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## G = Dic9.A4order 432 = 24·33

### The non-split extension by Dic9 of A4 acting via A4/C22=C3

Aliases: Dic9.A4, C9⋊(C4.A4), C6.1(S3×A4), C18.A41C2, C18.1(C2×A4), (Q8×C9).2C6, C2.2(D9⋊A4), Q83D92C3, Q8.2(C9⋊C6), C3.1(Dic3.A4), (C3×SL2(𝔽3)).1S3, (C3×Q8).11(C3×S3), SmallGroup(432,261)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2 — Q8×C9 — Dic9.A4
 Chief series C1 — C3 — C6 — C18 — Q8×C9 — C18.A4 — Dic9.A4
 Lower central Q8×C9 — Dic9.A4
 Upper central C1 — C2

Generators and relations for Dic9.A4
G = < a,b,c,d,e | a18=e3=1, b2=c2=d2=a9, bab-1=a-1, ac=ca, ad=da, eae-1=a13, bc=cb, bd=db, be=eb, dcd-1=a9c, ece-1=a9cd, ede-1=c >

Character table of Dic9.A4

 class 1 2A 2B 3A 3B 3C 4A 4B 4C 6A 6B 6C 9A 9B 9C 12A 12B 12C 12D 12E 18A 18B 18C 36A 36B 36C size 1 1 54 2 12 12 6 9 9 2 12 12 6 24 24 12 36 36 36 36 6 24 24 12 12 12 ρ1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 trivial ρ2 1 1 -1 1 1 1 1 -1 -1 1 1 1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 1 1 linear of order 2 ρ3 1 1 -1 1 ζ3 ζ32 1 -1 -1 1 ζ32 ζ3 1 ζ3 ζ32 1 ζ6 ζ65 ζ65 ζ6 1 ζ32 ζ3 1 1 1 linear of order 6 ρ4 1 1 1 1 ζ3 ζ32 1 1 1 1 ζ32 ζ3 1 ζ3 ζ32 1 ζ32 ζ3 ζ3 ζ32 1 ζ32 ζ3 1 1 1 linear of order 3 ρ5 1 1 -1 1 ζ32 ζ3 1 -1 -1 1 ζ3 ζ32 1 ζ32 ζ3 1 ζ65 ζ6 ζ6 ζ65 1 ζ3 ζ32 1 1 1 linear of order 6 ρ6 1 1 1 1 ζ32 ζ3 1 1 1 1 ζ3 ζ32 1 ζ32 ζ3 1 ζ3 ζ32 ζ32 ζ3 1 ζ3 ζ32 1 1 1 linear of order 3 ρ7 2 2 0 2 2 2 2 0 0 2 2 2 -1 -1 -1 2 0 0 0 0 -1 -1 -1 -1 -1 -1 orthogonal lifted from S3 ρ8 2 2 0 2 -1-√-3 -1+√-3 2 0 0 2 -1+√-3 -1-√-3 -1 ζ6 ζ65 2 0 0 0 0 -1 ζ65 ζ6 -1 -1 -1 complex lifted from C3×S3 ρ9 2 2 0 2 -1+√-3 -1-√-3 2 0 0 2 -1-√-3 -1+√-3 -1 ζ65 ζ6 2 0 0 0 0 -1 ζ6 ζ65 -1 -1 -1 complex lifted from C3×S3 ρ10 2 -2 0 2 -1 -1 0 2i -2i -2 1 1 2 -1 -1 0 -i i -i i -2 1 1 0 0 0 complex lifted from C4.A4 ρ11 2 -2 0 2 -1 -1 0 -2i 2i -2 1 1 2 -1 -1 0 i -i i -i -2 1 1 0 0 0 complex lifted from C4.A4 ρ12 2 -2 0 2 ζ65 ζ6 0 2i -2i -2 ζ32 ζ3 2 ζ65 ζ6 0 ζ43ζ32 ζ4ζ3 ζ43ζ3 ζ4ζ32 -2 ζ32 ζ3 0 0 0 complex lifted from C4.A4 ρ13 2 -2 0 2 ζ6 ζ65 0 2i -2i -2 ζ3 ζ32 2 ζ6 ζ65 0 ζ43ζ3 ζ4ζ32 ζ43ζ32 ζ4ζ3 -2 ζ3 ζ32 0 0 0 complex lifted from C4.A4 ρ14 2 -2 0 2 ζ65 ζ6 0 -2i 2i -2 ζ32 ζ3 2 ζ65 ζ6 0 ζ4ζ32 ζ43ζ3 ζ4ζ3 ζ43ζ32 -2 ζ32 ζ3 0 0 0 complex lifted from C4.A4 ρ15 2 -2 0 2 ζ6 ζ65 0 -2i 2i -2 ζ3 ζ32 2 ζ6 ζ65 0 ζ4ζ3 ζ43ζ32 ζ4ζ32 ζ43ζ3 -2 ζ3 ζ32 0 0 0 complex lifted from C4.A4 ρ16 3 3 1 3 0 0 -1 -3 -3 3 0 0 3 0 0 -1 0 0 0 0 3 0 0 -1 -1 -1 orthogonal lifted from C2×A4 ρ17 3 3 -1 3 0 0 -1 3 3 3 0 0 3 0 0 -1 0 0 0 0 3 0 0 -1 -1 -1 orthogonal lifted from A4 ρ18 4 -4 0 4 -2 -2 0 0 0 -4 2 2 -2 1 1 0 0 0 0 0 2 -1 -1 0 0 0 orthogonal lifted from Dic3.A4, Schur index 2 ρ19 4 -4 0 4 1+√-3 1-√-3 0 0 0 -4 -1+√-3 -1-√-3 -2 ζ32 ζ3 0 0 0 0 0 2 ζ65 ζ6 0 0 0 complex lifted from Dic3.A4 ρ20 4 -4 0 4 1-√-3 1+√-3 0 0 0 -4 -1-√-3 -1+√-3 -2 ζ3 ζ32 0 0 0 0 0 2 ζ6 ζ65 0 0 0 complex lifted from Dic3.A4 ρ21 6 6 0 6 0 0 -2 0 0 6 0 0 -3 0 0 -2 0 0 0 0 -3 0 0 1 1 1 orthogonal lifted from S3×A4 ρ22 6 6 0 -3 0 0 6 0 0 -3 0 0 0 0 0 -3 0 0 0 0 0 0 0 0 0 0 orthogonal lifted from C9⋊C6 ρ23 6 6 0 -3 0 0 -2 0 0 -3 0 0 0 0 0 1 0 0 0 0 0 0 0 2ζ97+2ζ92 2ζ95+2ζ94 2ζ98+2ζ9 orthogonal lifted from D9⋊A4 ρ24 6 6 0 -3 0 0 -2 0 0 -3 0 0 0 0 0 1 0 0 0 0 0 0 0 2ζ98+2ζ9 2ζ97+2ζ92 2ζ95+2ζ94 orthogonal lifted from D9⋊A4 ρ25 6 6 0 -3 0 0 -2 0 0 -3 0 0 0 0 0 1 0 0 0 0 0 0 0 2ζ95+2ζ94 2ζ98+2ζ9 2ζ97+2ζ92 orthogonal lifted from D9⋊A4 ρ26 12 -12 0 -6 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 orthogonal faithful, Schur index 2

Smallest permutation representation of Dic9.A4
On 144 points
Generators in S144
(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 74 10 83)(2 73 11 82)(3 90 12 81)(4 89 13 80)(5 88 14 79)(6 87 15 78)(7 86 16 77)(8 85 17 76)(9 84 18 75)(19 100 28 91)(20 99 29 108)(21 98 30 107)(22 97 31 106)(23 96 32 105)(24 95 33 104)(25 94 34 103)(26 93 35 102)(27 92 36 101)(37 126 46 117)(38 125 47 116)(39 124 48 115)(40 123 49 114)(41 122 50 113)(42 121 51 112)(43 120 52 111)(44 119 53 110)(45 118 54 109)(55 142 64 133)(56 141 65 132)(57 140 66 131)(58 139 67 130)(59 138 68 129)(60 137 69 128)(61 136 70 127)(62 135 71 144)(63 134 72 143)
(1 25 10 34)(2 26 11 35)(3 27 12 36)(4 28 13 19)(5 29 14 20)(6 30 15 21)(7 31 16 22)(8 32 17 23)(9 33 18 24)(37 60 46 69)(38 61 47 70)(39 62 48 71)(40 63 49 72)(41 64 50 55)(42 65 51 56)(43 66 52 57)(44 67 53 58)(45 68 54 59)(73 93 82 102)(74 94 83 103)(75 95 84 104)(76 96 85 105)(77 97 86 106)(78 98 87 107)(79 99 88 108)(80 100 89 91)(81 101 90 92)(109 138 118 129)(110 139 119 130)(111 140 120 131)(112 141 121 132)(113 142 122 133)(114 143 123 134)(115 144 124 135)(116 127 125 136)(117 128 126 137)
(1 39 10 48)(2 40 11 49)(3 41 12 50)(4 42 13 51)(5 43 14 52)(6 44 15 53)(7 45 16 54)(8 46 17 37)(9 47 18 38)(19 65 28 56)(20 66 29 57)(21 67 30 58)(22 68 31 59)(23 69 32 60)(24 70 33 61)(25 71 34 62)(26 72 35 63)(27 55 36 64)(73 123 82 114)(74 124 83 115)(75 125 84 116)(76 126 85 117)(77 109 86 118)(78 110 87 119)(79 111 88 120)(80 112 89 121)(81 113 90 122)(91 141 100 132)(92 142 101 133)(93 143 102 134)(94 144 103 135)(95 127 104 136)(96 128 105 137)(97 129 106 138)(98 130 107 139)(99 131 108 140)
(2 8 14)(3 15 9)(5 11 17)(6 18 12)(19 51 56)(20 40 69)(21 47 64)(22 54 59)(23 43 72)(24 50 67)(25 39 62)(26 46 57)(27 53 70)(28 42 65)(29 49 60)(30 38 55)(31 45 68)(32 52 63)(33 41 58)(34 48 71)(35 37 66)(36 44 61)(73 85 79)(75 81 87)(76 88 82)(78 84 90)(91 121 132)(92 110 127)(93 117 140)(94 124 135)(95 113 130)(96 120 143)(97 109 138)(98 116 133)(99 123 128)(100 112 141)(101 119 136)(102 126 131)(103 115 144)(104 122 139)(105 111 134)(106 118 129)(107 125 142)(108 114 137)

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

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

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

Matrix representation of Dic9.A4 in GL10(𝔽37)

 1 36 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 36 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 36 0 0 0 0 0 0 0 0 1 36 0 0 0 0 0 0 0 0 0 0 0 36 0 0 0 0 0 0 0 0 1 36 0 0 0 0 36 1 0 0 0 0 0 0 0 0 36 0 0 0 0 0
,
 0 31 0 0 0 0 0 0 0 0 31 0 0 0 0 0 0 0 0 0 0 0 0 31 0 0 0 0 0 0 0 0 31 0 0 0 0 0 0 0 0 0 0 0 10 32 0 0 0 0 0 0 0 0 5 27 0 0 0 0 0 0 0 0 0 0 0 0 32 10 0 0 0 0 0 0 0 0 5 5 0 0 0 0 0 0 32 10 0 0 0 0 0 0 0 0 5 5 0 0
,
 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 36 0 0 0 0 0 0 0 0 0 0 36 0 0 0 0 0 0 0 0 0 0 0 0 12 0 33 36 4 32 0 0 0 0 0 12 1 32 5 36 0 0 0 0 32 1 12 0 33 36 0 0 0 0 36 33 0 12 1 32 0 0 0 0 36 5 32 1 12 0 0 0 0 0 32 4 36 33 0 12
,
 27 0 26 0 0 0 0 0 0 0 0 27 0 26 0 0 0 0 0 0 26 0 10 0 0 0 0 0 0 0 0 26 0 10 0 0 0 0 0 0 0 0 0 0 12 0 5 33 32 1 0 0 0 0 0 12 4 1 36 33 0 0 0 0 1 4 12 0 5 33 0 0 0 0 33 5 0 12 4 1 0 0 0 0 33 36 1 4 12 0 0 0 0 0 1 32 33 5 0 12
,
 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 26 0 10 0 0 0 0 0 0 0 0 26 0 10 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 36 0 0 0 0 0 0 0 0 1 36 0 0 0 0 0 0 0 0 0 0 36 1 0 0 0 0 0 0 0 0 36 0

G:=sub<GL(10,GF(37))| [1,1,0,0,0,0,0,0,0,0,36,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,36,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,36,36,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,36,36,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,36,36,0,0],[0,31,0,0,0,0,0,0,0,0,31,0,0,0,0,0,0,0,0,0,0,0,0,31,0,0,0,0,0,0,0,0,31,0,0,0,0,0,0,0,0,0,0,0,10,5,0,0,0,0,0,0,0,0,32,27,0,0,0,0,0,0,0,0,0,0,0,0,32,5,0,0,0,0,0,0,0,0,10,5,0,0,0,0,0,0,32,5,0,0,0,0,0,0,0,0,10,5,0,0],[0,0,36,0,0,0,0,0,0,0,0,0,0,36,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,12,0,32,36,36,32,0,0,0,0,0,12,1,33,5,4,0,0,0,0,33,1,12,0,32,36,0,0,0,0,36,32,0,12,1,33,0,0,0,0,4,5,33,1,12,0,0,0,0,0,32,36,36,32,0,12],[27,0,26,0,0,0,0,0,0,0,0,27,0,26,0,0,0,0,0,0,26,0,10,0,0,0,0,0,0,0,0,26,0,10,0,0,0,0,0,0,0,0,0,0,12,0,1,33,33,1,0,0,0,0,0,12,4,5,36,32,0,0,0,0,5,4,12,0,1,33,0,0,0,0,33,1,0,12,4,5,0,0,0,0,32,36,5,4,12,0,0,0,0,0,1,33,33,1,0,12],[1,0,26,0,0,0,0,0,0,0,0,1,0,26,0,0,0,0,0,0,0,0,10,0,0,0,0,0,0,0,0,0,0,10,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,36,36,0,0,0,0,0,0,0,0,0,0,36,36,0,0,0,0,0,0,0,0,1,0] >;

Dic9.A4 in GAP, Magma, Sage, TeX

{\rm Dic}_9.A_4
% in TeX

G:=Group("Dic9.A4");
// GroupNames label

G:=SmallGroup(432,261);
// by ID

G=gap.SmallGroup(432,261);
# by ID

G:=PCGroup([7,-2,-3,-2,2,-3,-2,-3,504,198,268,94,409,192,6724,2951,452,14118]);
// Polycyclic

G:=Group<a,b,c,d,e|a^18=e^3=1,b^2=c^2=d^2=a^9,b*a*b^-1=a^-1,a*c=c*a,a*d=d*a,e*a*e^-1=a^13,b*c=c*b,b*d=d*b,b*e=e*b,d*c*d^-1=a^9*c,e*c*e^-1=a^9*c*d,e*d*e^-1=c>;
// generators/relations

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