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G = D4×C47order 376 = 23·47

Direct product of C47 and D4

direct product, metacyclic, nilpotent (class 2), monomial, 2-elementary

Aliases: D4×C47, C4⋊C94, C22⋊C94, C1883C2, C94.6C22, (C2×C94)⋊1C2, C2.1(C2×C94), SmallGroup(376,9)

Series: Derived Chief Lower central Upper central

C1C2 — D4×C47
C1C2C94C2×C94 — D4×C47
C1C2 — D4×C47
C1C94 — D4×C47

Generators and relations for D4×C47
 G = < a,b,c | a47=b4=c2=1, ab=ba, ac=ca, cbc=b-1 >

2C2
2C2
2C94
2C94

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

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

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

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

235 conjugacy classes

class 1 2A2B2C 4 47A···47AT94A···94AT94AU···94EH188A···188AT
order1222447···4794···9494···94188···188
size112221···11···12···22···2

235 irreducible representations

dim11111122
type++++
imageC1C2C2C47C94C94D4D4×C47
kernelD4×C47C188C2×C94D4C4C22C47C1
# reps112464692146

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

4800
0480
,
9402
9401
,
10
1940
G:=sub<GL(2,GF(941))| [480,0,0,480],[940,940,2,1],[1,1,0,940] >;

D4×C47 in GAP, Magma, Sage, TeX

D_4\times C_{47}
% in TeX

G:=Group("D4xC47");
// GroupNames label

G:=SmallGroup(376,9);
// by ID

G=gap.SmallGroup(376,9);
# by ID

G:=PCGroup([4,-2,-2,-47,-2,1521]);
// Polycyclic

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

Export

Subgroup lattice of D4×C47 in TeX

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