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G = C17×D11order 374 = 2·11·17

Direct product of C17 and D11

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

Aliases: C17×D11, C11⋊C34, C1873C2, SmallGroup(374,1)

Series: Derived Chief Lower central Upper central

C1C11 — C17×D11
C1C11C187 — C17×D11
C11 — C17×D11
C1C17

Generators and relations for C17×D11
 G = < a,b,c | a17=b11=c2=1, ab=ba, ac=ca, cbc=b-1 >

11C2
11C34

Smallest permutation representation of C17×D11
On 187 points
Generators in S187
(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)(171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187)
(1 181 98 121 77 164 25 111 67 150 49)(2 182 99 122 78 165 26 112 68 151 50)(3 183 100 123 79 166 27 113 52 152 51)(4 184 101 124 80 167 28 114 53 153 35)(5 185 102 125 81 168 29 115 54 137 36)(6 186 86 126 82 169 30 116 55 138 37)(7 187 87 127 83 170 31 117 56 139 38)(8 171 88 128 84 154 32 118 57 140 39)(9 172 89 129 85 155 33 119 58 141 40)(10 173 90 130 69 156 34 103 59 142 41)(11 174 91 131 70 157 18 104 60 143 42)(12 175 92 132 71 158 19 105 61 144 43)(13 176 93 133 72 159 20 106 62 145 44)(14 177 94 134 73 160 21 107 63 146 45)(15 178 95 135 74 161 22 108 64 147 46)(16 179 96 136 75 162 23 109 65 148 47)(17 180 97 120 76 163 24 110 66 149 48)
(1 49)(2 50)(3 51)(4 35)(5 36)(6 37)(7 38)(8 39)(9 40)(10 41)(11 42)(12 43)(13 44)(14 45)(15 46)(16 47)(17 48)(18 70)(19 71)(20 72)(21 73)(22 74)(23 75)(24 76)(25 77)(26 78)(27 79)(28 80)(29 81)(30 82)(31 83)(32 84)(33 85)(34 69)(52 100)(53 101)(54 102)(55 86)(56 87)(57 88)(58 89)(59 90)(60 91)(61 92)(62 93)(63 94)(64 95)(65 96)(66 97)(67 98)(68 99)(103 130)(104 131)(105 132)(106 133)(107 134)(108 135)(109 136)(110 120)(111 121)(112 122)(113 123)(114 124)(115 125)(116 126)(117 127)(118 128)(119 129)(137 185)(138 186)(139 187)(140 171)(141 172)(142 173)(143 174)(144 175)(145 176)(146 177)(147 178)(148 179)(149 180)(150 181)(151 182)(152 183)(153 184)

G:=sub<Sym(187)| (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)(171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187), (1,181,98,121,77,164,25,111,67,150,49)(2,182,99,122,78,165,26,112,68,151,50)(3,183,100,123,79,166,27,113,52,152,51)(4,184,101,124,80,167,28,114,53,153,35)(5,185,102,125,81,168,29,115,54,137,36)(6,186,86,126,82,169,30,116,55,138,37)(7,187,87,127,83,170,31,117,56,139,38)(8,171,88,128,84,154,32,118,57,140,39)(9,172,89,129,85,155,33,119,58,141,40)(10,173,90,130,69,156,34,103,59,142,41)(11,174,91,131,70,157,18,104,60,143,42)(12,175,92,132,71,158,19,105,61,144,43)(13,176,93,133,72,159,20,106,62,145,44)(14,177,94,134,73,160,21,107,63,146,45)(15,178,95,135,74,161,22,108,64,147,46)(16,179,96,136,75,162,23,109,65,148,47)(17,180,97,120,76,163,24,110,66,149,48), (1,49)(2,50)(3,51)(4,35)(5,36)(6,37)(7,38)(8,39)(9,40)(10,41)(11,42)(12,43)(13,44)(14,45)(15,46)(16,47)(17,48)(18,70)(19,71)(20,72)(21,73)(22,74)(23,75)(24,76)(25,77)(26,78)(27,79)(28,80)(29,81)(30,82)(31,83)(32,84)(33,85)(34,69)(52,100)(53,101)(54,102)(55,86)(56,87)(57,88)(58,89)(59,90)(60,91)(61,92)(62,93)(63,94)(64,95)(65,96)(66,97)(67,98)(68,99)(103,130)(104,131)(105,132)(106,133)(107,134)(108,135)(109,136)(110,120)(111,121)(112,122)(113,123)(114,124)(115,125)(116,126)(117,127)(118,128)(119,129)(137,185)(138,186)(139,187)(140,171)(141,172)(142,173)(143,174)(144,175)(145,176)(146,177)(147,178)(148,179)(149,180)(150,181)(151,182)(152,183)(153,184)>;

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)(171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187), (1,181,98,121,77,164,25,111,67,150,49)(2,182,99,122,78,165,26,112,68,151,50)(3,183,100,123,79,166,27,113,52,152,51)(4,184,101,124,80,167,28,114,53,153,35)(5,185,102,125,81,168,29,115,54,137,36)(6,186,86,126,82,169,30,116,55,138,37)(7,187,87,127,83,170,31,117,56,139,38)(8,171,88,128,84,154,32,118,57,140,39)(9,172,89,129,85,155,33,119,58,141,40)(10,173,90,130,69,156,34,103,59,142,41)(11,174,91,131,70,157,18,104,60,143,42)(12,175,92,132,71,158,19,105,61,144,43)(13,176,93,133,72,159,20,106,62,145,44)(14,177,94,134,73,160,21,107,63,146,45)(15,178,95,135,74,161,22,108,64,147,46)(16,179,96,136,75,162,23,109,65,148,47)(17,180,97,120,76,163,24,110,66,149,48), (1,49)(2,50)(3,51)(4,35)(5,36)(6,37)(7,38)(8,39)(9,40)(10,41)(11,42)(12,43)(13,44)(14,45)(15,46)(16,47)(17,48)(18,70)(19,71)(20,72)(21,73)(22,74)(23,75)(24,76)(25,77)(26,78)(27,79)(28,80)(29,81)(30,82)(31,83)(32,84)(33,85)(34,69)(52,100)(53,101)(54,102)(55,86)(56,87)(57,88)(58,89)(59,90)(60,91)(61,92)(62,93)(63,94)(64,95)(65,96)(66,97)(67,98)(68,99)(103,130)(104,131)(105,132)(106,133)(107,134)(108,135)(109,136)(110,120)(111,121)(112,122)(113,123)(114,124)(115,125)(116,126)(117,127)(118,128)(119,129)(137,185)(138,186)(139,187)(140,171)(141,172)(142,173)(143,174)(144,175)(145,176)(146,177)(147,178)(148,179)(149,180)(150,181)(151,182)(152,183)(153,184) );

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),(171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187)], [(1,181,98,121,77,164,25,111,67,150,49),(2,182,99,122,78,165,26,112,68,151,50),(3,183,100,123,79,166,27,113,52,152,51),(4,184,101,124,80,167,28,114,53,153,35),(5,185,102,125,81,168,29,115,54,137,36),(6,186,86,126,82,169,30,116,55,138,37),(7,187,87,127,83,170,31,117,56,139,38),(8,171,88,128,84,154,32,118,57,140,39),(9,172,89,129,85,155,33,119,58,141,40),(10,173,90,130,69,156,34,103,59,142,41),(11,174,91,131,70,157,18,104,60,143,42),(12,175,92,132,71,158,19,105,61,144,43),(13,176,93,133,72,159,20,106,62,145,44),(14,177,94,134,73,160,21,107,63,146,45),(15,178,95,135,74,161,22,108,64,147,46),(16,179,96,136,75,162,23,109,65,148,47),(17,180,97,120,76,163,24,110,66,149,48)], [(1,49),(2,50),(3,51),(4,35),(5,36),(6,37),(7,38),(8,39),(9,40),(10,41),(11,42),(12,43),(13,44),(14,45),(15,46),(16,47),(17,48),(18,70),(19,71),(20,72),(21,73),(22,74),(23,75),(24,76),(25,77),(26,78),(27,79),(28,80),(29,81),(30,82),(31,83),(32,84),(33,85),(34,69),(52,100),(53,101),(54,102),(55,86),(56,87),(57,88),(58,89),(59,90),(60,91),(61,92),(62,93),(63,94),(64,95),(65,96),(66,97),(67,98),(68,99),(103,130),(104,131),(105,132),(106,133),(107,134),(108,135),(109,136),(110,120),(111,121),(112,122),(113,123),(114,124),(115,125),(116,126),(117,127),(118,128),(119,129),(137,185),(138,186),(139,187),(140,171),(141,172),(142,173),(143,174),(144,175),(145,176),(146,177),(147,178),(148,179),(149,180),(150,181),(151,182),(152,183),(153,184)])

119 conjugacy classes

class 1  2 11A···11E17A···17P34A···34P187A···187CB
order1211···1117···1734···34187···187
size1112···21···111···112···2

119 irreducible representations

dim111122
type+++
imageC1C2C17C34D11C17×D11
kernelC17×D11C187D11C11C17C1
# reps111616580

Matrix representation of C17×D11 in GL2(𝔽1123) generated by

3090
0309
,
01
1122819
,
01
10
G:=sub<GL(2,GF(1123))| [309,0,0,309],[0,1122,1,819],[0,1,1,0] >;

C17×D11 in GAP, Magma, Sage, TeX

C_{17}\times D_{11}
% in TeX

G:=Group("C17xD11");
// GroupNames label

G:=SmallGroup(374,1);
// by ID

G=gap.SmallGroup(374,1);
# by ID

G:=PCGroup([3,-2,-17,-11,3062]);
// Polycyclic

G:=Group<a,b,c|a^17=b^11=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C17×D11 in TeX

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