metabelian, supersoluble, monomial
Aliases: C33⋊14SD16, C12.29S32, C32⋊4C8⋊9S3, (C3×C6).79D12, C33⋊8Q8⋊2C2, D12.1(C3⋊S3), (C3×D12).11S3, (C3×C12).117D6, (C32×C6).34D4, C32⋊8(D4.S3), (C32×D12).4C2, C2.5(C33⋊7D4), C6.2(C32⋊7D4), C32⋊15(C24⋊C2), C6.23(C3⋊D12), C3⋊2(D12.S3), C3⋊1(C32⋊9SD16), (C32×C12).13C22, C4.9(S3×C3⋊S3), C12.31(C2×C3⋊S3), (C3×C32⋊4C8)⋊4C2, (C3×C6).57(C3⋊D4), SmallGroup(432,441)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C33⋊14SD16
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, cd=dc, ece=c-1, ede=d3 >
Subgroups: 936 in 168 conjugacy classes, 46 normal (18 characteristic)
C1, C2, C2, C3, C3, C3, C4, C4, C22, S3, C6, C6, C6, C8, D4, Q8, C32, C32, C32, Dic3, C12, C12, C12, D6, C2×C6, SD16, C3×S3, C3×C6, C3×C6, C3×C6, C3⋊C8, C24, Dic6, D12, C3×D4, C33, C3⋊Dic3, C3×C12, C3×C12, C3×C12, S3×C6, C62, C24⋊C2, D4.S3, S3×C32, C32×C6, C3×C3⋊C8, C32⋊4C8, C3×D12, C32⋊4Q8, D4×C32, C33⋊5C4, C32×C12, S3×C3×C6, D12.S3, C32⋊9SD16, C3×C32⋊4C8, C32×D12, C33⋊8Q8, C33⋊14SD16
Quotients: C1, C2, C22, S3, D4, D6, SD16, C3⋊S3, D12, C3⋊D4, S32, C2×C3⋊S3, C24⋊C2, D4.S3, C3⋊D12, C32⋊7D4, S3×C3⋊S3, D12.S3, C32⋊9SD16, C33⋊7D4, C33⋊14SD16
►On 144 points
Generators in S144
(1 68 109)(2 110 69)(3 70 111)(4 112 71)(5 72 105)(6 106 65)(7 66 107)(8 108 67)(9 20 144)(10 137 21)(11 22 138)(12 139 23)(13 24 140)(14 141 17)(15 18 142)(16 143 19)(25 94 44)(26 45 95)(27 96 46)(28 47 89)(29 90 48)(30 41 91)(31 92 42)(32 43 93)(33 50 58)(34 59 51)(35 52 60)(36 61 53)(37 54 62)(38 63 55)(39 56 64)(40 57 49)(73 114 123)(74 124 115)(75 116 125)(76 126 117)(77 118 127)(78 128 119)(79 120 121)(80 122 113)(81 104 134)(82 135 97)(83 98 136)(84 129 99)(85 100 130)(86 131 101)(87 102 132)(88 133 103)
(1 102 116)(2 117 103)(3 104 118)(4 119 97)(5 98 120)(6 113 99)(7 100 114)(8 115 101)(9 44 49)(10 50 45)(11 46 51)(12 52 47)(13 48 53)(14 54 41)(15 42 55)(16 56 43)(17 37 30)(18 31 38)(19 39 32)(20 25 40)(21 33 26)(22 27 34)(23 35 28)(24 29 36)(57 144 94)(58 95 137)(59 138 96)(60 89 139)(61 140 90)(62 91 141)(63 142 92)(64 93 143)(65 122 129)(66 130 123)(67 124 131)(68 132 125)(69 126 133)(70 134 127)(71 128 135)(72 136 121)(73 107 85)(74 86 108)(75 109 87)(76 88 110)(77 111 81)(78 82 112)(79 105 83)(80 84 106)
(1 116 102)(2 117 103)(3 118 104)(4 119 97)(5 120 98)(6 113 99)(7 114 100)(8 115 101)(9 44 49)(10 45 50)(11 46 51)(12 47 52)(13 48 53)(14 41 54)(15 42 55)(16 43 56)(17 30 37)(18 31 38)(19 32 39)(20 25 40)(21 26 33)(22 27 34)(23 28 35)(24 29 36)(57 144 94)(58 137 95)(59 138 96)(60 139 89)(61 140 90)(62 141 91)(63 142 92)(64 143 93)(65 122 129)(66 123 130)(67 124 131)(68 125 132)(69 126 133)(70 127 134)(71 128 135)(72 121 136)(73 85 107)(74 86 108)(75 87 109)(76 88 110)(77 81 111)(78 82 112)(79 83 105)(80 84 106)
(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 24)(2 19)(3 22)(4 17)(5 20)(6 23)(7 18)(8 21)(9 105)(10 108)(11 111)(12 106)(13 109)(14 112)(15 107)(16 110)(25 98)(26 101)(27 104)(28 99)(29 102)(30 97)(31 100)(32 103)(33 115)(34 118)(35 113)(36 116)(37 119)(38 114)(39 117)(40 120)(41 82)(42 85)(43 88)(44 83)(45 86)(46 81)(47 84)(48 87)(49 79)(50 74)(51 77)(52 80)(53 75)(54 78)(55 73)(56 76)(57 121)(58 124)(59 127)(60 122)(61 125)(62 128)(63 123)(64 126)(65 139)(66 142)(67 137)(68 140)(69 143)(70 138)(71 141)(72 144)(89 129)(90 132)(91 135)(92 130)(93 133)(94 136)(95 131)(96 134)
G:=sub<Sym(144)| (1,68,109)(2,110,69)(3,70,111)(4,112,71)(5,72,105)(6,106,65)(7,66,107)(8,108,67)(9,20,144)(10,137,21)(11,22,138)(12,139,23)(13,24,140)(14,141,17)(15,18,142)(16,143,19)(25,94,44)(26,45,95)(27,96,46)(28,47,89)(29,90,48)(30,41,91)(31,92,42)(32,43,93)(33,50,58)(34,59,51)(35,52,60)(36,61,53)(37,54,62)(38,63,55)(39,56,64)(40,57,49)(73,114,123)(74,124,115)(75,116,125)(76,126,117)(77,118,127)(78,128,119)(79,120,121)(80,122,113)(81,104,134)(82,135,97)(83,98,136)(84,129,99)(85,100,130)(86,131,101)(87,102,132)(88,133,103), (1,102,116)(2,117,103)(3,104,118)(4,119,97)(5,98,120)(6,113,99)(7,100,114)(8,115,101)(9,44,49)(10,50,45)(11,46,51)(12,52,47)(13,48,53)(14,54,41)(15,42,55)(16,56,43)(17,37,30)(18,31,38)(19,39,32)(20,25,40)(21,33,26)(22,27,34)(23,35,28)(24,29,36)(57,144,94)(58,95,137)(59,138,96)(60,89,139)(61,140,90)(62,91,141)(63,142,92)(64,93,143)(65,122,129)(66,130,123)(67,124,131)(68,132,125)(69,126,133)(70,134,127)(71,128,135)(72,136,121)(73,107,85)(74,86,108)(75,109,87)(76,88,110)(77,111,81)(78,82,112)(79,105,83)(80,84,106), (1,116,102)(2,117,103)(3,118,104)(4,119,97)(5,120,98)(6,113,99)(7,114,100)(8,115,101)(9,44,49)(10,45,50)(11,46,51)(12,47,52)(13,48,53)(14,41,54)(15,42,55)(16,43,56)(17,30,37)(18,31,38)(19,32,39)(20,25,40)(21,26,33)(22,27,34)(23,28,35)(24,29,36)(57,144,94)(58,137,95)(59,138,96)(60,139,89)(61,140,90)(62,141,91)(63,142,92)(64,143,93)(65,122,129)(66,123,130)(67,124,131)(68,125,132)(69,126,133)(70,127,134)(71,128,135)(72,121,136)(73,85,107)(74,86,108)(75,87,109)(76,88,110)(77,81,111)(78,82,112)(79,83,105)(80,84,106), (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), (1,24)(2,19)(3,22)(4,17)(5,20)(6,23)(7,18)(8,21)(9,105)(10,108)(11,111)(12,106)(13,109)(14,112)(15,107)(16,110)(25,98)(26,101)(27,104)(28,99)(29,102)(30,97)(31,100)(32,103)(33,115)(34,118)(35,113)(36,116)(37,119)(38,114)(39,117)(40,120)(41,82)(42,85)(43,88)(44,83)(45,86)(46,81)(47,84)(48,87)(49,79)(50,74)(51,77)(52,80)(53,75)(54,78)(55,73)(56,76)(57,121)(58,124)(59,127)(60,122)(61,125)(62,128)(63,123)(64,126)(65,139)(66,142)(67,137)(68,140)(69,143)(70,138)(71,141)(72,144)(89,129)(90,132)(91,135)(92,130)(93,133)(94,136)(95,131)(96,134)>;
G:=Group( (1,68,109)(2,110,69)(3,70,111)(4,112,71)(5,72,105)(6,106,65)(7,66,107)(8,108,67)(9,20,144)(10,137,21)(11,22,138)(12,139,23)(13,24,140)(14,141,17)(15,18,142)(16,143,19)(25,94,44)(26,45,95)(27,96,46)(28,47,89)(29,90,48)(30,41,91)(31,92,42)(32,43,93)(33,50,58)(34,59,51)(35,52,60)(36,61,53)(37,54,62)(38,63,55)(39,56,64)(40,57,49)(73,114,123)(74,124,115)(75,116,125)(76,126,117)(77,118,127)(78,128,119)(79,120,121)(80,122,113)(81,104,134)(82,135,97)(83,98,136)(84,129,99)(85,100,130)(86,131,101)(87,102,132)(88,133,103), (1,102,116)(2,117,103)(3,104,118)(4,119,97)(5,98,120)(6,113,99)(7,100,114)(8,115,101)(9,44,49)(10,50,45)(11,46,51)(12,52,47)(13,48,53)(14,54,41)(15,42,55)(16,56,43)(17,37,30)(18,31,38)(19,39,32)(20,25,40)(21,33,26)(22,27,34)(23,35,28)(24,29,36)(57,144,94)(58,95,137)(59,138,96)(60,89,139)(61,140,90)(62,91,141)(63,142,92)(64,93,143)(65,122,129)(66,130,123)(67,124,131)(68,132,125)(69,126,133)(70,134,127)(71,128,135)(72,136,121)(73,107,85)(74,86,108)(75,109,87)(76,88,110)(77,111,81)(78,82,112)(79,105,83)(80,84,106), (1,116,102)(2,117,103)(3,118,104)(4,119,97)(5,120,98)(6,113,99)(7,114,100)(8,115,101)(9,44,49)(10,45,50)(11,46,51)(12,47,52)(13,48,53)(14,41,54)(15,42,55)(16,43,56)(17,30,37)(18,31,38)(19,32,39)(20,25,40)(21,26,33)(22,27,34)(23,28,35)(24,29,36)(57,144,94)(58,137,95)(59,138,96)(60,139,89)(61,140,90)(62,141,91)(63,142,92)(64,143,93)(65,122,129)(66,123,130)(67,124,131)(68,125,132)(69,126,133)(70,127,134)(71,128,135)(72,121,136)(73,85,107)(74,86,108)(75,87,109)(76,88,110)(77,81,111)(78,82,112)(79,83,105)(80,84,106), (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), (1,24)(2,19)(3,22)(4,17)(5,20)(6,23)(7,18)(8,21)(9,105)(10,108)(11,111)(12,106)(13,109)(14,112)(15,107)(16,110)(25,98)(26,101)(27,104)(28,99)(29,102)(30,97)(31,100)(32,103)(33,115)(34,118)(35,113)(36,116)(37,119)(38,114)(39,117)(40,120)(41,82)(42,85)(43,88)(44,83)(45,86)(46,81)(47,84)(48,87)(49,79)(50,74)(51,77)(52,80)(53,75)(54,78)(55,73)(56,76)(57,121)(58,124)(59,127)(60,122)(61,125)(62,128)(63,123)(64,126)(65,139)(66,142)(67,137)(68,140)(69,143)(70,138)(71,141)(72,144)(89,129)(90,132)(91,135)(92,130)(93,133)(94,136)(95,131)(96,134) );
G=PermutationGroup([[(1,68,109),(2,110,69),(3,70,111),(4,112,71),(5,72,105),(6,106,65),(7,66,107),(8,108,67),(9,20,144),(10,137,21),(11,22,138),(12,139,23),(13,24,140),(14,141,17),(15,18,142),(16,143,19),(25,94,44),(26,45,95),(27,96,46),(28,47,89),(29,90,48),(30,41,91),(31,92,42),(32,43,93),(33,50,58),(34,59,51),(35,52,60),(36,61,53),(37,54,62),(38,63,55),(39,56,64),(40,57,49),(73,114,123),(74,124,115),(75,116,125),(76,126,117),(77,118,127),(78,128,119),(79,120,121),(80,122,113),(81,104,134),(82,135,97),(83,98,136),(84,129,99),(85,100,130),(86,131,101),(87,102,132),(88,133,103)], [(1,102,116),(2,117,103),(3,104,118),(4,119,97),(5,98,120),(6,113,99),(7,100,114),(8,115,101),(9,44,49),(10,50,45),(11,46,51),(12,52,47),(13,48,53),(14,54,41),(15,42,55),(16,56,43),(17,37,30),(18,31,38),(19,39,32),(20,25,40),(21,33,26),(22,27,34),(23,35,28),(24,29,36),(57,144,94),(58,95,137),(59,138,96),(60,89,139),(61,140,90),(62,91,141),(63,142,92),(64,93,143),(65,122,129),(66,130,123),(67,124,131),(68,132,125),(69,126,133),(70,134,127),(71,128,135),(72,136,121),(73,107,85),(74,86,108),(75,109,87),(76,88,110),(77,111,81),(78,82,112),(79,105,83),(80,84,106)], [(1,116,102),(2,117,103),(3,118,104),(4,119,97),(5,120,98),(6,113,99),(7,114,100),(8,115,101),(9,44,49),(10,45,50),(11,46,51),(12,47,52),(13,48,53),(14,41,54),(15,42,55),(16,43,56),(17,30,37),(18,31,38),(19,32,39),(20,25,40),(21,26,33),(22,27,34),(23,28,35),(24,29,36),(57,144,94),(58,137,95),(59,138,96),(60,139,89),(61,140,90),(62,141,91),(63,142,92),(64,143,93),(65,122,129),(66,123,130),(67,124,131),(68,125,132),(69,126,133),(70,127,134),(71,128,135),(72,121,136),(73,85,107),(74,86,108),(75,87,109),(76,88,110),(77,81,111),(78,82,112),(79,83,105),(80,84,106)], [(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)], [(1,24),(2,19),(3,22),(4,17),(5,20),(6,23),(7,18),(8,21),(9,105),(10,108),(11,111),(12,106),(13,109),(14,112),(15,107),(16,110),(25,98),(26,101),(27,104),(28,99),(29,102),(30,97),(31,100),(32,103),(33,115),(34,118),(35,113),(36,116),(37,119),(38,114),(39,117),(40,120),(41,82),(42,85),(43,88),(44,83),(45,86),(46,81),(47,84),(48,87),(49,79),(50,74),(51,77),(52,80),(53,75),(54,78),(55,73),(56,76),(57,121),(58,124),(59,127),(60,122),(61,125),(62,128),(63,123),(64,126),(65,139),(66,142),(67,137),(68,140),(69,143),(70,138),(71,141),(72,144),(89,129),(90,132),(91,135),(92,130),(93,133),(94,136),(95,131),(96,134)]])
51 conjugacy classes
| class | 1 | 2A | 2B | 3A | ··· | 3E | 3F | 3G | 3H | 3I | 4A | 4B | 6A | ··· | 6E | 6F | 6G | 6H | 6I | 6J | ··· | 6Q | 8A | 8B | 12A | 12B | 12C | ··· | 12N | 24A | 24B | 24C | 24D |
| order | 1 | 2 | 2 | 3 | ··· | 3 | 3 | 3 | 3 | 3 | 4 | 4 | 6 | ··· | 6 | 6 | 6 | 6 | 6 | 6 | ··· | 6 | 8 | 8 | 12 | 12 | 12 | ··· | 12 | 24 | 24 | 24 | 24 |
| size | 1 | 1 | 12 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 2 | 108 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 12 | ··· | 12 | 18 | 18 | 2 | 2 | 4 | ··· | 4 | 18 | 18 | 18 | 18 |
51 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 | SD16 | D12 | C3⋊D4 | C24⋊C2 | S32 | D4.S3 | C3⋊D12 | D12.S3 |
| kernel | C33⋊14SD16 | C3×C32⋊4C8 | C32×D12 | C33⋊8Q8 | C32⋊4C8 | C3×D12 | C32×C6 | C3×C12 | C33 | C3×C6 | C3×C6 | C32 | C12 | C32 | C6 | C3 |
| # reps | 1 | 1 | 1 | 1 | 1 | 4 | 1 | 5 | 2 | 2 | 8 | 4 | 4 | 4 | 4 | 8 |
Matrix representation of C33⋊14SD16 ►in GL8(𝔽73)
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 72 | 71 | 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 |
| 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 |
| 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 |
| 0 | 12 | 0 | 0 | 0 | 0 | 0 | 0 |
| 67 | 12 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 41 | 54 | 0 | 0 | 0 | 0 |
| 0 | 0 | 50 | 32 | 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 |
| 68 | 19 | 0 | 0 | 0 | 0 | 0 | 0 |
| 41 | 5 | 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 | 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 |
G:=sub<GL(8,GF(73))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,72,0,0,0,0,0,0,3,71,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,72,1,0,0,0,0,0,0,72,0],[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],[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],[0,67,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,41,50,0,0,0,0,0,0,54,32,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,1,72,0,0,0,0,0,0,0,72],[68,41,0,0,0,0,0,0,19,5,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,72,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1] >;
C33⋊14SD16 in GAP, Magma, Sage, TeX
C_3^3\rtimes_{14}{\rm SD}_{16} % in TeX
G:=Group("C3^3:14SD16"); // GroupNames label
G:=SmallGroup(432,441);
// by ID
G=gap.SmallGroup(432,441);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,85,36,254,58,571,2028,14118]);
// 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,c*d=d*c,e*c*e=c^-1,e*d*e=d^3>;
// generators/relations