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G = C14×D11order 308 = 22·7·11

Direct product of C14 and D11

direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary

Aliases: C14×D11, C22⋊C14, C1542C2, C773C22, C11⋊(C2×C14), SmallGroup(308,6)

Series: Derived Chief Lower central Upper central

C1C11 — C14×D11
C1C11C77C7×D11 — C14×D11
C11 — C14×D11
C1C14

Generators and relations for C14×D11
 G = < a,b,c | a14=b11=c2=1, ab=ba, ac=ca, cbc=b-1 >

11C2
11C2
11C22
11C14
11C14
11C2×C14

Smallest permutation representation of C14×D11
On 154 points
Generators in S154
(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)(141 142 143 144 145 146 147 148 149 150 151 152 153 154)
(1 113 138 148 37 82 47 88 26 63 100)(2 114 139 149 38 83 48 89 27 64 101)(3 115 140 150 39 84 49 90 28 65 102)(4 116 127 151 40 71 50 91 15 66 103)(5 117 128 152 41 72 51 92 16 67 104)(6 118 129 153 42 73 52 93 17 68 105)(7 119 130 154 29 74 53 94 18 69 106)(8 120 131 141 30 75 54 95 19 70 107)(9 121 132 142 31 76 55 96 20 57 108)(10 122 133 143 32 77 56 97 21 58 109)(11 123 134 144 33 78 43 98 22 59 110)(12 124 135 145 34 79 44 85 23 60 111)(13 125 136 146 35 80 45 86 24 61 112)(14 126 137 147 36 81 46 87 25 62 99)
(1 107)(2 108)(3 109)(4 110)(5 111)(6 112)(7 99)(8 100)(9 101)(10 102)(11 103)(12 104)(13 105)(14 106)(15 134)(16 135)(17 136)(18 137)(19 138)(20 139)(21 140)(22 127)(23 128)(24 129)(25 130)(26 131)(27 132)(28 133)(29 46)(30 47)(31 48)(32 49)(33 50)(34 51)(35 52)(36 53)(37 54)(38 55)(39 56)(40 43)(41 44)(42 45)(57 114)(58 115)(59 116)(60 117)(61 118)(62 119)(63 120)(64 121)(65 122)(66 123)(67 124)(68 125)(69 126)(70 113)(71 78)(72 79)(73 80)(74 81)(75 82)(76 83)(77 84)(85 152)(86 153)(87 154)(88 141)(89 142)(90 143)(91 144)(92 145)(93 146)(94 147)(95 148)(96 149)(97 150)(98 151)

G:=sub<Sym(154)| (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)(141,142,143,144,145,146,147,148,149,150,151,152,153,154), (1,113,138,148,37,82,47,88,26,63,100)(2,114,139,149,38,83,48,89,27,64,101)(3,115,140,150,39,84,49,90,28,65,102)(4,116,127,151,40,71,50,91,15,66,103)(5,117,128,152,41,72,51,92,16,67,104)(6,118,129,153,42,73,52,93,17,68,105)(7,119,130,154,29,74,53,94,18,69,106)(8,120,131,141,30,75,54,95,19,70,107)(9,121,132,142,31,76,55,96,20,57,108)(10,122,133,143,32,77,56,97,21,58,109)(11,123,134,144,33,78,43,98,22,59,110)(12,124,135,145,34,79,44,85,23,60,111)(13,125,136,146,35,80,45,86,24,61,112)(14,126,137,147,36,81,46,87,25,62,99), (1,107)(2,108)(3,109)(4,110)(5,111)(6,112)(7,99)(8,100)(9,101)(10,102)(11,103)(12,104)(13,105)(14,106)(15,134)(16,135)(17,136)(18,137)(19,138)(20,139)(21,140)(22,127)(23,128)(24,129)(25,130)(26,131)(27,132)(28,133)(29,46)(30,47)(31,48)(32,49)(33,50)(34,51)(35,52)(36,53)(37,54)(38,55)(39,56)(40,43)(41,44)(42,45)(57,114)(58,115)(59,116)(60,117)(61,118)(62,119)(63,120)(64,121)(65,122)(66,123)(67,124)(68,125)(69,126)(70,113)(71,78)(72,79)(73,80)(74,81)(75,82)(76,83)(77,84)(85,152)(86,153)(87,154)(88,141)(89,142)(90,143)(91,144)(92,145)(93,146)(94,147)(95,148)(96,149)(97,150)(98,151)>;

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)(141,142,143,144,145,146,147,148,149,150,151,152,153,154), (1,113,138,148,37,82,47,88,26,63,100)(2,114,139,149,38,83,48,89,27,64,101)(3,115,140,150,39,84,49,90,28,65,102)(4,116,127,151,40,71,50,91,15,66,103)(5,117,128,152,41,72,51,92,16,67,104)(6,118,129,153,42,73,52,93,17,68,105)(7,119,130,154,29,74,53,94,18,69,106)(8,120,131,141,30,75,54,95,19,70,107)(9,121,132,142,31,76,55,96,20,57,108)(10,122,133,143,32,77,56,97,21,58,109)(11,123,134,144,33,78,43,98,22,59,110)(12,124,135,145,34,79,44,85,23,60,111)(13,125,136,146,35,80,45,86,24,61,112)(14,126,137,147,36,81,46,87,25,62,99), (1,107)(2,108)(3,109)(4,110)(5,111)(6,112)(7,99)(8,100)(9,101)(10,102)(11,103)(12,104)(13,105)(14,106)(15,134)(16,135)(17,136)(18,137)(19,138)(20,139)(21,140)(22,127)(23,128)(24,129)(25,130)(26,131)(27,132)(28,133)(29,46)(30,47)(31,48)(32,49)(33,50)(34,51)(35,52)(36,53)(37,54)(38,55)(39,56)(40,43)(41,44)(42,45)(57,114)(58,115)(59,116)(60,117)(61,118)(62,119)(63,120)(64,121)(65,122)(66,123)(67,124)(68,125)(69,126)(70,113)(71,78)(72,79)(73,80)(74,81)(75,82)(76,83)(77,84)(85,152)(86,153)(87,154)(88,141)(89,142)(90,143)(91,144)(92,145)(93,146)(94,147)(95,148)(96,149)(97,150)(98,151) );

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),(141,142,143,144,145,146,147,148,149,150,151,152,153,154)], [(1,113,138,148,37,82,47,88,26,63,100),(2,114,139,149,38,83,48,89,27,64,101),(3,115,140,150,39,84,49,90,28,65,102),(4,116,127,151,40,71,50,91,15,66,103),(5,117,128,152,41,72,51,92,16,67,104),(6,118,129,153,42,73,52,93,17,68,105),(7,119,130,154,29,74,53,94,18,69,106),(8,120,131,141,30,75,54,95,19,70,107),(9,121,132,142,31,76,55,96,20,57,108),(10,122,133,143,32,77,56,97,21,58,109),(11,123,134,144,33,78,43,98,22,59,110),(12,124,135,145,34,79,44,85,23,60,111),(13,125,136,146,35,80,45,86,24,61,112),(14,126,137,147,36,81,46,87,25,62,99)], [(1,107),(2,108),(3,109),(4,110),(5,111),(6,112),(7,99),(8,100),(9,101),(10,102),(11,103),(12,104),(13,105),(14,106),(15,134),(16,135),(17,136),(18,137),(19,138),(20,139),(21,140),(22,127),(23,128),(24,129),(25,130),(26,131),(27,132),(28,133),(29,46),(30,47),(31,48),(32,49),(33,50),(34,51),(35,52),(36,53),(37,54),(38,55),(39,56),(40,43),(41,44),(42,45),(57,114),(58,115),(59,116),(60,117),(61,118),(62,119),(63,120),(64,121),(65,122),(66,123),(67,124),(68,125),(69,126),(70,113),(71,78),(72,79),(73,80),(74,81),(75,82),(76,83),(77,84),(85,152),(86,153),(87,154),(88,141),(89,142),(90,143),(91,144),(92,145),(93,146),(94,147),(95,148),(96,149),(97,150),(98,151)])

98 conjugacy classes

class 1 2A2B2C7A···7F11A···11E14A···14F14G···14R22A···22E77A···77AD154A···154AD
order12227···711···1114···1414···1422···2277···77154···154
size1111111···12···21···111···112···22···22···2

98 irreducible representations

dim1111112222
type+++++
imageC1C2C2C7C14C14D11D22C7×D11C14×D11
kernelC14×D11C7×D11C154D22D11C22C14C7C2C1
# reps1216126553030

Matrix representation of C14×D11 in GL2(𝔽43) generated by

390
039
,
429
285
,
3836
285
G:=sub<GL(2,GF(43))| [39,0,0,39],[42,28,9,5],[38,28,36,5] >;

C14×D11 in GAP, Magma, Sage, TeX

C_{14}\times D_{11}
% in TeX

G:=Group("C14xD11");
// GroupNames label

G:=SmallGroup(308,6);
// by ID

G=gap.SmallGroup(308,6);
# by ID

G:=PCGroup([4,-2,-2,-7,-11,4483]);
// Polycyclic

G:=Group<a,b,c|a^14=b^11=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C14×D11 in TeX

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