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## G = C2×C33⋊4Q8order 432 = 24·33

### Direct product of C2 and C33⋊4Q8

Series: Derived Chief Lower central Upper central

 Derived series C1 — C32×C6 — C2×C33⋊4Q8
 Chief series C1 — C3 — C32 — C33 — C32×C6 — C32×Dic3 — C33⋊4Q8 — C2×C33⋊4Q8
 Lower central C33 — C32×C6 — C2×C33⋊4Q8
 Upper central C1 — C22

Generators and relations for C2×C334Q8
G = < a,b,c,d,e,f | a2=b3=c3=d3=e4=1, f2=e2, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, bd=db, ebe-1=b-1, bf=fb, cd=dc, ece-1=c-1, cf=fc, de=ed, fdf-1=d-1, fef-1=e-1 >

Subgroups: 1336 in 292 conjugacy classes, 92 normal (18 characteristic)
C1, C2, C2, C3, C3, C3, C4, C22, C6, C6, C6, C2×C4, Q8, C32, C32, C32, Dic3, Dic3, C12, C2×C6, C2×C6, C2×C6, C2×Q8, C3×C6, C3×C6, C3×C6, Dic6, C2×Dic3, C2×Dic3, C2×C12, C33, C3×Dic3, C3×Dic3, C3⋊Dic3, C3⋊Dic3, C3×C12, C62, C62, C62, C2×Dic6, C32×C6, C32×C6, C322Q8, C6×Dic3, C6×Dic3, C324Q8, C2×C3⋊Dic3, C2×C3⋊Dic3, C6×C12, C32×Dic3, C3×C3⋊Dic3, C335C4, C3×C62, C2×C322Q8, C2×C324Q8, C334Q8, Dic3×C3×C6, C6×C3⋊Dic3, C2×C335C4, C2×C334Q8
Quotients: C1, C2, C22, S3, Q8, C23, D6, C2×Q8, C3⋊S3, Dic6, C22×S3, S32, C2×C3⋊S3, C2×Dic6, C322Q8, C324Q8, C2×S32, C22×C3⋊S3, S3×C3⋊S3, C2×C322Q8, C2×C324Q8, C334Q8, C2×S3×C3⋊S3, C2×C334Q8

Smallest permutation representation of C2×C334Q8
On 144 points
Generators in S144
(1 83)(2 84)(3 81)(4 82)(5 73)(6 74)(7 75)(8 76)(9 130)(10 131)(11 132)(12 129)(13 35)(14 36)(15 33)(16 34)(17 109)(18 110)(19 111)(20 112)(21 25)(22 26)(23 27)(24 28)(29 58)(30 59)(31 60)(32 57)(37 86)(38 87)(39 88)(40 85)(41 61)(42 62)(43 63)(44 64)(45 80)(46 77)(47 78)(48 79)(49 71)(50 72)(51 69)(52 70)(53 66)(54 67)(55 68)(56 65)(89 108)(90 105)(91 106)(92 107)(93 124)(94 121)(95 122)(96 123)(97 125)(98 126)(99 127)(100 128)(101 134)(102 135)(103 136)(104 133)(113 143)(114 144)(115 141)(116 142)(117 137)(118 138)(119 139)(120 140)
(1 65 51)(2 52 66)(3 67 49)(4 50 68)(5 14 32)(6 29 15)(7 16 30)(8 31 13)(9 92 101)(10 102 89)(11 90 103)(12 104 91)(17 61 25)(18 26 62)(19 63 27)(20 28 64)(21 109 41)(22 42 110)(23 111 43)(24 44 112)(33 74 58)(34 59 75)(35 76 60)(36 57 73)(37 142 118)(38 119 143)(39 144 120)(40 117 141)(45 123 100)(46 97 124)(47 121 98)(48 99 122)(53 84 70)(54 71 81)(55 82 72)(56 69 83)(77 125 93)(78 94 126)(79 127 95)(80 96 128)(85 137 115)(86 116 138)(87 139 113)(88 114 140)(105 136 132)(106 129 133)(107 134 130)(108 131 135)
(1 62 29)(2 30 63)(3 64 31)(4 32 61)(5 25 50)(6 51 26)(7 27 52)(8 49 28)(9 100 117)(10 118 97)(11 98 119)(12 120 99)(13 67 20)(14 17 68)(15 65 18)(16 19 66)(21 72 73)(22 74 69)(23 70 75)(24 76 71)(33 56 110)(34 111 53)(35 54 112)(36 109 55)(37 124 102)(38 103 121)(39 122 104)(40 101 123)(41 82 57)(42 58 83)(43 84 59)(44 60 81)(45 141 92)(46 89 142)(47 143 90)(48 91 144)(77 108 116)(78 113 105)(79 106 114)(80 115 107)(85 134 96)(86 93 135)(87 136 94)(88 95 133)(125 131 138)(126 139 132)(127 129 140)(128 137 130)
(1 26 15)(2 27 16)(3 28 13)(4 25 14)(5 68 61)(6 65 62)(7 66 63)(8 67 64)(9 141 123)(10 142 124)(11 143 121)(12 144 122)(17 32 50)(18 29 51)(19 30 52)(20 31 49)(21 36 82)(22 33 83)(23 34 84)(24 35 81)(37 97 89)(38 98 90)(39 99 91)(40 100 92)(41 73 55)(42 74 56)(43 75 53)(44 76 54)(45 101 117)(46 102 118)(47 103 119)(48 104 120)(57 72 109)(58 69 110)(59 70 111)(60 71 112)(77 135 138)(78 136 139)(79 133 140)(80 134 137)(85 128 107)(86 125 108)(87 126 105)(88 127 106)(93 131 116)(94 132 113)(95 129 114)(96 130 115)
(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 85 3 87)(2 88 4 86)(5 77 7 79)(6 80 8 78)(9 112 11 110)(10 111 12 109)(13 126 15 128)(14 125 16 127)(17 131 19 129)(18 130 20 132)(21 89 23 91)(22 92 24 90)(25 108 27 106)(26 107 28 105)(29 96 31 94)(30 95 32 93)(33 100 35 98)(34 99 36 97)(37 84 39 82)(38 83 40 81)(41 102 43 104)(42 101 44 103)(45 76 47 74)(46 75 48 73)(49 113 51 115)(50 116 52 114)(53 120 55 118)(54 119 56 117)(57 124 59 122)(58 123 60 121)(61 135 63 133)(62 134 64 136)(65 137 67 139)(66 140 68 138)(69 141 71 143)(70 144 72 142)

G:=sub<Sym(144)| (1,83)(2,84)(3,81)(4,82)(5,73)(6,74)(7,75)(8,76)(9,130)(10,131)(11,132)(12,129)(13,35)(14,36)(15,33)(16,34)(17,109)(18,110)(19,111)(20,112)(21,25)(22,26)(23,27)(24,28)(29,58)(30,59)(31,60)(32,57)(37,86)(38,87)(39,88)(40,85)(41,61)(42,62)(43,63)(44,64)(45,80)(46,77)(47,78)(48,79)(49,71)(50,72)(51,69)(52,70)(53,66)(54,67)(55,68)(56,65)(89,108)(90,105)(91,106)(92,107)(93,124)(94,121)(95,122)(96,123)(97,125)(98,126)(99,127)(100,128)(101,134)(102,135)(103,136)(104,133)(113,143)(114,144)(115,141)(116,142)(117,137)(118,138)(119,139)(120,140), (1,65,51)(2,52,66)(3,67,49)(4,50,68)(5,14,32)(6,29,15)(7,16,30)(8,31,13)(9,92,101)(10,102,89)(11,90,103)(12,104,91)(17,61,25)(18,26,62)(19,63,27)(20,28,64)(21,109,41)(22,42,110)(23,111,43)(24,44,112)(33,74,58)(34,59,75)(35,76,60)(36,57,73)(37,142,118)(38,119,143)(39,144,120)(40,117,141)(45,123,100)(46,97,124)(47,121,98)(48,99,122)(53,84,70)(54,71,81)(55,82,72)(56,69,83)(77,125,93)(78,94,126)(79,127,95)(80,96,128)(85,137,115)(86,116,138)(87,139,113)(88,114,140)(105,136,132)(106,129,133)(107,134,130)(108,131,135), (1,62,29)(2,30,63)(3,64,31)(4,32,61)(5,25,50)(6,51,26)(7,27,52)(8,49,28)(9,100,117)(10,118,97)(11,98,119)(12,120,99)(13,67,20)(14,17,68)(15,65,18)(16,19,66)(21,72,73)(22,74,69)(23,70,75)(24,76,71)(33,56,110)(34,111,53)(35,54,112)(36,109,55)(37,124,102)(38,103,121)(39,122,104)(40,101,123)(41,82,57)(42,58,83)(43,84,59)(44,60,81)(45,141,92)(46,89,142)(47,143,90)(48,91,144)(77,108,116)(78,113,105)(79,106,114)(80,115,107)(85,134,96)(86,93,135)(87,136,94)(88,95,133)(125,131,138)(126,139,132)(127,129,140)(128,137,130), (1,26,15)(2,27,16)(3,28,13)(4,25,14)(5,68,61)(6,65,62)(7,66,63)(8,67,64)(9,141,123)(10,142,124)(11,143,121)(12,144,122)(17,32,50)(18,29,51)(19,30,52)(20,31,49)(21,36,82)(22,33,83)(23,34,84)(24,35,81)(37,97,89)(38,98,90)(39,99,91)(40,100,92)(41,73,55)(42,74,56)(43,75,53)(44,76,54)(45,101,117)(46,102,118)(47,103,119)(48,104,120)(57,72,109)(58,69,110)(59,70,111)(60,71,112)(77,135,138)(78,136,139)(79,133,140)(80,134,137)(85,128,107)(86,125,108)(87,126,105)(88,127,106)(93,131,116)(94,132,113)(95,129,114)(96,130,115), (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), (1,85,3,87)(2,88,4,86)(5,77,7,79)(6,80,8,78)(9,112,11,110)(10,111,12,109)(13,126,15,128)(14,125,16,127)(17,131,19,129)(18,130,20,132)(21,89,23,91)(22,92,24,90)(25,108,27,106)(26,107,28,105)(29,96,31,94)(30,95,32,93)(33,100,35,98)(34,99,36,97)(37,84,39,82)(38,83,40,81)(41,102,43,104)(42,101,44,103)(45,76,47,74)(46,75,48,73)(49,113,51,115)(50,116,52,114)(53,120,55,118)(54,119,56,117)(57,124,59,122)(58,123,60,121)(61,135,63,133)(62,134,64,136)(65,137,67,139)(66,140,68,138)(69,141,71,143)(70,144,72,142)>;

G:=Group( (1,83)(2,84)(3,81)(4,82)(5,73)(6,74)(7,75)(8,76)(9,130)(10,131)(11,132)(12,129)(13,35)(14,36)(15,33)(16,34)(17,109)(18,110)(19,111)(20,112)(21,25)(22,26)(23,27)(24,28)(29,58)(30,59)(31,60)(32,57)(37,86)(38,87)(39,88)(40,85)(41,61)(42,62)(43,63)(44,64)(45,80)(46,77)(47,78)(48,79)(49,71)(50,72)(51,69)(52,70)(53,66)(54,67)(55,68)(56,65)(89,108)(90,105)(91,106)(92,107)(93,124)(94,121)(95,122)(96,123)(97,125)(98,126)(99,127)(100,128)(101,134)(102,135)(103,136)(104,133)(113,143)(114,144)(115,141)(116,142)(117,137)(118,138)(119,139)(120,140), (1,65,51)(2,52,66)(3,67,49)(4,50,68)(5,14,32)(6,29,15)(7,16,30)(8,31,13)(9,92,101)(10,102,89)(11,90,103)(12,104,91)(17,61,25)(18,26,62)(19,63,27)(20,28,64)(21,109,41)(22,42,110)(23,111,43)(24,44,112)(33,74,58)(34,59,75)(35,76,60)(36,57,73)(37,142,118)(38,119,143)(39,144,120)(40,117,141)(45,123,100)(46,97,124)(47,121,98)(48,99,122)(53,84,70)(54,71,81)(55,82,72)(56,69,83)(77,125,93)(78,94,126)(79,127,95)(80,96,128)(85,137,115)(86,116,138)(87,139,113)(88,114,140)(105,136,132)(106,129,133)(107,134,130)(108,131,135), (1,62,29)(2,30,63)(3,64,31)(4,32,61)(5,25,50)(6,51,26)(7,27,52)(8,49,28)(9,100,117)(10,118,97)(11,98,119)(12,120,99)(13,67,20)(14,17,68)(15,65,18)(16,19,66)(21,72,73)(22,74,69)(23,70,75)(24,76,71)(33,56,110)(34,111,53)(35,54,112)(36,109,55)(37,124,102)(38,103,121)(39,122,104)(40,101,123)(41,82,57)(42,58,83)(43,84,59)(44,60,81)(45,141,92)(46,89,142)(47,143,90)(48,91,144)(77,108,116)(78,113,105)(79,106,114)(80,115,107)(85,134,96)(86,93,135)(87,136,94)(88,95,133)(125,131,138)(126,139,132)(127,129,140)(128,137,130), (1,26,15)(2,27,16)(3,28,13)(4,25,14)(5,68,61)(6,65,62)(7,66,63)(8,67,64)(9,141,123)(10,142,124)(11,143,121)(12,144,122)(17,32,50)(18,29,51)(19,30,52)(20,31,49)(21,36,82)(22,33,83)(23,34,84)(24,35,81)(37,97,89)(38,98,90)(39,99,91)(40,100,92)(41,73,55)(42,74,56)(43,75,53)(44,76,54)(45,101,117)(46,102,118)(47,103,119)(48,104,120)(57,72,109)(58,69,110)(59,70,111)(60,71,112)(77,135,138)(78,136,139)(79,133,140)(80,134,137)(85,128,107)(86,125,108)(87,126,105)(88,127,106)(93,131,116)(94,132,113)(95,129,114)(96,130,115), (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), (1,85,3,87)(2,88,4,86)(5,77,7,79)(6,80,8,78)(9,112,11,110)(10,111,12,109)(13,126,15,128)(14,125,16,127)(17,131,19,129)(18,130,20,132)(21,89,23,91)(22,92,24,90)(25,108,27,106)(26,107,28,105)(29,96,31,94)(30,95,32,93)(33,100,35,98)(34,99,36,97)(37,84,39,82)(38,83,40,81)(41,102,43,104)(42,101,44,103)(45,76,47,74)(46,75,48,73)(49,113,51,115)(50,116,52,114)(53,120,55,118)(54,119,56,117)(57,124,59,122)(58,123,60,121)(61,135,63,133)(62,134,64,136)(65,137,67,139)(66,140,68,138)(69,141,71,143)(70,144,72,142) );

G=PermutationGroup([[(1,83),(2,84),(3,81),(4,82),(5,73),(6,74),(7,75),(8,76),(9,130),(10,131),(11,132),(12,129),(13,35),(14,36),(15,33),(16,34),(17,109),(18,110),(19,111),(20,112),(21,25),(22,26),(23,27),(24,28),(29,58),(30,59),(31,60),(32,57),(37,86),(38,87),(39,88),(40,85),(41,61),(42,62),(43,63),(44,64),(45,80),(46,77),(47,78),(48,79),(49,71),(50,72),(51,69),(52,70),(53,66),(54,67),(55,68),(56,65),(89,108),(90,105),(91,106),(92,107),(93,124),(94,121),(95,122),(96,123),(97,125),(98,126),(99,127),(100,128),(101,134),(102,135),(103,136),(104,133),(113,143),(114,144),(115,141),(116,142),(117,137),(118,138),(119,139),(120,140)], [(1,65,51),(2,52,66),(3,67,49),(4,50,68),(5,14,32),(6,29,15),(7,16,30),(8,31,13),(9,92,101),(10,102,89),(11,90,103),(12,104,91),(17,61,25),(18,26,62),(19,63,27),(20,28,64),(21,109,41),(22,42,110),(23,111,43),(24,44,112),(33,74,58),(34,59,75),(35,76,60),(36,57,73),(37,142,118),(38,119,143),(39,144,120),(40,117,141),(45,123,100),(46,97,124),(47,121,98),(48,99,122),(53,84,70),(54,71,81),(55,82,72),(56,69,83),(77,125,93),(78,94,126),(79,127,95),(80,96,128),(85,137,115),(86,116,138),(87,139,113),(88,114,140),(105,136,132),(106,129,133),(107,134,130),(108,131,135)], [(1,62,29),(2,30,63),(3,64,31),(4,32,61),(5,25,50),(6,51,26),(7,27,52),(8,49,28),(9,100,117),(10,118,97),(11,98,119),(12,120,99),(13,67,20),(14,17,68),(15,65,18),(16,19,66),(21,72,73),(22,74,69),(23,70,75),(24,76,71),(33,56,110),(34,111,53),(35,54,112),(36,109,55),(37,124,102),(38,103,121),(39,122,104),(40,101,123),(41,82,57),(42,58,83),(43,84,59),(44,60,81),(45,141,92),(46,89,142),(47,143,90),(48,91,144),(77,108,116),(78,113,105),(79,106,114),(80,115,107),(85,134,96),(86,93,135),(87,136,94),(88,95,133),(125,131,138),(126,139,132),(127,129,140),(128,137,130)], [(1,26,15),(2,27,16),(3,28,13),(4,25,14),(5,68,61),(6,65,62),(7,66,63),(8,67,64),(9,141,123),(10,142,124),(11,143,121),(12,144,122),(17,32,50),(18,29,51),(19,30,52),(20,31,49),(21,36,82),(22,33,83),(23,34,84),(24,35,81),(37,97,89),(38,98,90),(39,99,91),(40,100,92),(41,73,55),(42,74,56),(43,75,53),(44,76,54),(45,101,117),(46,102,118),(47,103,119),(48,104,120),(57,72,109),(58,69,110),(59,70,111),(60,71,112),(77,135,138),(78,136,139),(79,133,140),(80,134,137),(85,128,107),(86,125,108),(87,126,105),(88,127,106),(93,131,116),(94,132,113),(95,129,114),(96,130,115)], [(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)], [(1,85,3,87),(2,88,4,86),(5,77,7,79),(6,80,8,78),(9,112,11,110),(10,111,12,109),(13,126,15,128),(14,125,16,127),(17,131,19,129),(18,130,20,132),(21,89,23,91),(22,92,24,90),(25,108,27,106),(26,107,28,105),(29,96,31,94),(30,95,32,93),(33,100,35,98),(34,99,36,97),(37,84,39,82),(38,83,40,81),(41,102,43,104),(42,101,44,103),(45,76,47,74),(46,75,48,73),(49,113,51,115),(50,116,52,114),(53,120,55,118),(54,119,56,117),(57,124,59,122),(58,123,60,121),(61,135,63,133),(62,134,64,136),(65,137,67,139),(66,140,68,138),(69,141,71,143),(70,144,72,142)]])

66 conjugacy classes

 class 1 2A 2B 2C 3A ··· 3E 3F 3G 3H 3I 4A 4B 4C 4D 4E 4F 6A ··· 6O 6P ··· 6AA 12A ··· 12P 12Q 12R 12S 12T order 1 2 2 2 3 ··· 3 3 3 3 3 4 4 4 4 4 4 6 ··· 6 6 ··· 6 12 ··· 12 12 12 12 12 size 1 1 1 1 2 ··· 2 4 4 4 4 6 6 18 18 54 54 2 ··· 2 4 ··· 4 6 ··· 6 18 18 18 18

66 irreducible representations

 dim 1 1 1 1 1 2 2 2 2 2 2 2 4 4 4 type + + + + + + + - + + + - + - + image C1 C2 C2 C2 C2 S3 S3 Q8 D6 D6 D6 Dic6 S32 C32⋊2Q8 C2×S32 kernel C2×C33⋊4Q8 C33⋊4Q8 Dic3×C3×C6 C6×C3⋊Dic3 C2×C33⋊5C4 C6×Dic3 C2×C3⋊Dic3 C32×C6 C3×Dic3 C3⋊Dic3 C62 C3×C6 C2×C6 C6 C6 # reps 1 4 1 1 1 4 1 2 8 2 5 20 4 8 4

Matrix representation of C2×C334Q8 in GL8(𝔽13)

 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 12 0 0 0 0 0 0 0 0 12 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 12 12 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 1 12 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 12 12 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 12 0 0 0 0 0 0 1 12
,
 4 11 0 0 0 0 0 0 2 9 0 0 0 0 0 0 0 0 3 10 0 0 0 0 0 0 7 10 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1
,
 5 0 0 0 0 0 0 0 7 8 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0

G:=sub<GL(8,GF(13))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,1,12,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,1,12,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,12,12],[4,2,0,0,0,0,0,0,11,9,0,0,0,0,0,0,0,0,3,7,0,0,0,0,0,0,10,10,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[5,7,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0] >;

C2×C334Q8 in GAP, Magma, Sage, TeX

C_2\times C_3^3\rtimes_4Q_8
% in TeX

G:=Group("C2xC3^3:4Q8");
// GroupNames label

G:=SmallGroup(432,683);
// by ID

G=gap.SmallGroup(432,683);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,56,141,64,571,2028,14118]);
// Polycyclic

G:=Group<a,b,c,d,e,f|a^2=b^3=c^3=d^3=e^4=1,f^2=e^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,b*c=c*b,b*d=d*b,e*b*e^-1=b^-1,b*f=f*b,c*d=d*c,e*c*e^-1=c^-1,c*f=f*c,d*e=e*d,f*d*f^-1=d^-1,f*e*f^-1=e^-1>;
// generators/relations

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