Copied to
clipboard

G = C11⋊D20order 440 = 23·5·11

The semidirect product of C11 and D20 acting via D20/D10=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C553D4, C112D20, Dic11⋊D5, D1104C2, D102D11, C22.6D10, C10.6D22, C110.6C22, (D5×C22)⋊2C2, C51(C11⋊D4), C2.6(D5×D11), (C5×Dic11)⋊3C2, SmallGroup(440,22)

Series: Derived Chief Lower central Upper central

C1C110 — C11⋊D20
C1C11C55C110C5×Dic11 — C11⋊D20
C55C110 — C11⋊D20
C1C2

Generators and relations for C11⋊D20
 G = < a,b,c | a11=b20=c2=1, bab-1=cac=a-1, cbc=b-1 >

10C2
110C2
5C22
11C4
55C22
2D5
22D5
10D11
10C22
55D4
11C20
11D10
5D22
5C2×C22
2D5×C11
2D55
11D20
5C11⋊D4

Smallest permutation representation of C11⋊D20
On 220 points
Generators in S220
(1 165 139 201 113 99 31 61 42 157 190)(2 191 158 43 62 32 100 114 202 140 166)(3 167 121 203 115 81 33 63 44 159 192)(4 193 160 45 64 34 82 116 204 122 168)(5 169 123 205 117 83 35 65 46 141 194)(6 195 142 47 66 36 84 118 206 124 170)(7 171 125 207 119 85 37 67 48 143 196)(8 197 144 49 68 38 86 120 208 126 172)(9 173 127 209 101 87 39 69 50 145 198)(10 199 146 51 70 40 88 102 210 128 174)(11 175 129 211 103 89 21 71 52 147 200)(12 181 148 53 72 22 90 104 212 130 176)(13 177 131 213 105 91 23 73 54 149 182)(14 183 150 55 74 24 92 106 214 132 178)(15 179 133 215 107 93 25 75 56 151 184)(16 185 152 57 76 26 94 108 216 134 180)(17 161 135 217 109 95 27 77 58 153 186)(18 187 154 59 78 28 96 110 218 136 162)(19 163 137 219 111 97 29 79 60 155 188)(20 189 156 41 80 30 98 112 220 138 164)
(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)
(1 5)(2 4)(6 20)(7 19)(8 18)(9 17)(10 16)(11 15)(12 14)(21 93)(22 92)(23 91)(24 90)(25 89)(26 88)(27 87)(28 86)(29 85)(30 84)(31 83)(32 82)(33 81)(34 100)(35 99)(36 98)(37 97)(38 96)(39 95)(40 94)(41 206)(42 205)(43 204)(44 203)(45 202)(46 201)(47 220)(48 219)(49 218)(50 217)(51 216)(52 215)(53 214)(54 213)(55 212)(56 211)(57 210)(58 209)(59 208)(60 207)(61 117)(62 116)(63 115)(64 114)(65 113)(66 112)(67 111)(68 110)(69 109)(70 108)(71 107)(72 106)(73 105)(74 104)(75 103)(76 102)(77 101)(78 120)(79 119)(80 118)(121 159)(122 158)(123 157)(124 156)(125 155)(126 154)(127 153)(128 152)(129 151)(130 150)(131 149)(132 148)(133 147)(134 146)(135 145)(136 144)(137 143)(138 142)(139 141)(140 160)(161 198)(162 197)(163 196)(164 195)(165 194)(166 193)(167 192)(168 191)(169 190)(170 189)(171 188)(172 187)(173 186)(174 185)(175 184)(176 183)(177 182)(178 181)(179 200)(180 199)

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

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

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

53 conjugacy classes

class 1 2A2B2C 4 5A5B10A10B11A···11E20A20B20C20D22A···22E22F···22O55A···55J110A···110J
order1222455101011···112020202022···2222···2255···55110···110
size11101102222222···2222222222···210···104···44···4

53 irreducible representations

dim1111222222244
type++++++++++++
imageC1C2C2C2D4D5D10D11D20D22C11⋊D4D5×D11C11⋊D20
kernelC11⋊D20C5×Dic11D5×C22D110C55Dic11C22D10C11C10C5C2C1
# reps1111122545101010

Matrix representation of C11⋊D20 in GL4(𝔽661) generated by

0100
66053800
0010
0001
,
660000
123100
00268226
00302341
,
1000
53866000
001125
000660
G:=sub<GL(4,GF(661))| [0,660,0,0,1,538,0,0,0,0,1,0,0,0,0,1],[660,123,0,0,0,1,0,0,0,0,268,302,0,0,226,341],[1,538,0,0,0,660,0,0,0,0,1,0,0,0,125,660] >;

C11⋊D20 in GAP, Magma, Sage, TeX

C_{11}\rtimes D_{20}
% in TeX

G:=Group("C11:D20");
// GroupNames label

G:=SmallGroup(440,22);
// by ID

G=gap.SmallGroup(440,22);
# by ID

G:=PCGroup([5,-2,-2,-2,-5,-11,20,61,328,10004]);
// Polycyclic

G:=Group<a,b,c|a^11=b^20=c^2=1,b*a*b^-1=c*a*c=a^-1,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C11⋊D20 in TeX

׿
×
𝔽