123 32)(13 25 124)(14 125 26)(15 27 126)(16 127 28)(33 57 135)(34 136 58)(35 59 129)(36 130 60)(37 61 131)(38 132 62)(39 63 133)(40 134 64)(49 78 101)(50 102 79)(51 80 103)(52 104 73)(53 74 97)(54 98 75)(55 76 99)(56 100 77)(65 107 90)(66 91 108)(67 109 92)(68 93 110)(69 111 94)(70 95 112)(71 105 96)(72 89 106)(81 144 120)(82 113 137)(83 138 114)(84 115 139)(85 140 116)(86 117 141)(87 142 118)(88 119 143)
(1 72 11)(2 12 65)(3 66 13)(4 14 67)(5 68 15)(6 16 69)(7 70 9)(8 10 71)(17 123 107)(18 108 124)(19 125 109)(20 110 126)(21 127 111)(22 112 128)(23 121 105)(24 106 122)(25 44 91)(26 92 45)(27 46 93)(28 94 47)(29 48 95)(30 96 41)(31 42 89)(32 90 43)(33 79 113)(34 114 80)(35 73 115)(36 116 74)(37 75 117)(38 118 76)(39 77 119)(40 120 78)(49 64 144)(50 137 57)(51 58 138)(52 139 59)(53 60 140)(54 141 61)(55 62 142)(56 143 63)(81 101 134)(82 135 102)(83 103 136)(84 129 104)(85 97 130)(86 131 98)(87 99 132)(88 133 100)
(1 106 31)(2 32 107)(3 108 25)(4 26 109)(5 110 27)(6 28 111)(7 112 29)(8 30 105)(9 22 95)(10 96 23)(11 24 89)(12 90 17)(13 18 91)(14 92 19)(15 20 93)(16 94 21)(33 137 102)(34 103 138)(35 139 104)(36 97 140)(37 141 98)(38 99 142)(39 143 100)(40 101 144)(41 121 71)(42 72 122)(43 123 65)(44 66 124)(45 125 67)(46 68 126)(47 127 69)(48 70 128)(49 120 134)(50 135 113)(51 114 136)(52 129 115)(53 116 130)(54 131 117)(55 118 132)(56 133 119)(57 82 79)(58 80 83)(59 84 73)(60 74 85)(61 86 75)(62 76 87)(63 88 77)(64 78 81)
(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 61 5 57)(2 60 6 64)(3 59 7 63)(4 58 8 62)(9 56 13 52)(10 55 14 51)(11 54 15 50)(12 53 16 49)(17 130 21 134)(18 129 22 133)(19 136 23 132)(20 135 24 131)(25 73 29 77)(26 80 30 76)(27 79 31 75)(28 78 32 74)(33 42 37 46)(34 41 38 45)(35 48 39 44)(36 47 40 43)(65 140 69 144)(66 139 70 143)(67 138 71 142)(68 137 72 141)(81 107 85 111)(82 106 86 110)(83 105 87 109)(84 112 88 108)(89 117 93 113)(90 116 94 120)(91 115 95 119)(92 114 96 118)(97 127 101 123)(98 126 102 122)(99 125 103 121)(100 124 104 128)
G:=sub<Sym(144)| (1,42,24)(2,17,43)(3,44,18)(4,19,45)(5,46,20)(6,21,47)(7,48,22)(8,23,41)(9,29,128)(10,121,30)(11,31,122)(12,123,32)(13,25,124)(14,125,26)(15,27,126)(16,127,28)(33,57,135)(34,136,58)(35,59,129)(36,130,60)(37,61,131)(38,132,62)(39,63,133)(40,134,64)(49,78,101)(50,102,79)(51,80,103)(52,104,73)(53,74,97)(54,98,75)(55,76,99)(56,100,77)(65,107,90)(66,91,108)(67,109,92)(68,93,110)(69,111,94)(70,95,112)(71,105,96)(72,89,106)(81,144,120)(82,113,137)(83,138,114)(84,115,139)(85,140,116)(86,117,141)(87,142,118)(88,119,143), (1,72,11)(2,12,65)(3,66,13)(4,14,67)(5,68,15)(6,16,69)(7,70,9)(8,10,71)(17,123,107)(18,108,124)(19,125,109)(20,110,126)(21,127,111)(22,112,128)(23,121,105)(24,106,122)(25,44,91)(26,92,45)(27,46,93)(28,94,47)(29,48,95)(30,96,41)(31,42,89)(32,90,43)(33,79,113)(34,114,80)(35,73,115)(36,116,74)(37,75,117)(38,118,76)(39,77,119)(40,120,78)(49,64,144)(50,137,57)(51,58,138)(52,139,59)(53,60,140)(54,141,61)(55,62,142)(56,143,63)(81,101,134)(82,135,102)(83,103,136)(84,129,104)(85,97,130)(86,131,98)(87,99,132)(88,133,100), (1,106,31)(2,32,107)(3,108,25)(4,26,109)(5,110,27)(6,28,111)(7,112,29)(8,30,105)(9,22,95)(10,96,23)(11,24,89)(12,90,17)(13,18,91)(14,92,19)(15,20,93)(16,94,21)(33,137,102)(34,103,138)(35,139,104)(36,97,140)(37,141,98)(38,99,142)(39,143,100)(40,101,144)(41,121,71)(42,72,122)(43,123,65)(44,66,124)(45,125,67)(46,68,126)(47,127,69)(48,70,128)(49,120,134)(50,135,113)(51,114,136)(52,129,115)(53,116,130)(54,131,117)(55,118,132)(56,133,119)(57,82,79)(58,80,83)(59,84,73)(60,74,85)(61,86,75)(62,76,87)(63,88,77)(64,78,81), (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), (1,61,5,57)(2,60,6,64)(3,59,7,63)(4,58,8,62)(9,56,13,52)(10,55,14,51)(11,54,15,50)(12,53,16,49)(17,130,21,134)(18,129,22,133)(19,136,23,132)(20,135,24,131)(25,73,29,77)(26,80,30,76)(27,79,31,75)(28,78,32,74)(33,42,37,46)(34,41,38,45)(35,48,39,44)(36,47,40,43)(65,140,69,144)(66,139,70,143)(67,138,71,142)(68,137,72,141)(81,107,85,111)(82,106,86,110)(83,105,87,109)(84,112,88,108)(89,117,93,113)(90,116,94,120)(91,115,95,119)(92,114,96,118)(97,127,101,123)(98,126,102,122)(99,125,103,121)(100,124,104,128)>;
G:=Group( (1,42,24)(2,17,43)(3,44,18)(4,19,45)(5,46,20)(6,21,47)(7,48,22)(8,23,41)(9,29,128)(10,121,30)(11,31,122)(12,123,32)(13,25,124)(14,125,26)(15,27,126)(16,127,28)(33,57,135)(34,136,58)(35,59,129)(36,130,60)(37,61,131)(38,132,62)(39,63,133)(40,134,64)(49,78,101)(50,102,79)(51,80,103)(52,104,73)(53,74,97)(54,98,75)(55,76,99)(56,100,77)(65,107,90)(66,91,108)(67,109,92)(68,93,110)(69,111,94)(70,95,112)(71,105,96)(72,89,106)(81,144,120)(82,113,137)(83,138,114)(84,115,139)(85,140,116)(86,117,141)(87,142,118)(88,119,143), (1,72,11)(2,12,65)(3,66,13)(4,14,67)(5,68,15)(6,16,69)(7,70,9)(8,10,71)(17,123,107)(18,108,124)(19,125,109)(20,110,126)(21,127,111)(22,112,128)(23,121,105)(24,106,122)(25,44,91)(26,92,45)(27,46,93)(28,94,47)(29,48,95)(30,96,41)(31,42,89)(32,90,43)(33,79,113)(34,114,80)(35,73,115)(36,116,74)(37,75,117)(38,118,76)(39,77,119)(40,120,78)(49,64,144)(50,137,57)(51,58,138)(52,139,59)(53,60,140)(54,141,61)(55,62,142)(56,143,63)(81,101,134)(82,135,102)(83,103,136)(84,129,104)(85,97,130)(86,131,98)(87,99,132)(88,133,100), (1,106,31)(2,32,107)(3,108,25)(4,26,109)(5,110,27)(6,28,111)(7,112,29)(8,30,105)(9,22,95)(10,96,23)(11,24,89)(12,90,17)(13,18,91)(14,92,19)(15,20,93)(16,94,21)(33,137,102)(34,103,138)(35,139,104)(36,97,140)(37,141,98)(38,99,142)(39,143,100)(40,101,144)(41,121,71)(42,72,122)(43,123,65)(44,66,124)(45,125,67)(46,68,126)(47,127,69)(48,70,128)(49,120,134)(50,135,113)(51,114,136)(52,129,115)(53,116,130)(54,131,117)(55,118,132)(56,133,119)(57,82,79)(58,80,83)(59,84,73)(60,74,85)(61,86,75)(62,76,87)(63,88,77)(64,78,81), (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), (1,61,5,57)(2,60,6,64)(3,59,7,63)(4,58,8,62)(9,56,13,52)(10,55,14,51)(11,54,15,50)(12,53,16,49)(17,130,21,134)(18,129,22,133)(19,136,23,132)(20,135,24,131)(25,73,29,77)(26,80,30,76)(27,79,31,75)(28,78,32,74)(33,42,37,46)(34,41,38,45)(35,48,39,44)(36,47,40,43)(65,140,69,144)(66,139,70,143)(67,138,71,142)(68,137,72,141)(81,107,85,111)(82,106,86,110)(83,105,87,109)(84,112,88,108)(89,117,93,113)(90,116,94,120)(91,115,95,119)(92,114,96,118)(97,127,101,123)(98,126,102,122)(99,125,103,121)(100,124,104,128) );
G=PermutationGroup([[(1,42,24),(2,17,43),(3,44,18),(4,19,45),(5,46,20),(6,21,47),(7,48,22),(8,23,41),(9,29,128),(10,121,30),(11,31,122),(12,123,32),(13,25,124),(14,125,26),(15,27,126),(16,127,28),(33,57,135),(34,136,58),(35,59,129),(36,130,60),(37,61,131),(38,132,62),(39,63,133),(40,134,64),(49,78,101),(50,102,79),(51,80,103),(52,104,73),(53,74,97),(54,98,75),(55,76,99),(56,100,77),(65,107,90),(66,91,108),(67,109,92),(68,93,110),(69,111,94),(70,95,112),(71,105,96),(72,89,106),(81,144,120),(82,113,137),(83,138,114),(84,115,139),(85,140,116),(86,117,141),(87,142,118),(88,119,143)], [(1,72,11),(2,12,65),(3,66,13),(4,14,67),(5,68,15),(6,16,69),(7,70,9),(8,10,71),(17,123,107),(18,108,124),(19,125,109),(20,110,126),(21,127,111),(22,112,128),(23,121,105),(24,106,122),(25,44,91),(26,92,45),(27,46,93),(28,94,47),(29,48,95),(30,96,41),(31,42,89),(32,90,43),(33,79,113),(34,114,80),(35,73,115),(36,116,74),(37,75,117),(38,118,76),(39,77,119),(40,120,78),(49,64,144),(50,137,57),(51,58,138),(52,139,59),(53,60,140),(54,141,61),(55,62,142),(56,143,63),(81,101,134),(82,135,102),(83,103,136),(84,129,104),(85,97,130),(86,131,98),(87,99,132),(88,133,100)], [(1,106,31),(2,32,107),(3,108,25),(4,26,109),(5,110,27),(6,28,111),(7,112,29),(8,30,105),(9,22,95),(10,96,23),(11,24,89),(12,90,17),(13,18,91),(14,92,19),(15,20,93),(16,94,21),(33,137,102),(34,103,138),(35,139,104),(36,97,140),(37,141,98),(38,99,142),(39,143,100),(40,101,144),(41,121,71),(42,72,122),(43,123,65),(44,66,124),(45,125,67),(46,68,126),(47,127,69),(48,70,128),(49,120,134),(50,135,113),(51,114,136),(52,129,115),(53,116,130),(54,131,117),(55,118,132),(56,133,119),(57,82,79),(58,80,83),(59,84,73),(60,74,85),(61,86,75),(62,76,87),(63,88,77),(64,78,81)], [(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)], [(1,61,5,57),(2,60,6,64),(3,59,7,63),(4,58,8,62),(9,56,13,52),(10,55,14,51),(11,54,15,50),(12,53,16,49),(17,130,21,134),(18,129,22,133),(19,136,23,132),(20,135,24,131),(25,73,29,77),(26,80,30,76),(27,79,31,75),(28,78,32,74),(33,42,37,46),(34,41,38,45),(35,48,39,44),(36,47,40,43),(65,140,69,144),(66,139,70,143),(67,138,71,142),(68,137,72,141),(81,107,85,111),(82,106,86,110),(83,105,87,109),(84,112,88,108),(89,117,93,113),(90,116,94,120),(91,115,95,119),(92,114,96,118),(97,127,101,123),(98,126,102,122),(99,125,103,121),(100,124,104,128)]])
48 conjugacy classes
| class | 1 | 2 | 3A | ··· | 3E | 3F | 3G | 3H | 3I | 4A | 4B | 4C | 6A | ··· | 6E | 6F | 6G | 6H | 6I | 8A | 8B | 12A | ··· | 12M | 12N | ··· | 12U | 12V | 12W |
| 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 |
| size | 1 | 1 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 2 | 12 | 36 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 54 | 54 | 4 | ··· | 4 | 12 | ··· | 12 | 36 | 36 |
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 | Q16 | C3⋊D4 | S32 | C3⋊Q16 | D6⋊S3 | C32⋊2Q16 |
| kernel | C33⋊6Q16 | C33⋊7C8 | C32×Dic6 | C3×C32⋊4Q8 | C3×Dic6 | C32⋊4Q8 | 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⋊6Q16 ►in GL8(𝔽73)
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 71 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 72 | 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 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 71 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 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 |
| 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 |
| 0 | 41 | 0 | 0 | 0 | 0 | 0 | 0 |
| 16 | 41 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 15 | 67 | 0 | 0 | 0 | 0 |
| 0 | 0 | 13 | 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 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 68 | 27 | 0 | 0 | 0 | 0 | 0 | 0 |
| 45 | 5 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 15 | 67 | 0 | 0 | 0 | 0 |
| 0 | 0 | 13 | 58 | 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 | 0 | 1 |
G:=sub<GL(8,GF(73))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,71,72,0,0,0,0,0,0,3,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,72,72,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,71,72,0,0,0,0,0,0,3,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[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],[0,16,0,0,0,0,0,0,41,41,0,0,0,0,0,0,0,0,15,13,0,0,0,0,0,0,67,58,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0],[68,45,0,0,0,0,0,0,27,5,0,0,0,0,0,0,0,0,15,13,0,0,0,0,0,0,67,58,0,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1] >;
C33⋊6Q16 in GAP, Magma, Sage, TeX
C_3^3\rtimes_6Q_{16} % in TeX
G:=Group("C3^3:6Q16"); // GroupNames label
G:=SmallGroup(432,445);
// by ID
G=gap.SmallGroup(432,445);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,56,85,64,254,135,58,571,2028,14118]);
// 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,d*a*d^-1=e*a*e^-1=a^-1,b*c=c*b,d*b*d^-1=e*b*e^-1=b^-1,d*c*d^-1=c^-1,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations