metabelian, supersoluble, monomial
Aliases: C33⋊7Q16, C32⋊10Dic12, C12.32S32, (C3×C6).81D12, (C3×C12).122D6, C32⋊4C8.2S3, (C32×C6).39D4, C33⋊8Q8.2C2, Dic6.1(C3⋊S3), (C3×Dic6).11S3, C3⋊1(C32⋊7Q16), C3⋊2(C32⋊3Q16), C32⋊6(C3⋊Q16), C6.4(C32⋊7D4), C2.7(C33⋊7D4), C6.25(C3⋊D12), (C32×Dic6).4C2, (C32×C12).18C22, C4.11(S3×C3⋊S3), C12.33(C2×C3⋊S3), (C3×C6).59(C3⋊D4), (C3×C32⋊4C8).2C2, SmallGroup(432,446)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C33⋊7Q16
G = < a,b,c,d,e | a3=b3=c3=d8=1, e2=d4, ab=ba, ac=ca, dad-1=a-1, ae=ea, bc=cb, dbd-1=b-1, be=eb, cd=dc, ece-1=c-1, ede-1=d-1 >
Subgroups: 840 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, Dic6, C3×Q8, C33, C3×Dic3, C3⋊Dic3, C3×C12, C3×C12, C3×C12, Dic12, C3⋊Q16, C32×C6, C3×C3⋊C8, C32⋊4C8, C3×Dic6, C32⋊4Q8, Q8×C32, C32×Dic3, C33⋊5C4, C32×C12, C32⋊3Q16, C32⋊7Q16, C3×C32⋊4C8, C32×Dic6, C33⋊8Q8, C33⋊7Q16
Quotients: C1, C2, C22, S3, D4, D6, Q16, C3⋊S3, D12, C3⋊D4, S32, C2×C3⋊S3, Dic12, C3⋊Q16, C3⋊D12, C32⋊7D4, S3×C3⋊S3, C32⋊3Q16, C32⋊7Q16, C33⋊7D4, C33⋊7Q16
►On 144 points
Generators in S144
(1 121 79)(2 80 122)(3 123 73)(4 74 124)(5 125 75)(6 76 126)(7 127 77)(8 78 128)(9 95 58)(10 59 96)(11 89 60)(12 61 90)(13 91 62)(14 63 92)(15 93 64)(16 57 94)(17 42 49)(18 50 43)(19 44 51)(20 52 45)(21 46 53)(22 54 47)(23 48 55)(24 56 41)(25 142 37)(26 38 143)(27 144 39)(28 40 137)(29 138 33)(30 34 139)(31 140 35)(32 36 141)(65 101 134)(66 135 102)(67 103 136)(68 129 104)(69 97 130)(70 131 98)(71 99 132)(72 133 100)(81 113 106)(82 107 114)(83 115 108)(84 109 116)(85 117 110)(86 111 118)(87 119 112)(88 105 120)
(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 49 28)(10 29 50)(11 51 30)(12 31 52)(13 53 32)(14 25 54)(15 55 26)(16 27 56)(17 40 95)(18 96 33)(19 34 89)(20 90 35)(21 36 91)(22 92 37)(23 38 93)(24 94 39)(41 57 144)(42 137 58)(43 59 138)(44 139 60)(45 61 140)(46 141 62)(47 63 142)(48 143 64)(73 98 86)(74 87 99)(75 100 88)(76 81 101)(77 102 82)(78 83 103)(79 104 84)(80 85 97)(113 134 126)(114 127 135)(115 136 128)(116 121 129)(117 130 122)(118 123 131)(119 132 124)(120 125 133)
(1 104 116)(2 97 117)(3 98 118)(4 99 119)(5 100 120)(6 101 113)(7 102 114)(8 103 115)(9 42 40)(10 43 33)(11 44 34)(12 45 35)(13 46 36)(14 47 37)(15 48 38)(16 41 39)(17 28 58)(18 29 59)(19 30 60)(20 31 61)(21 32 62)(22 25 63)(23 26 64)(24 27 57)(49 137 95)(50 138 96)(51 139 89)(52 140 90)(53 141 91)(54 142 92)(55 143 93)(56 144 94)(65 81 126)(66 82 127)(67 83 128)(68 84 121)(69 85 122)(70 86 123)(71 87 124)(72 88 125)(73 131 111)(74 132 112)(75 133 105)(76 134 106)(77 135 107)(78 136 108)(79 129 109)(80 130 110)
(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 57 5 61)(2 64 6 60)(3 63 7 59)(4 62 8 58)(9 74 13 78)(10 73 14 77)(11 80 15 76)(12 79 16 75)(17 119 21 115)(18 118 22 114)(19 117 23 113)(20 116 24 120)(25 102 29 98)(26 101 30 97)(27 100 31 104)(28 99 32 103)(33 131 37 135)(34 130 38 134)(35 129 39 133)(36 136 40 132)(41 105 45 109)(42 112 46 108)(43 111 47 107)(44 110 48 106)(49 87 53 83)(50 86 54 82)(51 85 55 81)(52 84 56 88)(65 139 69 143)(66 138 70 142)(67 137 71 141)(68 144 72 140)(89 122 93 126)(90 121 94 125)(91 128 95 124)(92 127 96 123)
G:=sub<Sym(144)| (1,121,79)(2,80,122)(3,123,73)(4,74,124)(5,125,75)(6,76,126)(7,127,77)(8,78,128)(9,95,58)(10,59,96)(11,89,60)(12,61,90)(13,91,62)(14,63,92)(15,93,64)(16,57,94)(17,42,49)(18,50,43)(19,44,51)(20,52,45)(21,46,53)(22,54,47)(23,48,55)(24,56,41)(25,142,37)(26,38,143)(27,144,39)(28,40,137)(29,138,33)(30,34,139)(31,140,35)(32,36,141)(65,101,134)(66,135,102)(67,103,136)(68,129,104)(69,97,130)(70,131,98)(71,99,132)(72,133,100)(81,113,106)(82,107,114)(83,115,108)(84,109,116)(85,117,110)(86,111,118)(87,119,112)(88,105,120), (1,68,109)(2,110,69)(3,70,111)(4,112,71)(5,72,105)(6,106,65)(7,66,107)(8,108,67)(9,49,28)(10,29,50)(11,51,30)(12,31,52)(13,53,32)(14,25,54)(15,55,26)(16,27,56)(17,40,95)(18,96,33)(19,34,89)(20,90,35)(21,36,91)(22,92,37)(23,38,93)(24,94,39)(41,57,144)(42,137,58)(43,59,138)(44,139,60)(45,61,140)(46,141,62)(47,63,142)(48,143,64)(73,98,86)(74,87,99)(75,100,88)(76,81,101)(77,102,82)(78,83,103)(79,104,84)(80,85,97)(113,134,126)(114,127,135)(115,136,128)(116,121,129)(117,130,122)(118,123,131)(119,132,124)(120,125,133), (1,104,116)(2,97,117)(3,98,118)(4,99,119)(5,100,120)(6,101,113)(7,102,114)(8,103,115)(9,42,40)(10,43,33)(11,44,34)(12,45,35)(13,46,36)(14,47,37)(15,48,38)(16,41,39)(17,28,58)(18,29,59)(19,30,60)(20,31,61)(21,32,62)(22,25,63)(23,26,64)(24,27,57)(49,137,95)(50,138,96)(51,139,89)(52,140,90)(53,141,91)(54,142,92)(55,143,93)(56,144,94)(65,81,126)(66,82,127)(67,83,128)(68,84,121)(69,85,122)(70,86,123)(71,87,124)(72,88,125)(73,131,111)(74,132,112)(75,133,105)(76,134,106)(77,135,107)(78,136,108)(79,129,109)(80,130,110), (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), (1,57,5,61)(2,64,6,60)(3,63,7,59)(4,62,8,58)(9,74,13,78)(10,73,14,77)(11,80,15,76)(12,79,16,75)(17,119,21,115)(18,118,22,114)(19,117,23,113)(20,116,24,120)(25,102,29,98)(26,101,30,97)(27,100,31,104)(28,99,32,103)(33,131,37,135)(34,130,38,134)(35,129,39,133)(36,136,40,132)(41,105,45,109)(42,112,46,108)(43,111,47,107)(44,110,48,106)(49,87,53,83)(50,86,54,82)(51,85,55,81)(52,84,56,88)(65,139,69,143)(66,138,70,142)(67,137,71,141)(68,144,72,140)(89,122,93,126)(90,121,94,125)(91,128,95,124)(92,127,96,123)>;
G:=Group( (1,121,79)(2,80,122)(3,123,73)(4,74,124)(5,125,75)(6,76,126)(7,127,77)(8,78,128)(9,95,58)(10,59,96)(11,89,60)(12,61,90)(13,91,62)(14,63,92)(15,93,64)(16,57,94)(17,42,49)(18,50,43)(19,44,51)(20,52,45)(21,46,53)(22,54,47)(23,48,55)(24,56,41)(25,142,37)(26,38,143)(27,144,39)(28,40,137)(29,138,33)(30,34,139)(31,140,35)(32,36,141)(65,101,134)(66,135,102)(67,103,136)(68,129,104)(69,97,130)(70,131,98)(71,99,132)(72,133,100)(81,113,106)(82,107,114)(83,115,108)(84,109,116)(85,117,110)(86,111,118)(87,119,112)(88,105,120), (1,68,109)(2,110,69)(3,70,111)(4,112,71)(5,72,105)(6,106,65)(7,66,107)(8,108,67)(9,49,28)(10,29,50)(11,51,30)(12,31,52)(13,53,32)(14,25,54)(15,55,26)(16,27,56)(17,40,95)(18,96,33)(19,34,89)(20,90,35)(21,36,91)(22,92,37)(23,38,93)(24,94,39)(41,57,144)(42,137,58)(43,59,138)(44,139,60)(45,61,140)(46,141,62)(47,63,142)(48,143,64)(73,98,86)(74,87,99)(75,100,88)(76,81,101)(77,102,82)(78,83,103)(79,104,84)(80,85,97)(113,134,126)(114,127,135)(115,136,128)(116,121,129)(117,130,122)(118,123,131)(119,132,124)(120,125,133), (1,104,116)(2,97,117)(3,98,118)(4,99,119)(5,100,120)(6,101,113)(7,102,114)(8,103,115)(9,42,40)(10,43,33)(11,44,34)(12,45,35)(13,46,36)(14,47,37)(15,48,38)(16,41,39)(17,28,58)(18,29,59)(19,30,60)(20,31,61)(21,32,62)(22,25,63)(23,26,64)(24,27,57)(49,137,95)(50,138,96)(51,139,89)(52,140,90)(53,141,91)(54,142,92)(55,143,93)(56,144,94)(65,81,126)(66,82,127)(67,83,128)(68,84,121)(69,85,122)(70,86,123)(71,87,124)(72,88,125)(73,131,111)(74,132,112)(75,133,105)(76,134,106)(77,135,107)(78,136,108)(79,129,109)(80,130,110), (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), (1,57,5,61)(2,64,6,60)(3,63,7,59)(4,62,8,58)(9,74,13,78)(10,73,14,77)(11,80,15,76)(12,79,16,75)(17,119,21,115)(18,118,22,114)(19,117,23,113)(20,116,24,120)(25,102,29,98)(26,101,30,97)(27,100,31,104)(28,99,32,103)(33,131,37,135)(34,130,38,134)(35,129,39,133)(36,136,40,132)(41,105,45,109)(42,112,46,108)(43,111,47,107)(44,110,48,106)(49,87,53,83)(50,86,54,82)(51,85,55,81)(52,84,56,88)(65,139,69,143)(66,138,70,142)(67,137,71,141)(68,144,72,140)(89,122,93,126)(90,121,94,125)(91,128,95,124)(92,127,96,123) );
G=PermutationGroup([[(1,121,79),(2,80,122),(3,123,73),(4,74,124),(5,125,75),(6,76,126),(7,127,77),(8,78,128),(9,95,58),(10,59,96),(11,89,60),(12,61,90),(13,91,62),(14,63,92),(15,93,64),(16,57,94),(17,42,49),(18,50,43),(19,44,51),(20,52,45),(21,46,53),(22,54,47),(23,48,55),(24,56,41),(25,142,37),(26,38,143),(27,144,39),(28,40,137),(29,138,33),(30,34,139),(31,140,35),(32,36,141),(65,101,134),(66,135,102),(67,103,136),(68,129,104),(69,97,130),(70,131,98),(71,99,132),(72,133,100),(81,113,106),(82,107,114),(83,115,108),(84,109,116),(85,117,110),(86,111,118),(87,119,112),(88,105,120)], [(1,68,109),(2,110,69),(3,70,111),(4,112,71),(5,72,105),(6,106,65),(7,66,107),(8,108,67),(9,49,28),(10,29,50),(11,51,30),(12,31,52),(13,53,32),(14,25,54),(15,55,26),(16,27,56),(17,40,95),(18,96,33),(19,34,89),(20,90,35),(21,36,91),(22,92,37),(23,38,93),(24,94,39),(41,57,144),(42,137,58),(43,59,138),(44,139,60),(45,61,140),(46,141,62),(47,63,142),(48,143,64),(73,98,86),(74,87,99),(75,100,88),(76,81,101),(77,102,82),(78,83,103),(79,104,84),(80,85,97),(113,134,126),(114,127,135),(115,136,128),(116,121,129),(117,130,122),(118,123,131),(119,132,124),(120,125,133)], [(1,104,116),(2,97,117),(3,98,118),(4,99,119),(5,100,120),(6,101,113),(7,102,114),(8,103,115),(9,42,40),(10,43,33),(11,44,34),(12,45,35),(13,46,36),(14,47,37),(15,48,38),(16,41,39),(17,28,58),(18,29,59),(19,30,60),(20,31,61),(21,32,62),(22,25,63),(23,26,64),(24,27,57),(49,137,95),(50,138,96),(51,139,89),(52,140,90),(53,141,91),(54,142,92),(55,143,93),(56,144,94),(65,81,126),(66,82,127),(67,83,128),(68,84,121),(69,85,122),(70,86,123),(71,87,124),(72,88,125),(73,131,111),(74,132,112),(75,133,105),(76,134,106),(77,135,107),(78,136,108),(79,129,109),(80,130,110)], [(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)], [(1,57,5,61),(2,64,6,60),(3,63,7,59),(4,62,8,58),(9,74,13,78),(10,73,14,77),(11,80,15,76),(12,79,16,75),(17,119,21,115),(18,118,22,114),(19,117,23,113),(20,116,24,120),(25,102,29,98),(26,101,30,97),(27,100,31,104),(28,99,32,103),(33,131,37,135),(34,130,38,134),(35,129,39,133),(36,136,40,132),(41,105,45,109),(42,112,46,108),(43,111,47,107),(44,110,48,106),(49,87,53,83),(50,86,54,82),(51,85,55,81),(52,84,56,88),(65,139,69,143),(66,138,70,142),(67,137,71,141),(68,144,72,140),(89,122,93,126),(90,121,94,125),(91,128,95,124),(92,127,96,123)]])
51 conjugacy classes
| class | 1 | 2 | 3A | ··· | 3E | 3F | 3G | 3H | 3I | 4A | 4B | 4C | 6A | ··· | 6E | 6F | 6G | 6H | 6I | 8A | 8B | 12A | 12B | 12C | ··· | 12N | 12O | ··· | 12V | 24A | 24B | 24C | 24D |
| 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 | 24 | 24 |
| size | 1 | 1 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 2 | 12 | 108 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 18 | 18 | 2 | 2 | 4 | ··· | 4 | 12 | ··· | 12 | 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 | Q16 | D12 | C3⋊D4 | Dic12 | S32 | C3⋊Q16 | C3⋊D12 | C32⋊3Q16 |
| kernel | C33⋊7Q16 | C3×C32⋊4C8 | C32×Dic6 | C33⋊8Q8 | C32⋊4C8 | C3×Dic6 | 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⋊7Q16 ►in GL8(𝔽73)
| 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 | 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 | 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 | 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 |
| 61 | 10 | 0 | 0 | 0 | 0 | 0 | 0 |
| 22 | 12 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 57 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 16 | 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 |
| 30 | 60 | 0 | 0 | 0 | 0 | 0 | 0 |
| 13 | 43 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 43 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 30 | 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))| [0,72,0,0,0,0,0,0,1,72,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,72,72,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[0,72,0,0,0,0,0,0,1,72,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[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],[61,22,0,0,0,0,0,0,10,12,0,0,0,0,0,0,0,0,16,16,0,0,0,0,0,0,57,16,0,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[30,13,0,0,0,0,0,0,60,43,0,0,0,0,0,0,0,0,43,11,0,0,0,0,0,0,11,30,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,1,72,0,0,0,0,0,0,0,72] >;
C33⋊7Q16 in GAP, Magma, Sage, TeX
C_3^3\rtimes_7Q_{16} % in TeX
G:=Group("C3^3:7Q16"); // GroupNames label
G:=SmallGroup(432,446);
// by ID
G=gap.SmallGroup(432,446);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,56,85,92,254,58,571,2028,14118]);
// 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=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^-1=c^-1,e*d*e^-1=d^-1>;
// generators/relations