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G = C4○D4×C29order 464 = 24·29

Direct product of C29 and C4○D4

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

Aliases: C4○D4×C29, D42C58, Q82C58, C58.13C23, C116.21C22, (C2×C4)⋊3C58, (C2×C116)⋊7C2, (D4×C29)⋊5C2, C4.5(C2×C58), (Q8×C29)⋊5C2, C22.(C2×C58), C2.3(C22×C58), (C2×C58).2C22, SmallGroup(464,48)

Series: Derived Chief Lower central Upper central

C1C2 — C4○D4×C29
C1C2C58C2×C58D4×C29 — C4○D4×C29
C1C2 — C4○D4×C29
C1C116 — C4○D4×C29

Generators and relations for C4○D4×C29
 G = < a,b,c,d | a29=b4=d2=1, c2=b2, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd=b2c >

2C2
2C2
2C2
2C58
2C58
2C58

Smallest permutation representation of C4○D4×C29
On 232 points
Generators in S232
(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)(204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232)
(1 133 214 150)(2 134 215 151)(3 135 216 152)(4 136 217 153)(5 137 218 154)(6 138 219 155)(7 139 220 156)(8 140 221 157)(9 141 222 158)(10 142 223 159)(11 143 224 160)(12 144 225 161)(13 145 226 162)(14 117 227 163)(15 118 228 164)(16 119 229 165)(17 120 230 166)(18 121 231 167)(19 122 232 168)(20 123 204 169)(21 124 205 170)(22 125 206 171)(23 126 207 172)(24 127 208 173)(25 128 209 174)(26 129 210 146)(27 130 211 147)(28 131 212 148)(29 132 213 149)(30 109 69 192)(31 110 70 193)(32 111 71 194)(33 112 72 195)(34 113 73 196)(35 114 74 197)(36 115 75 198)(37 116 76 199)(38 88 77 200)(39 89 78 201)(40 90 79 202)(41 91 80 203)(42 92 81 175)(43 93 82 176)(44 94 83 177)(45 95 84 178)(46 96 85 179)(47 97 86 180)(48 98 87 181)(49 99 59 182)(50 100 60 183)(51 101 61 184)(52 102 62 185)(53 103 63 186)(54 104 64 187)(55 105 65 188)(56 106 66 189)(57 107 67 190)(58 108 68 191)
(1 183 214 100)(2 184 215 101)(3 185 216 102)(4 186 217 103)(5 187 218 104)(6 188 219 105)(7 189 220 106)(8 190 221 107)(9 191 222 108)(10 192 223 109)(11 193 224 110)(12 194 225 111)(13 195 226 112)(14 196 227 113)(15 197 228 114)(16 198 229 115)(17 199 230 116)(18 200 231 88)(19 201 232 89)(20 202 204 90)(21 203 205 91)(22 175 206 92)(23 176 207 93)(24 177 208 94)(25 178 209 95)(26 179 210 96)(27 180 211 97)(28 181 212 98)(29 182 213 99)(30 159 69 142)(31 160 70 143)(32 161 71 144)(33 162 72 145)(34 163 73 117)(35 164 74 118)(36 165 75 119)(37 166 76 120)(38 167 77 121)(39 168 78 122)(40 169 79 123)(41 170 80 124)(42 171 81 125)(43 172 82 126)(44 173 83 127)(45 174 84 128)(46 146 85 129)(47 147 86 130)(48 148 87 131)(49 149 59 132)(50 150 60 133)(51 151 61 134)(52 152 62 135)(53 153 63 136)(54 154 64 137)(55 155 65 138)(56 156 66 139)(57 157 67 140)(58 158 68 141)
(30 69)(31 70)(32 71)(33 72)(34 73)(35 74)(36 75)(37 76)(38 77)(39 78)(40 79)(41 80)(42 81)(43 82)(44 83)(45 84)(46 85)(47 86)(48 87)(49 59)(50 60)(51 61)(52 62)(53 63)(54 64)(55 65)(56 66)(57 67)(58 68)(88 200)(89 201)(90 202)(91 203)(92 175)(93 176)(94 177)(95 178)(96 179)(97 180)(98 181)(99 182)(100 183)(101 184)(102 185)(103 186)(104 187)(105 188)(106 189)(107 190)(108 191)(109 192)(110 193)(111 194)(112 195)(113 196)(114 197)(115 198)(116 199)

G:=sub<Sym(232)| (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)(204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232), (1,133,214,150)(2,134,215,151)(3,135,216,152)(4,136,217,153)(5,137,218,154)(6,138,219,155)(7,139,220,156)(8,140,221,157)(9,141,222,158)(10,142,223,159)(11,143,224,160)(12,144,225,161)(13,145,226,162)(14,117,227,163)(15,118,228,164)(16,119,229,165)(17,120,230,166)(18,121,231,167)(19,122,232,168)(20,123,204,169)(21,124,205,170)(22,125,206,171)(23,126,207,172)(24,127,208,173)(25,128,209,174)(26,129,210,146)(27,130,211,147)(28,131,212,148)(29,132,213,149)(30,109,69,192)(31,110,70,193)(32,111,71,194)(33,112,72,195)(34,113,73,196)(35,114,74,197)(36,115,75,198)(37,116,76,199)(38,88,77,200)(39,89,78,201)(40,90,79,202)(41,91,80,203)(42,92,81,175)(43,93,82,176)(44,94,83,177)(45,95,84,178)(46,96,85,179)(47,97,86,180)(48,98,87,181)(49,99,59,182)(50,100,60,183)(51,101,61,184)(52,102,62,185)(53,103,63,186)(54,104,64,187)(55,105,65,188)(56,106,66,189)(57,107,67,190)(58,108,68,191), (1,183,214,100)(2,184,215,101)(3,185,216,102)(4,186,217,103)(5,187,218,104)(6,188,219,105)(7,189,220,106)(8,190,221,107)(9,191,222,108)(10,192,223,109)(11,193,224,110)(12,194,225,111)(13,195,226,112)(14,196,227,113)(15,197,228,114)(16,198,229,115)(17,199,230,116)(18,200,231,88)(19,201,232,89)(20,202,204,90)(21,203,205,91)(22,175,206,92)(23,176,207,93)(24,177,208,94)(25,178,209,95)(26,179,210,96)(27,180,211,97)(28,181,212,98)(29,182,213,99)(30,159,69,142)(31,160,70,143)(32,161,71,144)(33,162,72,145)(34,163,73,117)(35,164,74,118)(36,165,75,119)(37,166,76,120)(38,167,77,121)(39,168,78,122)(40,169,79,123)(41,170,80,124)(42,171,81,125)(43,172,82,126)(44,173,83,127)(45,174,84,128)(46,146,85,129)(47,147,86,130)(48,148,87,131)(49,149,59,132)(50,150,60,133)(51,151,61,134)(52,152,62,135)(53,153,63,136)(54,154,64,137)(55,155,65,138)(56,156,66,139)(57,157,67,140)(58,158,68,141), (30,69)(31,70)(32,71)(33,72)(34,73)(35,74)(36,75)(37,76)(38,77)(39,78)(40,79)(41,80)(42,81)(43,82)(44,83)(45,84)(46,85)(47,86)(48,87)(49,59)(50,60)(51,61)(52,62)(53,63)(54,64)(55,65)(56,66)(57,67)(58,68)(88,200)(89,201)(90,202)(91,203)(92,175)(93,176)(94,177)(95,178)(96,179)(97,180)(98,181)(99,182)(100,183)(101,184)(102,185)(103,186)(104,187)(105,188)(106,189)(107,190)(108,191)(109,192)(110,193)(111,194)(112,195)(113,196)(114,197)(115,198)(116,199)>;

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)(175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203)(204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232), (1,133,214,150)(2,134,215,151)(3,135,216,152)(4,136,217,153)(5,137,218,154)(6,138,219,155)(7,139,220,156)(8,140,221,157)(9,141,222,158)(10,142,223,159)(11,143,224,160)(12,144,225,161)(13,145,226,162)(14,117,227,163)(15,118,228,164)(16,119,229,165)(17,120,230,166)(18,121,231,167)(19,122,232,168)(20,123,204,169)(21,124,205,170)(22,125,206,171)(23,126,207,172)(24,127,208,173)(25,128,209,174)(26,129,210,146)(27,130,211,147)(28,131,212,148)(29,132,213,149)(30,109,69,192)(31,110,70,193)(32,111,71,194)(33,112,72,195)(34,113,73,196)(35,114,74,197)(36,115,75,198)(37,116,76,199)(38,88,77,200)(39,89,78,201)(40,90,79,202)(41,91,80,203)(42,92,81,175)(43,93,82,176)(44,94,83,177)(45,95,84,178)(46,96,85,179)(47,97,86,180)(48,98,87,181)(49,99,59,182)(50,100,60,183)(51,101,61,184)(52,102,62,185)(53,103,63,186)(54,104,64,187)(55,105,65,188)(56,106,66,189)(57,107,67,190)(58,108,68,191), (1,183,214,100)(2,184,215,101)(3,185,216,102)(4,186,217,103)(5,187,218,104)(6,188,219,105)(7,189,220,106)(8,190,221,107)(9,191,222,108)(10,192,223,109)(11,193,224,110)(12,194,225,111)(13,195,226,112)(14,196,227,113)(15,197,228,114)(16,198,229,115)(17,199,230,116)(18,200,231,88)(19,201,232,89)(20,202,204,90)(21,203,205,91)(22,175,206,92)(23,176,207,93)(24,177,208,94)(25,178,209,95)(26,179,210,96)(27,180,211,97)(28,181,212,98)(29,182,213,99)(30,159,69,142)(31,160,70,143)(32,161,71,144)(33,162,72,145)(34,163,73,117)(35,164,74,118)(36,165,75,119)(37,166,76,120)(38,167,77,121)(39,168,78,122)(40,169,79,123)(41,170,80,124)(42,171,81,125)(43,172,82,126)(44,173,83,127)(45,174,84,128)(46,146,85,129)(47,147,86,130)(48,148,87,131)(49,149,59,132)(50,150,60,133)(51,151,61,134)(52,152,62,135)(53,153,63,136)(54,154,64,137)(55,155,65,138)(56,156,66,139)(57,157,67,140)(58,158,68,141), (30,69)(31,70)(32,71)(33,72)(34,73)(35,74)(36,75)(37,76)(38,77)(39,78)(40,79)(41,80)(42,81)(43,82)(44,83)(45,84)(46,85)(47,86)(48,87)(49,59)(50,60)(51,61)(52,62)(53,63)(54,64)(55,65)(56,66)(57,67)(58,68)(88,200)(89,201)(90,202)(91,203)(92,175)(93,176)(94,177)(95,178)(96,179)(97,180)(98,181)(99,182)(100,183)(101,184)(102,185)(103,186)(104,187)(105,188)(106,189)(107,190)(108,191)(109,192)(110,193)(111,194)(112,195)(113,196)(114,197)(115,198)(116,199) );

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),(175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203),(204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232)], [(1,133,214,150),(2,134,215,151),(3,135,216,152),(4,136,217,153),(5,137,218,154),(6,138,219,155),(7,139,220,156),(8,140,221,157),(9,141,222,158),(10,142,223,159),(11,143,224,160),(12,144,225,161),(13,145,226,162),(14,117,227,163),(15,118,228,164),(16,119,229,165),(17,120,230,166),(18,121,231,167),(19,122,232,168),(20,123,204,169),(21,124,205,170),(22,125,206,171),(23,126,207,172),(24,127,208,173),(25,128,209,174),(26,129,210,146),(27,130,211,147),(28,131,212,148),(29,132,213,149),(30,109,69,192),(31,110,70,193),(32,111,71,194),(33,112,72,195),(34,113,73,196),(35,114,74,197),(36,115,75,198),(37,116,76,199),(38,88,77,200),(39,89,78,201),(40,90,79,202),(41,91,80,203),(42,92,81,175),(43,93,82,176),(44,94,83,177),(45,95,84,178),(46,96,85,179),(47,97,86,180),(48,98,87,181),(49,99,59,182),(50,100,60,183),(51,101,61,184),(52,102,62,185),(53,103,63,186),(54,104,64,187),(55,105,65,188),(56,106,66,189),(57,107,67,190),(58,108,68,191)], [(1,183,214,100),(2,184,215,101),(3,185,216,102),(4,186,217,103),(5,187,218,104),(6,188,219,105),(7,189,220,106),(8,190,221,107),(9,191,222,108),(10,192,223,109),(11,193,224,110),(12,194,225,111),(13,195,226,112),(14,196,227,113),(15,197,228,114),(16,198,229,115),(17,199,230,116),(18,200,231,88),(19,201,232,89),(20,202,204,90),(21,203,205,91),(22,175,206,92),(23,176,207,93),(24,177,208,94),(25,178,209,95),(26,179,210,96),(27,180,211,97),(28,181,212,98),(29,182,213,99),(30,159,69,142),(31,160,70,143),(32,161,71,144),(33,162,72,145),(34,163,73,117),(35,164,74,118),(36,165,75,119),(37,166,76,120),(38,167,77,121),(39,168,78,122),(40,169,79,123),(41,170,80,124),(42,171,81,125),(43,172,82,126),(44,173,83,127),(45,174,84,128),(46,146,85,129),(47,147,86,130),(48,148,87,131),(49,149,59,132),(50,150,60,133),(51,151,61,134),(52,152,62,135),(53,153,63,136),(54,154,64,137),(55,155,65,138),(56,156,66,139),(57,157,67,140),(58,158,68,141)], [(30,69),(31,70),(32,71),(33,72),(34,73),(35,74),(36,75),(37,76),(38,77),(39,78),(40,79),(41,80),(42,81),(43,82),(44,83),(45,84),(46,85),(47,86),(48,87),(49,59),(50,60),(51,61),(52,62),(53,63),(54,64),(55,65),(56,66),(57,67),(58,68),(88,200),(89,201),(90,202),(91,203),(92,175),(93,176),(94,177),(95,178),(96,179),(97,180),(98,181),(99,182),(100,183),(101,184),(102,185),(103,186),(104,187),(105,188),(106,189),(107,190),(108,191),(109,192),(110,193),(111,194),(112,195),(113,196),(114,197),(115,198),(116,199)])

290 conjugacy classes

class 1 2A2B2C2D4A4B4C4D4E29A···29AB58A···58AB58AC···58DH116A···116BD116BE···116EJ
order122224444429···2958···5858···58116···116116···116
size11222112221···11···12···21···12···2

290 irreducible representations

dim1111111122
type++++
imageC1C2C2C2C29C58C58C58C4○D4C4○D4×C29
kernelC4○D4×C29C2×C116D4×C29Q8×C29C4○D4C2×C4D4Q8C29C1
# reps133128848428256

Matrix representation of C4○D4×C29 in GL2(𝔽233) generated by

20
02
,
890
089
,
14528
23188
,
1145
0232
G:=sub<GL(2,GF(233))| [2,0,0,2],[89,0,0,89],[145,231,28,88],[1,0,145,232] >;

C4○D4×C29 in GAP, Magma, Sage, TeX

C_4\circ D_4\times C_{29}
% in TeX

G:=Group("C4oD4xC29");
// GroupNames label

G:=SmallGroup(464,48);
// by ID

G=gap.SmallGroup(464,48);
# by ID

G:=PCGroup([5,-2,-2,-2,-29,-2,2341,882]);
// Polycyclic

G:=Group<a,b,c,d|a^29=b^4=d^2=1,c^2=b^2,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d=b^2*c>;
// generators/relations

Export

Subgroup lattice of C4○D4×C29 in TeX

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