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G = C8×D23order 368 = 24·23

Direct product of C8 and D23

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

Aliases: C8×D23, C1843C2, D46.2C4, C4.12D46, C92.12C22, Dic23.2C4, C23⋊C86C2, C231(C2×C8), C46.1(C2×C4), C2.1(C4×D23), (C4×D23).3C2, SmallGroup(368,3)

Series: Derived Chief Lower central Upper central

C1C23 — C8×D23
C1C23C46C92C4×D23 — C8×D23
C23 — C8×D23
C1C8

Generators and relations for C8×D23
 G = < a,b,c | a8=b23=c2=1, ab=ba, ac=ca, cbc=b-1 >

23C2
23C2
23C22
23C4
23C2×C4
23C8
23C2×C8

Smallest permutation representation of C8×D23
On 184 points
Generators in S184
(1 182 83 129 38 140 52 97)(2 183 84 130 39 141 53 98)(3 184 85 131 40 142 54 99)(4 162 86 132 41 143 55 100)(5 163 87 133 42 144 56 101)(6 164 88 134 43 145 57 102)(7 165 89 135 44 146 58 103)(8 166 90 136 45 147 59 104)(9 167 91 137 46 148 60 105)(10 168 92 138 24 149 61 106)(11 169 70 116 25 150 62 107)(12 170 71 117 26 151 63 108)(13 171 72 118 27 152 64 109)(14 172 73 119 28 153 65 110)(15 173 74 120 29 154 66 111)(16 174 75 121 30 155 67 112)(17 175 76 122 31 156 68 113)(18 176 77 123 32 157 69 114)(19 177 78 124 33 158 47 115)(20 178 79 125 34 159 48 93)(21 179 80 126 35 160 49 94)(22 180 81 127 36 161 50 95)(23 181 82 128 37 139 51 96)
(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)
(1 37)(2 36)(3 35)(4 34)(5 33)(6 32)(7 31)(8 30)(9 29)(10 28)(11 27)(12 26)(13 25)(14 24)(15 46)(16 45)(17 44)(18 43)(19 42)(20 41)(21 40)(22 39)(23 38)(47 87)(48 86)(49 85)(50 84)(51 83)(52 82)(53 81)(54 80)(55 79)(56 78)(57 77)(58 76)(59 75)(60 74)(61 73)(62 72)(63 71)(64 70)(65 92)(66 91)(67 90)(68 89)(69 88)(93 132)(94 131)(95 130)(96 129)(97 128)(98 127)(99 126)(100 125)(101 124)(102 123)(103 122)(104 121)(105 120)(106 119)(107 118)(108 117)(109 116)(110 138)(111 137)(112 136)(113 135)(114 134)(115 133)(139 182)(140 181)(141 180)(142 179)(143 178)(144 177)(145 176)(146 175)(147 174)(148 173)(149 172)(150 171)(151 170)(152 169)(153 168)(154 167)(155 166)(156 165)(157 164)(158 163)(159 162)(160 184)(161 183)

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

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

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

104 conjugacy classes

class 1 2A2B2C4A4B4C4D8A8B8C8D8E8F8G8H23A···23K46A···46K92A···92V184A···184AR
order122244448888888823···2346···4692···92184···184
size1123231123231111232323232···22···22···22···2

104 irreducible representations

dim11111112222
type++++++
imageC1C2C2C2C4C4C8D23D46C4×D23C8×D23
kernelC8×D23C23⋊C8C184C4×D23Dic23D46D23C8C4C2C1
# reps111122811112244

Matrix representation of C8×D23 in GL3(𝔽1289) generated by

88700
010
001
,
100
08281
081815
,
100
06535
010211224
G:=sub<GL(3,GF(1289))| [887,0,0,0,1,0,0,0,1],[1,0,0,0,828,818,0,1,15],[1,0,0,0,65,1021,0,35,1224] >;

C8×D23 in GAP, Magma, Sage, TeX

C_8\times D_{23}
% in TeX

G:=Group("C8xD23");
// GroupNames label

G:=SmallGroup(368,3);
// by ID

G=gap.SmallGroup(368,3);
# by ID

G:=PCGroup([5,-2,-2,-2,-2,-23,26,42,8804]);
// Polycyclic

G:=Group<a,b,c|a^8=b^23=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C8×D23 in TeX

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