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G = C8⋊D29order 464 = 24·29

3rd semidirect product of C8 and D29 acting via D29/C29=C2

metacyclic, supersoluble, monomial, 2-hyperelementary

Aliases: C83D29, C2324C2, D58.1C4, C4.13D58, C293M4(2), Dic29.1C4, C116.13C22, C292C84C2, C58.9(C2×C4), C2.3(C4×D29), (C4×D29).2C2, SmallGroup(464,5)

Series: Derived Chief Lower central Upper central

C1C58 — C8⋊D29
C1C29C58C116C4×D29 — C8⋊D29
C29C58 — C8⋊D29
C1C4C8

Generators and relations for C8⋊D29
 G = < a,b,c | a8=b29=c2=1, ab=ba, cac=a5, cbc=b-1 >

58C2
29C22
29C4
2D29
29C2×C4
29C8
29M4(2)

Smallest permutation representation of C8⋊D29
On 232 points
Generators in S232
(1 226 104 158 51 196 76 136)(2 227 105 159 52 197 77 137)(3 228 106 160 53 198 78 138)(4 229 107 161 54 199 79 139)(5 230 108 162 55 200 80 140)(6 231 109 163 56 201 81 141)(7 232 110 164 57 202 82 142)(8 204 111 165 58 203 83 143)(9 205 112 166 30 175 84 144)(10 206 113 167 31 176 85 145)(11 207 114 168 32 177 86 117)(12 208 115 169 33 178 87 118)(13 209 116 170 34 179 59 119)(14 210 88 171 35 180 60 120)(15 211 89 172 36 181 61 121)(16 212 90 173 37 182 62 122)(17 213 91 174 38 183 63 123)(18 214 92 146 39 184 64 124)(19 215 93 147 40 185 65 125)(20 216 94 148 41 186 66 126)(21 217 95 149 42 187 67 127)(22 218 96 150 43 188 68 128)(23 219 97 151 44 189 69 129)(24 220 98 152 45 190 70 130)(25 221 99 153 46 191 71 131)(26 222 100 154 47 192 72 132)(27 223 101 155 48 193 73 133)(28 224 102 156 49 194 74 134)(29 225 103 157 50 195 75 135)
(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)(204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232)
(1 29)(2 28)(3 27)(4 26)(5 25)(6 24)(7 23)(8 22)(9 21)(10 20)(11 19)(12 18)(13 17)(14 16)(30 42)(31 41)(32 40)(33 39)(34 38)(35 37)(43 58)(44 57)(45 56)(46 55)(47 54)(48 53)(49 52)(50 51)(59 63)(60 62)(64 87)(65 86)(66 85)(67 84)(68 83)(69 82)(70 81)(71 80)(72 79)(73 78)(74 77)(75 76)(88 90)(91 116)(92 115)(93 114)(94 113)(95 112)(96 111)(97 110)(98 109)(99 108)(100 107)(101 106)(102 105)(103 104)(117 147)(118 146)(119 174)(120 173)(121 172)(122 171)(123 170)(124 169)(125 168)(126 167)(127 166)(128 165)(129 164)(130 163)(131 162)(132 161)(133 160)(134 159)(135 158)(136 157)(137 156)(138 155)(139 154)(140 153)(141 152)(142 151)(143 150)(144 149)(145 148)(175 217)(176 216)(177 215)(178 214)(179 213)(180 212)(181 211)(182 210)(183 209)(184 208)(185 207)(186 206)(187 205)(188 204)(189 232)(190 231)(191 230)(192 229)(193 228)(194 227)(195 226)(196 225)(197 224)(198 223)(199 222)(200 221)(201 220)(202 219)(203 218)

G:=sub<Sym(232)| (1,226,104,158,51,196,76,136)(2,227,105,159,52,197,77,137)(3,228,106,160,53,198,78,138)(4,229,107,161,54,199,79,139)(5,230,108,162,55,200,80,140)(6,231,109,163,56,201,81,141)(7,232,110,164,57,202,82,142)(8,204,111,165,58,203,83,143)(9,205,112,166,30,175,84,144)(10,206,113,167,31,176,85,145)(11,207,114,168,32,177,86,117)(12,208,115,169,33,178,87,118)(13,209,116,170,34,179,59,119)(14,210,88,171,35,180,60,120)(15,211,89,172,36,181,61,121)(16,212,90,173,37,182,62,122)(17,213,91,174,38,183,63,123)(18,214,92,146,39,184,64,124)(19,215,93,147,40,185,65,125)(20,216,94,148,41,186,66,126)(21,217,95,149,42,187,67,127)(22,218,96,150,43,188,68,128)(23,219,97,151,44,189,69,129)(24,220,98,152,45,190,70,130)(25,221,99,153,46,191,71,131)(26,222,100,154,47,192,72,132)(27,223,101,155,48,193,73,133)(28,224,102,156,49,194,74,134)(29,225,103,157,50,195,75,135), (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)(204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232), (1,29)(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)(30,42)(31,41)(32,40)(33,39)(34,38)(35,37)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)(59,63)(60,62)(64,87)(65,86)(66,85)(67,84)(68,83)(69,82)(70,81)(71,80)(72,79)(73,78)(74,77)(75,76)(88,90)(91,116)(92,115)(93,114)(94,113)(95,112)(96,111)(97,110)(98,109)(99,108)(100,107)(101,106)(102,105)(103,104)(117,147)(118,146)(119,174)(120,173)(121,172)(122,171)(123,170)(124,169)(125,168)(126,167)(127,166)(128,165)(129,164)(130,163)(131,162)(132,161)(133,160)(134,159)(135,158)(136,157)(137,156)(138,155)(139,154)(140,153)(141,152)(142,151)(143,150)(144,149)(145,148)(175,217)(176,216)(177,215)(178,214)(179,213)(180,212)(181,211)(182,210)(183,209)(184,208)(185,207)(186,206)(187,205)(188,204)(189,232)(190,231)(191,230)(192,229)(193,228)(194,227)(195,226)(196,225)(197,224)(198,223)(199,222)(200,221)(201,220)(202,219)(203,218)>;

G:=Group( (1,226,104,158,51,196,76,136)(2,227,105,159,52,197,77,137)(3,228,106,160,53,198,78,138)(4,229,107,161,54,199,79,139)(5,230,108,162,55,200,80,140)(6,231,109,163,56,201,81,141)(7,232,110,164,57,202,82,142)(8,204,111,165,58,203,83,143)(9,205,112,166,30,175,84,144)(10,206,113,167,31,176,85,145)(11,207,114,168,32,177,86,117)(12,208,115,169,33,178,87,118)(13,209,116,170,34,179,59,119)(14,210,88,171,35,180,60,120)(15,211,89,172,36,181,61,121)(16,212,90,173,37,182,62,122)(17,213,91,174,38,183,63,123)(18,214,92,146,39,184,64,124)(19,215,93,147,40,185,65,125)(20,216,94,148,41,186,66,126)(21,217,95,149,42,187,67,127)(22,218,96,150,43,188,68,128)(23,219,97,151,44,189,69,129)(24,220,98,152,45,190,70,130)(25,221,99,153,46,191,71,131)(26,222,100,154,47,192,72,132)(27,223,101,155,48,193,73,133)(28,224,102,156,49,194,74,134)(29,225,103,157,50,195,75,135), (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)(204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232), (1,29)(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)(30,42)(31,41)(32,40)(33,39)(34,38)(35,37)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)(59,63)(60,62)(64,87)(65,86)(66,85)(67,84)(68,83)(69,82)(70,81)(71,80)(72,79)(73,78)(74,77)(75,76)(88,90)(91,116)(92,115)(93,114)(94,113)(95,112)(96,111)(97,110)(98,109)(99,108)(100,107)(101,106)(102,105)(103,104)(117,147)(118,146)(119,174)(120,173)(121,172)(122,171)(123,170)(124,169)(125,168)(126,167)(127,166)(128,165)(129,164)(130,163)(131,162)(132,161)(133,160)(134,159)(135,158)(136,157)(137,156)(138,155)(139,154)(140,153)(141,152)(142,151)(143,150)(144,149)(145,148)(175,217)(176,216)(177,215)(178,214)(179,213)(180,212)(181,211)(182,210)(183,209)(184,208)(185,207)(186,206)(187,205)(188,204)(189,232)(190,231)(191,230)(192,229)(193,228)(194,227)(195,226)(196,225)(197,224)(198,223)(199,222)(200,221)(201,220)(202,219)(203,218) );

G=PermutationGroup([(1,226,104,158,51,196,76,136),(2,227,105,159,52,197,77,137),(3,228,106,160,53,198,78,138),(4,229,107,161,54,199,79,139),(5,230,108,162,55,200,80,140),(6,231,109,163,56,201,81,141),(7,232,110,164,57,202,82,142),(8,204,111,165,58,203,83,143),(9,205,112,166,30,175,84,144),(10,206,113,167,31,176,85,145),(11,207,114,168,32,177,86,117),(12,208,115,169,33,178,87,118),(13,209,116,170,34,179,59,119),(14,210,88,171,35,180,60,120),(15,211,89,172,36,181,61,121),(16,212,90,173,37,182,62,122),(17,213,91,174,38,183,63,123),(18,214,92,146,39,184,64,124),(19,215,93,147,40,185,65,125),(20,216,94,148,41,186,66,126),(21,217,95,149,42,187,67,127),(22,218,96,150,43,188,68,128),(23,219,97,151,44,189,69,129),(24,220,98,152,45,190,70,130),(25,221,99,153,46,191,71,131),(26,222,100,154,47,192,72,132),(27,223,101,155,48,193,73,133),(28,224,102,156,49,194,74,134),(29,225,103,157,50,195,75,135)], [(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),(204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232)], [(1,29),(2,28),(3,27),(4,26),(5,25),(6,24),(7,23),(8,22),(9,21),(10,20),(11,19),(12,18),(13,17),(14,16),(30,42),(31,41),(32,40),(33,39),(34,38),(35,37),(43,58),(44,57),(45,56),(46,55),(47,54),(48,53),(49,52),(50,51),(59,63),(60,62),(64,87),(65,86),(66,85),(67,84),(68,83),(69,82),(70,81),(71,80),(72,79),(73,78),(74,77),(75,76),(88,90),(91,116),(92,115),(93,114),(94,113),(95,112),(96,111),(97,110),(98,109),(99,108),(100,107),(101,106),(102,105),(103,104),(117,147),(118,146),(119,174),(120,173),(121,172),(122,171),(123,170),(124,169),(125,168),(126,167),(127,166),(128,165),(129,164),(130,163),(131,162),(132,161),(133,160),(134,159),(135,158),(136,157),(137,156),(138,155),(139,154),(140,153),(141,152),(142,151),(143,150),(144,149),(145,148),(175,217),(176,216),(177,215),(178,214),(179,213),(180,212),(181,211),(182,210),(183,209),(184,208),(185,207),(186,206),(187,205),(188,204),(189,232),(190,231),(191,230),(192,229),(193,228),(194,227),(195,226),(196,225),(197,224),(198,223),(199,222),(200,221),(201,220),(202,219),(203,218)])

122 conjugacy classes

class 1 2A2B4A4B4C8A8B8C8D29A···29N58A···58N116A···116AB232A···232BD
order122444888829···2958···58116···116232···232
size115811582258582···22···22···22···2

122 irreducible representations

dim11111122222
type++++++
imageC1C2C2C2C4C4M4(2)D29D58C4×D29C8⋊D29
kernelC8⋊D29C292C8C232C4×D29Dic29D58C29C8C4C2C1
# reps111122214142856

Matrix representation of C8⋊D29 in GL2(𝔽233) generated by

1734
22960
,
2031
2320
,
14544
20088
G:=sub<GL(2,GF(233))| [173,229,4,60],[203,232,1,0],[145,200,44,88] >;

C8⋊D29 in GAP, Magma, Sage, TeX

C_8\rtimes D_{29}
% in TeX

G:=Group("C8:D29");
// GroupNames label

G:=SmallGroup(464,5);
// by ID

G=gap.SmallGroup(464,5);
# by ID

G:=PCGroup([5,-2,-2,-2,-2,-29,101,26,42,11204]);
// Polycyclic

G:=Group<a,b,c|a^8=b^29=c^2=1,a*b=b*a,c*a*c=a^5,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C8⋊D29 in TeX

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