Copied to
clipboard

G = C47⋊D4order 376 = 23·47

The semidirect product of C47 and D4 acting via D4/C22=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C472D4, C22⋊D47, D942C2, Dic47⋊C2, C2.5D94, C94.5C22, (C2×C94)⋊2C2, SmallGroup(376,7)

Series: Derived Chief Lower central Upper central

C1C94 — C47⋊D4
C1C47C94D94 — C47⋊D4
C47C94 — C47⋊D4
C1C2C22

Generators and relations for C47⋊D4
 G = < a,b,c | a47=b4=c2=1, bab-1=cac=a-1, cbc=b-1 >

2C2
94C2
47C4
47C22
2D47
2C94
47D4

Smallest permutation representation of C47⋊D4
On 188 points
Generators in S188
(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)
(1 140 83 152)(2 139 84 151)(3 138 85 150)(4 137 86 149)(5 136 87 148)(6 135 88 147)(7 134 89 146)(8 133 90 145)(9 132 91 144)(10 131 92 143)(11 130 93 142)(12 129 94 188)(13 128 48 187)(14 127 49 186)(15 126 50 185)(16 125 51 184)(17 124 52 183)(18 123 53 182)(19 122 54 181)(20 121 55 180)(21 120 56 179)(22 119 57 178)(23 118 58 177)(24 117 59 176)(25 116 60 175)(26 115 61 174)(27 114 62 173)(28 113 63 172)(29 112 64 171)(30 111 65 170)(31 110 66 169)(32 109 67 168)(33 108 68 167)(34 107 69 166)(35 106 70 165)(36 105 71 164)(37 104 72 163)(38 103 73 162)(39 102 74 161)(40 101 75 160)(41 100 76 159)(42 99 77 158)(43 98 78 157)(44 97 79 156)(45 96 80 155)(46 95 81 154)(47 141 82 153)
(2 47)(3 46)(4 45)(5 44)(6 43)(7 42)(8 41)(9 40)(10 39)(11 38)(12 37)(13 36)(14 35)(15 34)(16 33)(17 32)(18 31)(19 30)(20 29)(21 28)(22 27)(23 26)(24 25)(48 71)(49 70)(50 69)(51 68)(52 67)(53 66)(54 65)(55 64)(56 63)(57 62)(58 61)(59 60)(72 94)(73 93)(74 92)(75 91)(76 90)(77 89)(78 88)(79 87)(80 86)(81 85)(82 84)(95 150)(96 149)(97 148)(98 147)(99 146)(100 145)(101 144)(102 143)(103 142)(104 188)(105 187)(106 186)(107 185)(108 184)(109 183)(110 182)(111 181)(112 180)(113 179)(114 178)(115 177)(116 176)(117 175)(118 174)(119 173)(120 172)(121 171)(122 170)(123 169)(124 168)(125 167)(126 166)(127 165)(128 164)(129 163)(130 162)(131 161)(132 160)(133 159)(134 158)(135 157)(136 156)(137 155)(138 154)(139 153)(140 152)(141 151)

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

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

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

97 conjugacy classes

class 1 2A2B2C 4 47A···47W94A···94BQ
order1222447···4794···94
size11294942···22···2

97 irreducible representations

dim11112222
type+++++++
imageC1C2C2C2D4D47D94C47⋊D4
kernelC47⋊D4Dic47D94C2×C94C47C22C2C1
# reps11111232346

Matrix representation of C47⋊D4 in GL2(𝔽941) generated by

01
94045
,
841109
314100
,
10
45940
G:=sub<GL(2,GF(941))| [0,940,1,45],[841,314,109,100],[1,45,0,940] >;

C47⋊D4 in GAP, Magma, Sage, TeX

C_{47}\rtimes D_4
% in TeX

G:=Group("C47:D4");
// GroupNames label

G:=SmallGroup(376,7);
// by ID

G=gap.SmallGroup(376,7);
# by ID

G:=PCGroup([4,-2,-2,-2,-47,49,5891]);
// Polycyclic

G:=Group<a,b,c|a^47=b^4=c^2=1,b*a*b^-1=c*a*c=a^-1,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C47⋊D4 in TeX

׿
×
𝔽