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G = D5×C46order 460 = 22·5·23

Direct product of C46 and D5

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

Aliases: D5×C46, C10⋊C46, C2303C2, C1154C22, C5⋊(C2×C46), SmallGroup(460,9)

Series: Derived Chief Lower central Upper central

C1C5 — D5×C46
C1C5C115D5×C23 — D5×C46
C5 — D5×C46
C1C46

Generators and relations for D5×C46
 G = < a,b,c | a46=b5=c2=1, ab=ba, ac=ca, cbc=b-1 >

5C2
5C2
5C22
5C46
5C46
5C2×C46

Smallest permutation representation of D5×C46
On 230 points
Generators in S230
(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)
(1 81 203 117 154)(2 82 204 118 155)(3 83 205 119 156)(4 84 206 120 157)(5 85 207 121 158)(6 86 208 122 159)(7 87 209 123 160)(8 88 210 124 161)(9 89 211 125 162)(10 90 212 126 163)(11 91 213 127 164)(12 92 214 128 165)(13 47 215 129 166)(14 48 216 130 167)(15 49 217 131 168)(16 50 218 132 169)(17 51 219 133 170)(18 52 220 134 171)(19 53 221 135 172)(20 54 222 136 173)(21 55 223 137 174)(22 56 224 138 175)(23 57 225 93 176)(24 58 226 94 177)(25 59 227 95 178)(26 60 228 96 179)(27 61 229 97 180)(28 62 230 98 181)(29 63 185 99 182)(30 64 186 100 183)(31 65 187 101 184)(32 66 188 102 139)(33 67 189 103 140)(34 68 190 104 141)(35 69 191 105 142)(36 70 192 106 143)(37 71 193 107 144)(38 72 194 108 145)(39 73 195 109 146)(40 74 196 110 147)(41 75 197 111 148)(42 76 198 112 149)(43 77 199 113 150)(44 78 200 114 151)(45 79 201 115 152)(46 80 202 116 153)
(1 177)(2 178)(3 179)(4 180)(5 181)(6 182)(7 183)(8 184)(9 139)(10 140)(11 141)(12 142)(13 143)(14 144)(15 145)(16 146)(17 147)(18 148)(19 149)(20 150)(21 151)(22 152)(23 153)(24 154)(25 155)(26 156)(27 157)(28 158)(29 159)(30 160)(31 161)(32 162)(33 163)(34 164)(35 165)(36 166)(37 167)(38 168)(39 169)(40 170)(41 171)(42 172)(43 173)(44 174)(45 175)(46 176)(47 106)(48 107)(49 108)(50 109)(51 110)(52 111)(53 112)(54 113)(55 114)(56 115)(57 116)(58 117)(59 118)(60 119)(61 120)(62 121)(63 122)(64 123)(65 124)(66 125)(67 126)(68 127)(69 128)(70 129)(71 130)(72 131)(73 132)(74 133)(75 134)(76 135)(77 136)(78 137)(79 138)(80 93)(81 94)(82 95)(83 96)(84 97)(85 98)(86 99)(87 100)(88 101)(89 102)(90 103)(91 104)(92 105)(185 208)(186 209)(187 210)(188 211)(189 212)(190 213)(191 214)(192 215)(193 216)(194 217)(195 218)(196 219)(197 220)(198 221)(199 222)(200 223)(201 224)(202 225)(203 226)(204 227)(205 228)(206 229)(207 230)

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

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

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

184 conjugacy classes

class 1 2A2B2C5A5B10A10B23A···23V46A···46V46W···46BN115A···115AR230A···230AR
order122255101023···2346···4646···46115···115230···230
size115522221···11···15···52···22···2

184 irreducible representations

dim1111112222
type+++++
imageC1C2C2C23C46C46D5D10D5×C23D5×C46
kernelD5×C46D5×C23C230D10D5C10C46C23C2C1
# reps121224422224444

Matrix representation of D5×C46 in GL2(𝔽461) generated by

1390
0139
,
01
460439
,
4600
221
G:=sub<GL(2,GF(461))| [139,0,0,139],[0,460,1,439],[460,22,0,1] >;

D5×C46 in GAP, Magma, Sage, TeX

D_5\times C_{46}
% in TeX

G:=Group("D5xC46");
// GroupNames label

G:=SmallGroup(460,9);
// by ID

G=gap.SmallGroup(460,9);
# by ID

G:=PCGroup([4,-2,-2,-23,-5,5891]);
// Polycyclic

G:=Group<a,b,c|a^46=b^5=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of D5×C46 in TeX

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