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G = Dic9.A4  order 432 = 24·33

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

non-abelian, soluble

Aliases: Dic9.A4, C9⋊(C4.A4), C6.1(S3×A4), C18.A4⋊1C2, C18.1(C2×A4), (Q8×C9).2C6, C2.2(D9⋊A4), Q8⋊3D9⋊2C3, 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 >

C1
C2
54C2
C3
12C3
3C4
9C4
27C22
C6
12C6
18S3
C9
4C32
8C9
Q8
27C2×C4
27D4
3Dic3
3C12
9D6
36C12
C18
4C3×C6
6D9
8C18
43- 1+2
9C4○D4
C3×Q8
3SL2(𝔽3)
9C4×S3
9D12
Dic9
3C36
3D18
12C3×Dic3
4C2×3- 1+2
3Q8⋊3S3
9C4.A4
C3×SL2(𝔽3)
Q8×C9
2Q8⋊C9
3C4×D9
3D36
4C9⋊C12
Q8⋊3D9
3Dic3.A4
C18.A4
Dic9.A4

Character table of Dic9.A4

 class 12A2B3A3B3C4A4B4C6A6B6C9A9B9C12A12B12C12D12E18A18B18C36A36B36C
 size 1154212126992121262424123636363662424121212
ρ111111111111111111111111111    trivial
ρ211-11111-1-11111111-1-1-1-1111111    linear of order 2
ρ311-11ζ3ζ321-1-11ζ32ζ31ζ3ζ321ζ6ζ65ζ65ζ61ζ32ζ3111    linear of order 6
ρ41111ζ3ζ321111ζ32ζ31ζ3ζ321ζ32ζ3ζ3ζ321ζ32ζ3111    linear of order 3
ρ511-11ζ32ζ31-1-11ζ3ζ321ζ32ζ31ζ65ζ6ζ6ζ651ζ3ζ32111    linear of order 6
ρ61111ζ32ζ31111ζ3ζ321ζ32ζ31ζ3ζ32ζ32ζ31ζ3ζ32111    linear of order 3
ρ7220222200222-1-1-120000-1-1-1-1-1-1    orthogonal lifted from S3
ρ82202-1-√-3-1+√-32002-1+√-3-1-√-3-1ζ6ζ6520000-1ζ65ζ6-1-1-1    complex lifted from C3×S3
ρ92202-1+√-3-1-√-32002-1-√-3-1+√-3-1ζ65ζ620000-1ζ6ζ65-1-1-1    complex lifted from C3×S3
ρ102-202-1-102i-2i-2112-1-10-ii-ii-211000    complex lifted from C4.A4
ρ112-202-1-10-2i2i-2112-1-10i-ii-i-211000    complex lifted from C4.A4
ρ122-202ζ65ζ602i-2i-2ζ32ζ32ζ65ζ60ζ43ζ32ζ4ζ3ζ43ζ3ζ4ζ32-2ζ32ζ3000    complex lifted from C4.A4
ρ132-202ζ6ζ6502i-2i-2ζ3ζ322ζ6ζ650ζ43ζ3ζ4ζ32ζ43ζ32ζ4ζ3-2ζ3ζ32000    complex lifted from C4.A4
ρ142-202ζ65ζ60-2i2i-2ζ32ζ32ζ65ζ60ζ4ζ32ζ43ζ3ζ4ζ3ζ43ζ32-2ζ32ζ3000    complex lifted from C4.A4
ρ152-202ζ6ζ650-2i2i-2ζ3ζ322ζ6ζ650ζ4ζ3ζ43ζ32ζ4ζ32ζ43ζ3-2ζ3ζ32000    complex lifted from C4.A4
ρ16331300-1-3-3300300-10000300-1-1-1    orthogonal lifted from C2×A4
ρ1733-1300-133300300-10000300-1-1-1    orthogonal lifted from A4
ρ184-404-2-2000-422-211000002-1-1000    orthogonal lifted from Dic3.A4, Schur index 2
ρ194-4041+√-31-√-3000-4-1+√-3-1-√-3-2ζ32ζ3000002ζ65ζ6000    complex lifted from Dic3.A4
ρ204-4041-√-31+√-3000-4-1-√-3-1+√-3-2ζ3ζ32000002ζ6ζ65000    complex lifted from Dic3.A4
ρ21660600-200600-300-20000-300111    orthogonal lifted from S3×A4
ρ22660-300600-300000-30000000000    orthogonal lifted from C9⋊C6
ρ23660-300-200-300000100000002ζ97+2ζ922ζ95+2ζ942ζ98+2ζ9    orthogonal lifted from D9⋊A4
ρ24660-300-200-300000100000002ζ98+2ζ92ζ97+2ζ922ζ95+2ζ94    orthogonal lifted from D9⋊A4
ρ25660-300-200-300000100000002ζ95+2ζ942ζ98+2ζ92ζ97+2ζ92    orthogonal lifted from D9⋊A4
ρ2612-120-60000060000000000000000    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)

13600000000
1000000000
00136000000
0010000000
00000003600
00000013600
00000000036
00000000136
00003610000
00003600000
,
03100000000
31000000000
00031000000
00310000000
000010320000
00005270000
000000003210
0000000055
000000321000
0000005500
,
0010000000
0001000000
36000000000
03600000000
00001203336432
0000012132536
00003211203336
00003633012132
0000365321120
00003243633012
,
270260000000
027026000000
260100000000
026010000000
0000120533321
0000012413633
000014120533
000033501241
0000333614120
0000132335012
,
1000000000
0100000000
260100000000
026010000000
0000100000
0000010000
00000003600
00000013600
00000000361
00000000360

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
 

Export

Subgroup lattice of Dic9.A4 in TeX
Character table of Dic9.A4 in TeX

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