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G = C17×D13order 442 = 2·13·17

Direct product of C17 and D13

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

Aliases: C17×D13, C13⋊C34, C2213C2, SmallGroup(442,1)

Series: Derived Chief Lower central Upper central

C1C13 — C17×D13
C1C13C221 — C17×D13
C13 — C17×D13
C1C17

Generators and relations for C17×D13
 G = < a,b,c | a17=b13=c2=1, ab=ba, ac=ca, cbc=b-1 >

13C2
13C34

Smallest permutation representation of C17×D13
On 221 points
Generators in S221
(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)(188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204)(205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221)
(1 46 95 207 84 144 158 178 111 19 56 198 131)(2 47 96 208 85 145 159 179 112 20 57 199 132)(3 48 97 209 69 146 160 180 113 21 58 200 133)(4 49 98 210 70 147 161 181 114 22 59 201 134)(5 50 99 211 71 148 162 182 115 23 60 202 135)(6 51 100 212 72 149 163 183 116 24 61 203 136)(7 35 101 213 73 150 164 184 117 25 62 204 120)(8 36 102 214 74 151 165 185 118 26 63 188 121)(9 37 86 215 75 152 166 186 119 27 64 189 122)(10 38 87 216 76 153 167 187 103 28 65 190 123)(11 39 88 217 77 137 168 171 104 29 66 191 124)(12 40 89 218 78 138 169 172 105 30 67 192 125)(13 41 90 219 79 139 170 173 106 31 68 193 126)(14 42 91 220 80 140 154 174 107 32 52 194 127)(15 43 92 221 81 141 155 175 108 33 53 195 128)(16 44 93 205 82 142 156 176 109 34 54 196 129)(17 45 94 206 83 143 157 177 110 18 55 197 130)
(1 131)(2 132)(3 133)(4 134)(5 135)(6 136)(7 120)(8 121)(9 122)(10 123)(11 124)(12 125)(13 126)(14 127)(15 128)(16 129)(17 130)(18 206)(19 207)(20 208)(21 209)(22 210)(23 211)(24 212)(25 213)(26 214)(27 215)(28 216)(29 217)(30 218)(31 219)(32 220)(33 221)(34 205)(35 204)(36 188)(37 189)(38 190)(39 191)(40 192)(41 193)(42 194)(43 195)(44 196)(45 197)(46 198)(47 199)(48 200)(49 201)(50 202)(51 203)(52 91)(53 92)(54 93)(55 94)(56 95)(57 96)(58 97)(59 98)(60 99)(61 100)(62 101)(63 102)(64 86)(65 87)(66 88)(67 89)(68 90)(69 113)(70 114)(71 115)(72 116)(73 117)(74 118)(75 119)(76 103)(77 104)(78 105)(79 106)(80 107)(81 108)(82 109)(83 110)(84 111)(85 112)(137 171)(138 172)(139 173)(140 174)(141 175)(142 176)(143 177)(144 178)(145 179)(146 180)(147 181)(148 182)(149 183)(150 184)(151 185)(152 186)(153 187)

G:=sub<Sym(221)| (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)(188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204)(205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221), (1,46,95,207,84,144,158,178,111,19,56,198,131)(2,47,96,208,85,145,159,179,112,20,57,199,132)(3,48,97,209,69,146,160,180,113,21,58,200,133)(4,49,98,210,70,147,161,181,114,22,59,201,134)(5,50,99,211,71,148,162,182,115,23,60,202,135)(6,51,100,212,72,149,163,183,116,24,61,203,136)(7,35,101,213,73,150,164,184,117,25,62,204,120)(8,36,102,214,74,151,165,185,118,26,63,188,121)(9,37,86,215,75,152,166,186,119,27,64,189,122)(10,38,87,216,76,153,167,187,103,28,65,190,123)(11,39,88,217,77,137,168,171,104,29,66,191,124)(12,40,89,218,78,138,169,172,105,30,67,192,125)(13,41,90,219,79,139,170,173,106,31,68,193,126)(14,42,91,220,80,140,154,174,107,32,52,194,127)(15,43,92,221,81,141,155,175,108,33,53,195,128)(16,44,93,205,82,142,156,176,109,34,54,196,129)(17,45,94,206,83,143,157,177,110,18,55,197,130), (1,131)(2,132)(3,133)(4,134)(5,135)(6,136)(7,120)(8,121)(9,122)(10,123)(11,124)(12,125)(13,126)(14,127)(15,128)(16,129)(17,130)(18,206)(19,207)(20,208)(21,209)(22,210)(23,211)(24,212)(25,213)(26,214)(27,215)(28,216)(29,217)(30,218)(31,219)(32,220)(33,221)(34,205)(35,204)(36,188)(37,189)(38,190)(39,191)(40,192)(41,193)(42,194)(43,195)(44,196)(45,197)(46,198)(47,199)(48,200)(49,201)(50,202)(51,203)(52,91)(53,92)(54,93)(55,94)(56,95)(57,96)(58,97)(59,98)(60,99)(61,100)(62,101)(63,102)(64,86)(65,87)(66,88)(67,89)(68,90)(69,113)(70,114)(71,115)(72,116)(73,117)(74,118)(75,119)(76,103)(77,104)(78,105)(79,106)(80,107)(81,108)(82,109)(83,110)(84,111)(85,112)(137,171)(138,172)(139,173)(140,174)(141,175)(142,176)(143,177)(144,178)(145,179)(146,180)(147,181)(148,182)(149,183)(150,184)(151,185)(152,186)(153,187)>;

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)(188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204)(205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221), (1,46,95,207,84,144,158,178,111,19,56,198,131)(2,47,96,208,85,145,159,179,112,20,57,199,132)(3,48,97,209,69,146,160,180,113,21,58,200,133)(4,49,98,210,70,147,161,181,114,22,59,201,134)(5,50,99,211,71,148,162,182,115,23,60,202,135)(6,51,100,212,72,149,163,183,116,24,61,203,136)(7,35,101,213,73,150,164,184,117,25,62,204,120)(8,36,102,214,74,151,165,185,118,26,63,188,121)(9,37,86,215,75,152,166,186,119,27,64,189,122)(10,38,87,216,76,153,167,187,103,28,65,190,123)(11,39,88,217,77,137,168,171,104,29,66,191,124)(12,40,89,218,78,138,169,172,105,30,67,192,125)(13,41,90,219,79,139,170,173,106,31,68,193,126)(14,42,91,220,80,140,154,174,107,32,52,194,127)(15,43,92,221,81,141,155,175,108,33,53,195,128)(16,44,93,205,82,142,156,176,109,34,54,196,129)(17,45,94,206,83,143,157,177,110,18,55,197,130), (1,131)(2,132)(3,133)(4,134)(5,135)(6,136)(7,120)(8,121)(9,122)(10,123)(11,124)(12,125)(13,126)(14,127)(15,128)(16,129)(17,130)(18,206)(19,207)(20,208)(21,209)(22,210)(23,211)(24,212)(25,213)(26,214)(27,215)(28,216)(29,217)(30,218)(31,219)(32,220)(33,221)(34,205)(35,204)(36,188)(37,189)(38,190)(39,191)(40,192)(41,193)(42,194)(43,195)(44,196)(45,197)(46,198)(47,199)(48,200)(49,201)(50,202)(51,203)(52,91)(53,92)(54,93)(55,94)(56,95)(57,96)(58,97)(59,98)(60,99)(61,100)(62,101)(63,102)(64,86)(65,87)(66,88)(67,89)(68,90)(69,113)(70,114)(71,115)(72,116)(73,117)(74,118)(75,119)(76,103)(77,104)(78,105)(79,106)(80,107)(81,108)(82,109)(83,110)(84,111)(85,112)(137,171)(138,172)(139,173)(140,174)(141,175)(142,176)(143,177)(144,178)(145,179)(146,180)(147,181)(148,182)(149,183)(150,184)(151,185)(152,186)(153,187) );

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),(188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204),(205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221)], [(1,46,95,207,84,144,158,178,111,19,56,198,131),(2,47,96,208,85,145,159,179,112,20,57,199,132),(3,48,97,209,69,146,160,180,113,21,58,200,133),(4,49,98,210,70,147,161,181,114,22,59,201,134),(5,50,99,211,71,148,162,182,115,23,60,202,135),(6,51,100,212,72,149,163,183,116,24,61,203,136),(7,35,101,213,73,150,164,184,117,25,62,204,120),(8,36,102,214,74,151,165,185,118,26,63,188,121),(9,37,86,215,75,152,166,186,119,27,64,189,122),(10,38,87,216,76,153,167,187,103,28,65,190,123),(11,39,88,217,77,137,168,171,104,29,66,191,124),(12,40,89,218,78,138,169,172,105,30,67,192,125),(13,41,90,219,79,139,170,173,106,31,68,193,126),(14,42,91,220,80,140,154,174,107,32,52,194,127),(15,43,92,221,81,141,155,175,108,33,53,195,128),(16,44,93,205,82,142,156,176,109,34,54,196,129),(17,45,94,206,83,143,157,177,110,18,55,197,130)], [(1,131),(2,132),(3,133),(4,134),(5,135),(6,136),(7,120),(8,121),(9,122),(10,123),(11,124),(12,125),(13,126),(14,127),(15,128),(16,129),(17,130),(18,206),(19,207),(20,208),(21,209),(22,210),(23,211),(24,212),(25,213),(26,214),(27,215),(28,216),(29,217),(30,218),(31,219),(32,220),(33,221),(34,205),(35,204),(36,188),(37,189),(38,190),(39,191),(40,192),(41,193),(42,194),(43,195),(44,196),(45,197),(46,198),(47,199),(48,200),(49,201),(50,202),(51,203),(52,91),(53,92),(54,93),(55,94),(56,95),(57,96),(58,97),(59,98),(60,99),(61,100),(62,101),(63,102),(64,86),(65,87),(66,88),(67,89),(68,90),(69,113),(70,114),(71,115),(72,116),(73,117),(74,118),(75,119),(76,103),(77,104),(78,105),(79,106),(80,107),(81,108),(82,109),(83,110),(84,111),(85,112),(137,171),(138,172),(139,173),(140,174),(141,175),(142,176),(143,177),(144,178),(145,179),(146,180),(147,181),(148,182),(149,183),(150,184),(151,185),(152,186),(153,187)])

136 conjugacy classes

class 1  2 13A···13F17A···17P34A···34P221A···221CR
order1213···1317···1734···34221···221
size1132···21···113···132···2

136 irreducible representations

dim111122
type+++
imageC1C2C17C34D13C17×D13
kernelC17×D13C221D13C13C17C1
# reps111616696

Matrix representation of C17×D13 in GL2(𝔽443) generated by

3800
0380
,
4421
36874
,
4420
3681
G:=sub<GL(2,GF(443))| [380,0,0,380],[442,368,1,74],[442,368,0,1] >;

C17×D13 in GAP, Magma, Sage, TeX

C_{17}\times D_{13}
% in TeX

G:=Group("C17xD13");
// GroupNames label

G:=SmallGroup(442,1);
// by ID

G=gap.SmallGroup(442,1);
# by ID

G:=PCGroup([3,-2,-17,-13,3674]);
// Polycyclic

G:=Group<a,b,c|a^17=b^13=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C17×D13 in TeX

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