Copied to
clipboard

## G = C22×C32⋊C12order 432 = 24·33

### Direct product of C22 and C32⋊C12

Series: Derived Chief Lower central Upper central

 Derived series C1 — C32 — C22×C32⋊C12
 Chief series C1 — C3 — C32 — C3×C6 — C2×He3 — C32⋊C12 — C2×C32⋊C12 — C22×C32⋊C12
 Lower central C32 — C22×C32⋊C12
 Upper central C1 — C23

Generators and relations for C22×C32⋊C12
G = < a,b,c,d,e | a2=b2=c3=d3=e12=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ece-1=c-1d, ede-1=d-1 >

Subgroups: 689 in 221 conjugacy classes, 102 normal (17 characteristic)
C1, C2, C2 [×6], C3, C3 [×3], C4 [×4], C22 [×7], C6, C6 [×6], C6 [×21], C2×C4 [×6], C23, C32 [×2], C32, Dic3 [×8], C12 [×4], C2×C6 [×7], C2×C6 [×21], C22×C4, C3×C6 [×2], C3×C6 [×12], C3×C6 [×7], C2×Dic3 [×12], C2×C12 [×6], C22×C6, C22×C6 [×3], He3, C3×Dic3 [×4], C3⋊Dic3 [×4], C62 [×14], C62 [×7], C22×Dic3 [×2], C22×C12, C2×He3, C2×He3 [×6], C6×Dic3 [×6], C2×C3⋊Dic3 [×6], C2×C62 [×2], C2×C62, C32⋊C12 [×4], C22×He3 [×7], Dic3×C2×C6, C22×C3⋊Dic3, C2×C32⋊C12 [×6], C23×He3, C22×C32⋊C12
Quotients: C1, C2 [×7], C3, C4 [×4], C22 [×7], S3, C6 [×7], C2×C4 [×6], C23, Dic3 [×4], C12 [×4], D6 [×3], C2×C6 [×7], C22×C4, C3×S3, C2×Dic3 [×6], C2×C12 [×6], C22×S3, C22×C6, C3×Dic3 [×4], S3×C6 [×3], C22×Dic3, C22×C12, C32⋊C6, C6×Dic3 [×6], S3×C2×C6, C32⋊C12 [×4], C2×C32⋊C6 [×3], Dic3×C2×C6, C2×C32⋊C12 [×6], C22×C32⋊C6, C22×C32⋊C12

Smallest permutation representation of C22×C32⋊C12
On 144 points
Generators in S144
(1 32)(2 29)(3 30)(4 31)(5 25)(6 26)(7 27)(8 28)(9 34)(10 35)(11 36)(12 33)(13 23)(14 24)(15 21)(16 22)(17 46)(18 47)(19 48)(20 45)(37 43)(38 44)(39 41)(40 42)(49 126)(50 127)(51 128)(52 129)(53 130)(54 131)(55 132)(56 121)(57 122)(58 123)(59 124)(60 125)(61 90)(62 91)(63 92)(64 93)(65 94)(66 95)(67 96)(68 85)(69 86)(70 87)(71 88)(72 89)(73 113)(74 114)(75 115)(76 116)(77 117)(78 118)(79 119)(80 120)(81 109)(82 110)(83 111)(84 112)(97 143)(98 144)(99 133)(100 134)(101 135)(102 136)(103 137)(104 138)(105 139)(106 140)(107 141)(108 142)
(1 48)(2 45)(3 46)(4 47)(5 37)(6 38)(7 39)(8 40)(9 14)(10 15)(11 16)(12 13)(17 30)(18 31)(19 32)(20 29)(21 35)(22 36)(23 33)(24 34)(25 43)(26 44)(27 41)(28 42)(49 138)(50 139)(51 140)(52 141)(53 142)(54 143)(55 144)(56 133)(57 134)(58 135)(59 136)(60 137)(61 117)(62 118)(63 119)(64 120)(65 109)(66 110)(67 111)(68 112)(69 113)(70 114)(71 115)(72 116)(73 86)(74 87)(75 88)(76 89)(77 90)(78 91)(79 92)(80 93)(81 94)(82 95)(83 96)(84 85)(97 131)(98 132)(99 121)(100 122)(101 123)(102 124)(103 125)(104 126)(105 127)(106 128)(107 129)(108 130)
(1 99 94)(2 91 108)(3 105 88)(4 85 102)(5 70 134)(6 143 67)(7 64 140)(8 137 61)(9 66 138)(10 135 63)(11 72 144)(12 141 69)(13 52 113)(14 110 49)(15 58 119)(16 116 55)(17 50 115)(18 112 59)(19 56 109)(20 118 53)(21 123 79)(22 76 132)(23 129 73)(24 82 126)(25 87 100)(26 97 96)(27 93 106)(28 103 90)(29 62 142)(30 139 71)(31 68 136)(32 133 65)(33 107 86)(34 95 104)(35 101 92)(36 89 98)(37 114 57)(38 54 111)(39 120 51)(40 60 117)(41 80 128)(42 125 77)(43 74 122)(44 131 83)(45 78 130)(46 127 75)(47 84 124)(48 121 81)
(1 28 33)(2 34 25)(3 26 35)(4 36 27)(5 29 9)(6 10 30)(7 31 11)(8 12 32)(13 19 40)(14 37 20)(15 17 38)(16 39 18)(21 46 44)(22 41 47)(23 48 42)(24 43 45)(49 57 53)(50 54 58)(51 59 55)(52 56 60)(61 69 65)(62 66 70)(63 71 67)(64 68 72)(73 81 77)(74 78 82)(75 83 79)(76 80 84)(85 89 93)(86 94 90)(87 91 95)(88 96 92)(97 101 105)(98 106 102)(99 103 107)(100 108 104)(109 117 113)(110 114 118)(111 119 115)(112 116 120)(121 125 129)(122 130 126)(123 127 131)(124 132 128)(133 137 141)(134 142 138)(135 139 143)(136 144 140)
(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)

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

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

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

80 conjugacy classes

 class 1 2A ··· 2G 3A 3B 3C 3D 3E 3F 4A ··· 4H 6A ··· 6G 6H ··· 6U 6V ··· 6AP 12A ··· 12P order 1 2 ··· 2 3 3 3 3 3 3 4 ··· 4 6 ··· 6 6 ··· 6 6 ··· 6 12 ··· 12 size 1 1 ··· 1 2 3 3 6 6 6 9 ··· 9 2 ··· 2 3 ··· 3 6 ··· 6 9 ··· 9

80 irreducible representations

 dim 1 1 1 1 1 1 1 1 2 2 2 2 2 2 6 6 6 type + + + + - + + - + image C1 C2 C2 C3 C4 C6 C6 C12 S3 Dic3 D6 C3×S3 C3×Dic3 S3×C6 C32⋊C6 C32⋊C12 C2×C32⋊C6 kernel C22×C32⋊C12 C2×C32⋊C12 C23×He3 C22×C3⋊Dic3 C22×He3 C2×C3⋊Dic3 C2×C62 C62 C2×C62 C62 C62 C22×C6 C2×C6 C2×C6 C23 C22 C22 # reps 1 6 1 2 8 12 2 16 1 4 3 2 8 6 1 4 3

Matrix representation of C22×C32⋊C12 in GL10(𝔽13)

 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 12 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 1 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 1
,
 12 0 0 0 0 0 0 0 0 0 0 12 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 1 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 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1
,
 0 12 0 0 0 0 0 0 0 0 1 12 0 0 0 0 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 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 1 12 0 0 0 0 0 12 0 0 0 0 0 0 0 0 1 12 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 1 12 0 0
,
 1 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 1 0 0 0 0 0 0 0 0 0 0 12 1 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 12 1 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 12 1 0 0 0 0 0 0 0 0 12 0
,
 8 5 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 6 6 0 0 0 0 0 0 0 0 0 0 8 5 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 5 8 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 8 0 0 0

G:=sub<GL(10,GF(13))| [1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1],[12,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,0,0,12,1,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,1,0,0,0,0,0,0,0,0,12,12,0,0,0,0],[1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,1,0],[8,0,0,0,0,0,0,0,0,0,5,5,0,0,0,0,0,0,0,0,0,0,7,6,0,0,0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,5,5,0,0,0,0,0,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,5,5,0,0,0,0,0,0,0,0,0,8,0,0] >;

C22×C32⋊C12 in GAP, Magma, Sage, TeX

C_2^2\times C_3^2\rtimes C_{12}
% in TeX

G:=Group("C2^2xC3^2:C12");
// GroupNames label

G:=SmallGroup(432,376);
// by ID

G=gap.SmallGroup(432,376);
# by ID

G:=PCGroup([7,-2,-2,-2,-3,-2,-3,-3,168,4037,1034,14118]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^2=c^3=d^3=e^12=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,e*c*e^-1=c^-1*d,e*d*e^-1=d^-1>;
// generators/relations

׿
×
𝔽