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G = Dic47order 188 = 22·47

Dicyclic group

metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary

Aliases: Dic47, C47⋊C4, C94.C2, C2.D47, SmallGroup(188,1)

Series: Derived Chief Lower central Upper central

C1C47 — Dic47
C1C47C94 — Dic47
C47 — Dic47
C1C2

Generators and relations for Dic47
 G = < a,b | a94=1, b2=a47, bab-1=a-1 >

47C4

Smallest permutation representation of Dic47
Regular action 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)
(1 166 48 119)(2 165 49 118)(3 164 50 117)(4 163 51 116)(5 162 52 115)(6 161 53 114)(7 160 54 113)(8 159 55 112)(9 158 56 111)(10 157 57 110)(11 156 58 109)(12 155 59 108)(13 154 60 107)(14 153 61 106)(15 152 62 105)(16 151 63 104)(17 150 64 103)(18 149 65 102)(19 148 66 101)(20 147 67 100)(21 146 68 99)(22 145 69 98)(23 144 70 97)(24 143 71 96)(25 142 72 95)(26 141 73 188)(27 140 74 187)(28 139 75 186)(29 138 76 185)(30 137 77 184)(31 136 78 183)(32 135 79 182)(33 134 80 181)(34 133 81 180)(35 132 82 179)(36 131 83 178)(37 130 84 177)(38 129 85 176)(39 128 86 175)(40 127 87 174)(41 126 88 173)(42 125 89 172)(43 124 90 171)(44 123 91 170)(45 122 92 169)(46 121 93 168)(47 120 94 167)

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

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

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

Dic47 is a maximal subgroup of   Dic94  C4×D47  C47⋊D4
Dic47 is a maximal quotient of   C47⋊C8

50 conjugacy classes

class 1  2 4A4B47A···47W94A···94W
order124447···4794···94
size1147472···22···2

50 irreducible representations

dim11122
type+++-
imageC1C2C4D47Dic47
kernelDic47C94C47C2C1
# reps1122323

Matrix representation of Dic47 in GL2(𝔽941) generated by

1761
9400
,
253739
438688
G:=sub<GL(2,GF(941))| [176,940,1,0],[253,438,739,688] >;

Dic47 in GAP, Magma, Sage, TeX

{\rm Dic}_{47}
% in TeX

G:=Group("Dic47");
// GroupNames label

G:=SmallGroup(188,1);
// by ID

G=gap.SmallGroup(188,1);
# by ID

G:=PCGroup([3,-2,-2,-47,6,1658]);
// Polycyclic

G:=Group<a,b|a^94=1,b^2=a^47,b*a*b^-1=a^-1>;
// generators/relations

Export

Subgroup lattice of Dic47 in TeX

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