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G = C16×D11order 352 = 25·11

Direct product of C16 and D11

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

Aliases: C16×D11, C1763C2, D22.2C8, C8.19D22, C88.19C22, Dic11.2C8, C11⋊C166C2, C111(C2×C16), C11⋊C8.3C4, C22.1(C2×C8), C2.1(C8×D11), C44.21(C2×C4), (C4×D11).4C4, (C8×D11).3C2, C4.16(C4×D11), SmallGroup(352,3)

Series: Derived Chief Lower central Upper central

C1C11 — C16×D11
C1C11C22C44C88C8×D11 — C16×D11
C11 — C16×D11
C1C16

Generators and relations for C16×D11
 G = < a,b,c | a16=b11=c2=1, ab=ba, ac=ca, cbc=b-1 >

11C2
11C2
11C22
11C4
11C2×C4
11C8
11C2×C8
11C16
11C2×C16

Smallest permutation representation of C16×D11
On 176 points
Generators in S176
(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)(145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160)(161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176)
(1 103 79 39 60 125 26 139 157 166 96)(2 104 80 40 61 126 27 140 158 167 81)(3 105 65 41 62 127 28 141 159 168 82)(4 106 66 42 63 128 29 142 160 169 83)(5 107 67 43 64 113 30 143 145 170 84)(6 108 68 44 49 114 31 144 146 171 85)(7 109 69 45 50 115 32 129 147 172 86)(8 110 70 46 51 116 17 130 148 173 87)(9 111 71 47 52 117 18 131 149 174 88)(10 112 72 48 53 118 19 132 150 175 89)(11 97 73 33 54 119 20 133 151 176 90)(12 98 74 34 55 120 21 134 152 161 91)(13 99 75 35 56 121 22 135 153 162 92)(14 100 76 36 57 122 23 136 154 163 93)(15 101 77 37 58 123 24 137 155 164 94)(16 102 78 38 59 124 25 138 156 165 95)
(1 88)(2 89)(3 90)(4 91)(5 92)(6 93)(7 94)(8 95)(9 96)(10 81)(11 82)(12 83)(13 84)(14 85)(15 86)(16 87)(17 59)(18 60)(19 61)(20 62)(21 63)(22 64)(23 49)(24 50)(25 51)(26 52)(27 53)(28 54)(29 55)(30 56)(31 57)(32 58)(33 141)(34 142)(35 143)(36 144)(37 129)(38 130)(39 131)(40 132)(41 133)(42 134)(43 135)(44 136)(45 137)(46 138)(47 139)(48 140)(65 151)(66 152)(67 153)(68 154)(69 155)(70 156)(71 157)(72 158)(73 159)(74 160)(75 145)(76 146)(77 147)(78 148)(79 149)(80 150)(97 168)(98 169)(99 170)(100 171)(101 172)(102 173)(103 174)(104 175)(105 176)(106 161)(107 162)(108 163)(109 164)(110 165)(111 166)(112 167)(113 121)(114 122)(115 123)(116 124)(117 125)(118 126)(119 127)(120 128)

G:=sub<Sym(176)| (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)(145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176), (1,103,79,39,60,125,26,139,157,166,96)(2,104,80,40,61,126,27,140,158,167,81)(3,105,65,41,62,127,28,141,159,168,82)(4,106,66,42,63,128,29,142,160,169,83)(5,107,67,43,64,113,30,143,145,170,84)(6,108,68,44,49,114,31,144,146,171,85)(7,109,69,45,50,115,32,129,147,172,86)(8,110,70,46,51,116,17,130,148,173,87)(9,111,71,47,52,117,18,131,149,174,88)(10,112,72,48,53,118,19,132,150,175,89)(11,97,73,33,54,119,20,133,151,176,90)(12,98,74,34,55,120,21,134,152,161,91)(13,99,75,35,56,121,22,135,153,162,92)(14,100,76,36,57,122,23,136,154,163,93)(15,101,77,37,58,123,24,137,155,164,94)(16,102,78,38,59,124,25,138,156,165,95), (1,88)(2,89)(3,90)(4,91)(5,92)(6,93)(7,94)(8,95)(9,96)(10,81)(11,82)(12,83)(13,84)(14,85)(15,86)(16,87)(17,59)(18,60)(19,61)(20,62)(21,63)(22,64)(23,49)(24,50)(25,51)(26,52)(27,53)(28,54)(29,55)(30,56)(31,57)(32,58)(33,141)(34,142)(35,143)(36,144)(37,129)(38,130)(39,131)(40,132)(41,133)(42,134)(43,135)(44,136)(45,137)(46,138)(47,139)(48,140)(65,151)(66,152)(67,153)(68,154)(69,155)(70,156)(71,157)(72,158)(73,159)(74,160)(75,145)(76,146)(77,147)(78,148)(79,149)(80,150)(97,168)(98,169)(99,170)(100,171)(101,172)(102,173)(103,174)(104,175)(105,176)(106,161)(107,162)(108,163)(109,164)(110,165)(111,166)(112,167)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)>;

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)(145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176), (1,103,79,39,60,125,26,139,157,166,96)(2,104,80,40,61,126,27,140,158,167,81)(3,105,65,41,62,127,28,141,159,168,82)(4,106,66,42,63,128,29,142,160,169,83)(5,107,67,43,64,113,30,143,145,170,84)(6,108,68,44,49,114,31,144,146,171,85)(7,109,69,45,50,115,32,129,147,172,86)(8,110,70,46,51,116,17,130,148,173,87)(9,111,71,47,52,117,18,131,149,174,88)(10,112,72,48,53,118,19,132,150,175,89)(11,97,73,33,54,119,20,133,151,176,90)(12,98,74,34,55,120,21,134,152,161,91)(13,99,75,35,56,121,22,135,153,162,92)(14,100,76,36,57,122,23,136,154,163,93)(15,101,77,37,58,123,24,137,155,164,94)(16,102,78,38,59,124,25,138,156,165,95), (1,88)(2,89)(3,90)(4,91)(5,92)(6,93)(7,94)(8,95)(9,96)(10,81)(11,82)(12,83)(13,84)(14,85)(15,86)(16,87)(17,59)(18,60)(19,61)(20,62)(21,63)(22,64)(23,49)(24,50)(25,51)(26,52)(27,53)(28,54)(29,55)(30,56)(31,57)(32,58)(33,141)(34,142)(35,143)(36,144)(37,129)(38,130)(39,131)(40,132)(41,133)(42,134)(43,135)(44,136)(45,137)(46,138)(47,139)(48,140)(65,151)(66,152)(67,153)(68,154)(69,155)(70,156)(71,157)(72,158)(73,159)(74,160)(75,145)(76,146)(77,147)(78,148)(79,149)(80,150)(97,168)(98,169)(99,170)(100,171)(101,172)(102,173)(103,174)(104,175)(105,176)(106,161)(107,162)(108,163)(109,164)(110,165)(111,166)(112,167)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128) );

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),(145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160),(161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176)], [(1,103,79,39,60,125,26,139,157,166,96),(2,104,80,40,61,126,27,140,158,167,81),(3,105,65,41,62,127,28,141,159,168,82),(4,106,66,42,63,128,29,142,160,169,83),(5,107,67,43,64,113,30,143,145,170,84),(6,108,68,44,49,114,31,144,146,171,85),(7,109,69,45,50,115,32,129,147,172,86),(8,110,70,46,51,116,17,130,148,173,87),(9,111,71,47,52,117,18,131,149,174,88),(10,112,72,48,53,118,19,132,150,175,89),(11,97,73,33,54,119,20,133,151,176,90),(12,98,74,34,55,120,21,134,152,161,91),(13,99,75,35,56,121,22,135,153,162,92),(14,100,76,36,57,122,23,136,154,163,93),(15,101,77,37,58,123,24,137,155,164,94),(16,102,78,38,59,124,25,138,156,165,95)], [(1,88),(2,89),(3,90),(4,91),(5,92),(6,93),(7,94),(8,95),(9,96),(10,81),(11,82),(12,83),(13,84),(14,85),(15,86),(16,87),(17,59),(18,60),(19,61),(20,62),(21,63),(22,64),(23,49),(24,50),(25,51),(26,52),(27,53),(28,54),(29,55),(30,56),(31,57),(32,58),(33,141),(34,142),(35,143),(36,144),(37,129),(38,130),(39,131),(40,132),(41,133),(42,134),(43,135),(44,136),(45,137),(46,138),(47,139),(48,140),(65,151),(66,152),(67,153),(68,154),(69,155),(70,156),(71,157),(72,158),(73,159),(74,160),(75,145),(76,146),(77,147),(78,148),(79,149),(80,150),(97,168),(98,169),(99,170),(100,171),(101,172),(102,173),(103,174),(104,175),(105,176),(106,161),(107,162),(108,163),(109,164),(110,165),(111,166),(112,167),(113,121),(114,122),(115,123),(116,124),(117,125),(118,126),(119,127),(120,128)])

112 conjugacy classes

class 1 2A2B2C4A4B4C4D8A8B8C8D8E8F8G8H11A···11E16A···16H16I···16P22A···22E44A···44J88A···88T176A···176AN
order122244448888888811···1116···1616···1622···2244···4488···88176···176
size1111111111111111111111112···21···111···112···22···22···22···2

112 irreducible representations

dim11111111122222
type++++++
imageC1C2C2C2C4C4C8C8C16D11D22C4×D11C8×D11C16×D11
kernelC16×D11C11⋊C16C176C8×D11C11⋊C8C4×D11Dic11D22D11C16C8C4C2C1
# reps111122441655102040

Matrix representation of C16×D11 in GL2(𝔽353) generated by

1000
0100
,
951
3520
,
0352
3520
G:=sub<GL(2,GF(353))| [100,0,0,100],[95,352,1,0],[0,352,352,0] >;

C16×D11 in GAP, Magma, Sage, TeX

C_{16}\times D_{11}
% in TeX

G:=Group("C16xD11");
// GroupNames label

G:=SmallGroup(352,3);
// by ID

G=gap.SmallGroup(352,3);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-2,-11,31,50,69,11525]);
// Polycyclic

G:=Group<a,b,c|a^16=b^11=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C16×D11 in TeX

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